Skip to main content

2016 | OriginalPaper | Buchkapitel

6. Electronic Band Structure of 2D TMDCs

verfasst von : Alexander V. Kolobov, Junji Tominaga

Erschienen in: Two-Dimensional Transition-Metal Dichalcogenides

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Monolayer transition-metal dichalcogenides acquire a direct band gap, opening up a broad range of applications in optoelectronics. In this chapter the progress achieved in theoretical and experimental studies of the electronic structure of mono- and few-layer systems is discussed in detail, including methods for modulating the electronic structure, e.g. by applying strain or manipulating interlayer coupling.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Fußnoten
1
The notation \(\varLambda \) used in [46] is not usual. Usually this point is referred to as Q.
 
2
Trions are described later in this volume (Chap. 9).
 
Literatur
1.
Zurück zum Zitat K.F. Mak, C. Lee, J. Hone, J. Shan, T.F. Heinz, Atomically thin MoS\(_{2}\): a new direct-gap semiconductor. Phys. Rev. Lett. 105(13), 136805 (2010)CrossRef K.F. Mak, C. Lee, J. Hone, J. Shan, T.F. Heinz, Atomically thin MoS\(_{2}\): a new direct-gap semiconductor. Phys. Rev. Lett. 105(13), 136805 (2010)CrossRef
2.
Zurück zum Zitat W. Zhao, R. Ribeiro, M. Toh, A.H. Carvalho, C. Kloc, A. Castro Neto, G. Eda, Origin of indirect optical transitions in few-layer MoS\(_2\), WS\(_2\), and WSe\(_2\). Nano Lett. 13(11), 5627 (2013) W. Zhao, R. Ribeiro, M. Toh, A.H. Carvalho, C. Kloc, A. Castro Neto, G. Eda, Origin of indirect optical transitions in few-layer MoS\(_2\), WS\(_2\), and WSe\(_2\). Nano Lett. 13(11), 5627 (2013)
3.
Zurück zum Zitat H. Zeng, G.B. Liu, J. Dai, Y. Yan, B. Zhu, R. He, L. Xie, S. Xu, X. Chen, W. Yao, et al., Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides. Sci. Rep. 3 (2013). doi:10.1038/srep01608 H. Zeng, G.B. Liu, J. Dai, Y. Yan, B. Zhu, R. He, L. Xie, S. Xu, X. Chen, W. Yao, et al., Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides. Sci. Rep. 3 (2013). doi:10.​1038/​srep01608
4.
Zurück zum Zitat A. Ramasubramaniam, D. Naveh, E. Towe, Tunable band gaps in bilayer transition-metal dichalcogenides. Phys. Rev. B 84(20), 205325 (2011)CrossRef A. Ramasubramaniam, D. Naveh, E. Towe, Tunable band gaps in bilayer transition-metal dichalcogenides. Phys. Rev. B 84(20), 205325 (2011)CrossRef
5.
Zurück zum Zitat T. Cheiwchanchamnangij, W.R. Lambrecht, Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS\(_2\). Phys. Rev. B 85(20), 205302 (2012)CrossRef T. Cheiwchanchamnangij, W.R. Lambrecht, Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS\(_2\). Phys. Rev. B 85(20), 205302 (2012)CrossRef
6.
Zurück zum Zitat Y. Zhang, T.R. Chang, B. Zhou, Y.T. Cui, H. Yan, Z. Liu, F. Schmitt, J. Lee, R. Moore, Y. Chen et al., Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe\(_2\). Nat. Nanotech. 9(2), 111 (2014)CrossRef Y. Zhang, T.R. Chang, B. Zhou, Y.T. Cui, H. Yan, Z. Liu, F. Schmitt, J. Lee, R. Moore, Y. Chen et al., Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe\(_2\). Nat. Nanotech. 9(2), 111 (2014)CrossRef
7.
Zurück zum Zitat Y. Ma, Y. Dai, M. Guo, C. Niu, J. Lu, B. Huang, Electronic and magnetic properties of perfect, vacancy-doped, and nonmetal adsorbed MoSe\(_2\), MoTe\(_2\) and WS\(_2\) monolayers. Phys. Chem. Chem. Phys. 13(34), 15546 (2011)CrossRef Y. Ma, Y. Dai, M. Guo, C. Niu, J. Lu, B. Huang, Electronic and magnetic properties of perfect, vacancy-doped, and nonmetal adsorbed MoSe\(_2\), MoTe\(_2\) and WS\(_2\) monolayers. Phys. Chem. Chem. Phys. 13(34), 15546 (2011)CrossRef
8.
Zurück zum Zitat A. Kumar, P. Ahluwalia, Electronic structure of transition metal dichalcogenides monolayers \(1H\)–\(MX_2\) (M = Mo, W; X = S, Se, Te) from ab-initio theory: new direct band gap semiconductors. Eur. Phys. J. B 85(6), 186 (2012) A. Kumar, P. Ahluwalia, Electronic structure of transition metal dichalcogenides monolayers \(1H\)\(MX_2\) (M = Mo, W; X = S, Se, Te) from ab-initio theory: new direct band gap semiconductors. Eur. Phys. J. B 85(6), 186 (2012)
9.
Zurück zum Zitat E.S. Kadantsev, P. Hawrylak, Electronic structure of a single MoS\(_2\) monolayer. Solid State Commun. 152(10), 909 (2012)CrossRef E.S. Kadantsev, P. Hawrylak, Electronic structure of a single MoS\(_2\) monolayer. Solid State Commun. 152(10), 909 (2012)CrossRef
10.
Zurück zum Zitat W. Huang, X. Luo, C.K. Gan, S.Y. Quek, G. Liang, Theoretical study of thermoelectric properties of few-layer MoS\(_2\) and WSe\(_2\). Phys. Chem. Chem. Phys. 16(22), 10866 (2014)CrossRef W. Huang, X. Luo, C.K. Gan, S.Y. Quek, G. Liang, Theoretical study of thermoelectric properties of few-layer MoS\(_2\) and WSe\(_2\). Phys. Chem. Chem. Phys. 16(22), 10866 (2014)CrossRef
11.
Zurück zum Zitat Y. Ding, Y. Wang, J. Ni, L. Shi, S. Shi, W. Tang, First principles study of structural, vibrational and electronic properties of graphene-like MX\(_2\) (M = Mo, Nb, W, Ta; X = S, Se, Te) monolayers. Phys. B 406(11), 2254 (2011) Y. Ding, Y. Wang, J. Ni, L. Shi, S. Shi, W. Tang, First principles study of structural, vibrational and electronic properties of graphene-like MX\(_2\) (M = Mo, Nb, W, Ta; X = S, Se, Te) monolayers. Phys. B 406(11), 2254 (2011)
12.
Zurück zum Zitat J.K. Ellis, M.J. Lucero, G.E. Scuseria, The indirect to direct band gap transition in multilayered MoS\(_2\) as predicted by screened hybrid density functional theory. Appl. Phys. Lett. 99(26), 261908 (2011)CrossRef J.K. Ellis, M.J. Lucero, G.E. Scuseria, The indirect to direct band gap transition in multilayered MoS\(_2\) as predicted by screened hybrid density functional theory. Appl. Phys. Lett. 99(26), 261908 (2011)CrossRef
13.
Zurück zum Zitat A. Molina-Sánchez, D. Sangalli, K. Hummer, A. Marini, L. Wirtz, Effect of spin-orbit interaction on the optical spectra of single-layer, double-layer, and bulk MoS\(_2\). Phys. Rev. B 88(4), 045412 (2013)CrossRef A. Molina-Sánchez, D. Sangalli, K. Hummer, A. Marini, L. Wirtz, Effect of spin-orbit interaction on the optical spectra of single-layer, double-layer, and bulk MoS\(_2\). Phys. Rev. B 88(4), 045412 (2013)CrossRef
14.
Zurück zum Zitat H.P. Komsa, A.V. Krasheninnikov, Electronic structures and optical properties of realistic transition metal dichalcogenide heterostructures from first principles. Phys. Rev. B 88(8), 085318 (2013)CrossRef H.P. Komsa, A.V. Krasheninnikov, Electronic structures and optical properties of realistic transition metal dichalcogenide heterostructures from first principles. Phys. Rev. B 88(8), 085318 (2013)CrossRef
15.
Zurück zum Zitat H. Sahin, S. Tongay, S. Horzum, W. Fan, J. Zhou, J. Li, J. Wu, F. Peeters, Anomalous Raman spectra and thickness-dependent electronic properties of WSe\(_2\). Phys. Rev. B 87(16), 165409 (2013)CrossRef H. Sahin, S. Tongay, S. Horzum, W. Fan, J. Zhou, J. Li, J. Wu, F. Peeters, Anomalous Raman spectra and thickness-dependent electronic properties of WSe\(_2\). Phys. Rev. B 87(16), 165409 (2013)CrossRef
16.
Zurück zum Zitat A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.Y. Chim, G. Galli, F. Wang, Emerging photoluminescence in monolayer MoS\(_2\). Nano Lett. 10(4), 1271 (2010)CrossRef A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.Y. Chim, G. Galli, F. Wang, Emerging photoluminescence in monolayer MoS\(_2\). Nano Lett. 10(4), 1271 (2010)CrossRef
17.
Zurück zum Zitat T. Eknapakul, P.D. King, M. Asakawa, P. Buaphet, R.H. He, S.K. Mo, H. Takagi, K.M. Shen, F. Baumberger, T. Sasagawa et al., Electronic structure of a quasi-freestanding MoS\(_2\) monolayer. Nano Lett. 14(3), 1312 (2014)CrossRef T. Eknapakul, P.D. King, M. Asakawa, P. Buaphet, R.H. He, S.K. Mo, H. Takagi, K.M. Shen, F. Baumberger, T. Sasagawa et al., Electronic structure of a quasi-freestanding MoS\(_2\) monolayer. Nano Lett. 14(3), 1312 (2014)CrossRef
18.
Zurück zum Zitat A. Kuc, N. Zibouche, T. Heine, Influence of quantum confinement on the electronic structure of the transition metal sulfide TS\(_2\). Phys. Rev. B 83(24), 245213 (2011) A. Kuc, N. Zibouche, T. Heine, Influence of quantum confinement on the electronic structure of the transition metal sulfide TS\(_2\). Phys. Rev. B 83(24), 245213 (2011)
19.
Zurück zum Zitat L. Debbichi, O. Eriksson, S. Lebègue, Electronic structure of two-dimensional transition metal dichalcogenide bilayers from ab initio theory. Phys. Rev. B 89(20), 205311 (2014)CrossRef L. Debbichi, O. Eriksson, S. Lebègue, Electronic structure of two-dimensional transition metal dichalcogenide bilayers from ab initio theory. Phys. Rev. B 89(20), 205311 (2014)CrossRef
20.
Zurück zum Zitat S. Lebegue, O. Eriksson, Electronic structure of two-dimensional crystals from ab initio theory. Phys. Rev. B 79(11), 115409 (2009)CrossRef S. Lebegue, O. Eriksson, Electronic structure of two-dimensional crystals from ab initio theory. Phys. Rev. B 79(11), 115409 (2009)CrossRef
21.
Zurück zum Zitat H. Jiang, Electronic band structures of molybdenum and tungsten dichalcogenides by the GW approach. J. Phys. Chem. C 116(14), 7664 (2012)CrossRef H. Jiang, Electronic band structures of molybdenum and tungsten dichalcogenides by the GW approach. J. Phys. Chem. C 116(14), 7664 (2012)CrossRef
22.
Zurück zum Zitat T. Böker, R. Severin, A. Müller, C. Janowitz, R. Manzke, D. Voß, P. Krüger, A. Mazur, J. Pollmann, Band structure of MoS\(_2\), MoSe\(_2\), and \(\alpha \)-MoTe\(_2\): angle-resolved photoelectron spectroscopy and ab initio calculations. Phys. Rev. B 64(23), 235305 (2001)CrossRef T. Böker, R. Severin, A. Müller, C. Janowitz, R. Manzke, D. Voß, P. Krüger, A. Mazur, J. Pollmann, Band structure of MoS\(_2\), MoSe\(_2\), and \(\alpha \)-MoTe\(_2\): angle-resolved photoelectron spectroscopy and ab initio calculations. Phys. Rev. B 64(23), 235305 (2001)CrossRef
23.
Zurück zum Zitat F. Hüser, T. Olsen, K.S. Thygesen, How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer MoS\(_2\). Phys. Rev. B 88(24), 245309 (2013)CrossRef F. Hüser, T. Olsen, K.S. Thygesen, How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer MoS\(_2\). Phys. Rev. B 88(24), 245309 (2013)CrossRef
24.
Zurück zum Zitat C. Espejo, T. Rangel, A. Romero, X. Gonze, G.M. Rignanese, Band structure tunability in MoS\(_2\) under interlayer compression: a DFT and GW study. Phys. Rev. B 87(24), 245114 (2013)CrossRef C. Espejo, T. Rangel, A. Romero, X. Gonze, G.M. Rignanese, Band structure tunability in MoS\(_2\) under interlayer compression: a DFT and GW study. Phys. Rev. B 87(24), 245114 (2013)CrossRef
25.
Zurück zum Zitat I.G. Lezama, A. Ubaldini, M. Longobardi, E. Giannini, C. Renner, A.B. Kuzmenko, A.F. Morpurgo, Surface transport and band gap structure of exfoliated 2H-MoTe\(_{2}\) crystals. 2D Mater. 1(2), 021002 (2014) I.G. Lezama, A. Ubaldini, M. Longobardi, E. Giannini, C. Renner, A.B. Kuzmenko, A.F. Morpurgo, Surface transport and band gap structure of exfoliated 2H-MoTe\(_{2}\) crystals. 2D Mater. 1(2), 021002 (2014)
26.
Zurück zum Zitat G.B. Liu, D. Xiao, Y. Yao, X. Xu, W. Yao, Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides. Chem. Soc. Rev. 44(9), 2643 (2015)CrossRef G.B. Liu, D. Xiao, Y. Yao, X. Xu, W. Yao, Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides. Chem. Soc. Rev. 44(9), 2643 (2015)CrossRef
27.
Zurück zum Zitat D. Xiao, G.B. Liu, W. Feng, X. Xu, W. Yao, Coupled spin and valley physics in monolayers of MoS\(_2\) and other group-VI dichalcogenides. Phys. Rev. Lett. 108(19), 196802 (2012)CrossRef D. Xiao, G.B. Liu, W. Feng, X. Xu, W. Yao, Coupled spin and valley physics in monolayers of MoS\(_2\) and other group-VI dichalcogenides. Phys. Rev. Lett. 108(19), 196802 (2012)CrossRef
28.
Zurück zum Zitat F. Rose, M. Goerbig, F. Piéchon, Spin-and valley-dependent magneto-optical properties of MoS\(_2\). Phys. Rev. B 88(12), 125438 (2013)CrossRef F. Rose, M. Goerbig, F. Piéchon, Spin-and valley-dependent magneto-optical properties of MoS\(_2\). Phys. Rev. B 88(12), 125438 (2013)CrossRef
29.
Zurück zum Zitat E. Cappelluti, R. Roldán, J. Silva-Guillén, P. Ordejón, F. Guinea, Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer MoS\(_2\). Phys. Rev. B 88(7), 075409 (2013)CrossRef E. Cappelluti, R. Roldán, J. Silva-Guillén, P. Ordejón, F. Guinea, Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer MoS\(_2\). Phys. Rev. B 88(7), 075409 (2013)CrossRef
30.
Zurück zum Zitat E. Ridolfi, D. Le, T.S. Rahman, E.R. Mucciolo, C.H. Lewenkopf, A tight-binding model for MoS\(_2\) monolayers. J. Phys. Condens. Matter 27(36), 365501 (2015)CrossRef E. Ridolfi, D. Le, T.S. Rahman, E.R. Mucciolo, C.H. Lewenkopf, A tight-binding model for MoS\(_2\) monolayers. J. Phys. Condens. Matter 27(36), 365501 (2015)CrossRef
31.
Zurück zum Zitat M. Erementchouk, M. Khan, M.N. Leuenberger, Optical signatures of states bound to vacancy defects in monolayer MoS\(_2\). Phys. Rev. B 92, 121401 (2015)CrossRef M. Erementchouk, M. Khan, M.N. Leuenberger, Optical signatures of states bound to vacancy defects in monolayer MoS\(_2\). Phys. Rev. B 92, 121401 (2015)CrossRef
32.
Zurück zum Zitat X. Li, F. Zhang, Q. Niu, Unconventional quantum hall effect and tunable spin hall effect in dirac materials: application to an isolated MoS\(_2\) trilayer. Phys. Rev. Lett. 110(6), 066803 (2013)CrossRef X. Li, F. Zhang, Q. Niu, Unconventional quantum hall effect and tunable spin hall effect in dirac materials: application to an isolated MoS\(_2\) trilayer. Phys. Rev. Lett. 110(6), 066803 (2013)CrossRef
33.
Zurück zum Zitat F. Parhizgar, H. Rostami, R. Asgari, Indirect exchange interaction between magnetic adatoms in monolayer MoS\(_2\). Phys. Rev. B 87(12), 125401 (2013)CrossRef F. Parhizgar, H. Rostami, R. Asgari, Indirect exchange interaction between magnetic adatoms in monolayer MoS\(_2\). Phys. Rev. B 87(12), 125401 (2013)CrossRef
34.
Zurück zum Zitat G.B. Liu, W.Y. Shan, Y. Yao, W. Yao, D. Xiao, Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides. Phys. Rev. B 88(8), 085433 (2013)CrossRef G.B. Liu, W.Y. Shan, Y. Yao, W. Yao, D. Xiao, Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides. Phys. Rev. B 88(8), 085433 (2013)CrossRef
35.
Zurück zum Zitat R.L. Chu, G.B. Liu, W. Yao, X. Xu, D. Xiao, C. Zhang, Spin-orbit-coupled quantum wires and Majorana fermions on zigzag edges of monolayer transition-metal dichalcogenides. Phys. Rev. B 89(15), 155317 (2014) R.L. Chu, G.B. Liu, W. Yao, X. Xu, D. Xiao, C. Zhang, Spin-orbit-coupled quantum wires and Majorana fermions on zigzag edges of monolayer transition-metal dichalcogenides. Phys. Rev. B 89(15), 155317 (2014)
36.
Zurück zum Zitat A. Kormányos, V. Zólyomi, N.D. Drummond, G. Burkard, Spin-orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides. Phys. Rev. X 4(1), 011034 (2014) A. Kormányos, V. Zólyomi, N.D. Drummond, G. Burkard, Spin-orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides. Phys. Rev. X 4(1), 011034 (2014)
37.
Zurück zum Zitat Y. Song, H. Dery, Transport theory of monolayer transition-metal dichalcogenides through symmetry. Phys. Rev. Lett. 111(2), 026601 (2013)CrossRef Y. Song, H. Dery, Transport theory of monolayer transition-metal dichalcogenides through symmetry. Phys. Rev. Lett. 111(2), 026601 (2013)CrossRef
38.
Zurück zum Zitat C. Wang, X. Lei, Linear magnetotransport in monolayer MoS\(_2\). Phys. Rev. B 92(12), 125303 (2015)CrossRef C. Wang, X. Lei, Linear magnetotransport in monolayer MoS\(_2\). Phys. Rev. B 92(12), 125303 (2015)CrossRef
39.
Zurück zum Zitat A. Thilagam, Excitonic polarons in low-dimensional transition metal dichalcogenides. Phys. B 464, 44 (2015)CrossRef A. Thilagam, Excitonic polarons in low-dimensional transition metal dichalcogenides. Phys. B 464, 44 (2015)CrossRef
40.
Zurück zum Zitat Y.N. Gartstein, X. Li, C. Zhang, Exciton-polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer. Phys. Rev. B 92, 075445 (2015)CrossRef Y.N. Gartstein, X. Li, C. Zhang, Exciton-polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer. Phys. Rev. B 92, 075445 (2015)CrossRef
41.
Zurück zum Zitat T. Li, G. Galli, Electronic properties of MoS\(_2\) nanoparticles. J. Phys. Chem. C 111(44), 16192 (2007)CrossRef T. Li, G. Galli, Electronic properties of MoS\(_2\) nanoparticles. J. Phys. Chem. C 111(44), 16192 (2007)CrossRef
42.
Zurück zum Zitat H.S.S.R. Matte, A. Gomathi, A.K. Manna, D.J. Late, R. Datta, S.K. Pati, C.N.R. Rao, MoS\(_2\) and WS\(_2\) analogues of graphene. Angew. Chem. 122(24), 4153 (2010)CrossRef H.S.S.R. Matte, A. Gomathi, A.K. Manna, D.J. Late, R. Datta, S.K. Pati, C.N.R. Rao, MoS\(_2\) and WS\(_2\) analogues of graphene. Angew. Chem. 122(24), 4153 (2010)CrossRef
43.
Zurück zum Zitat R. Roldán, J.A. Silva-Guillén, M.P. López-Sancho, F. Guinea, E. Cappelluti, P. Ordejón, Electronic properties of single-layer and multilayer transition metal dichalcogenides MX\(_2\) (M = Mo, W and X = S, Se). Ann. Phys. 526(9–10), 347 (2014) R. Roldán, J.A. Silva-Guillén, M.P. López-Sancho, F. Guinea, E. Cappelluti, P. Ordejón, Electronic properties of single-layer and multilayer transition metal dichalcogenides MX\(_2\) (M = Mo, W and X = S, Se). Ann. Phys. 526(9–10), 347 (2014)
44.
Zurück zum Zitat K. Albe, A. Klein, Density-functional-theory calculations of electronic band structure of single-crystal and single-layer WS\(_2\). Phys. Rev. B 66(7), 073413 (2002)CrossRef K. Albe, A. Klein, Density-functional-theory calculations of electronic band structure of single-crystal and single-layer WS\(_2\). Phys. Rev. B 66(7), 073413 (2002)CrossRef
45.
Zurück zum Zitat O.V. Yazyev, A. Kis, MoS\(_2\) and semiconductors in the flatland. Mater. Today 18(1), 20 (2015)CrossRef O.V. Yazyev, A. Kis, MoS\(_2\) and semiconductors in the flatland. Mater. Today 18(1), 20 (2015)CrossRef
46.
Zurück zum Zitat J. Padilha, H. Peelaers, A. Janotti, C. Van de Walle, Nature and evolution of the band-edge states in MoS\(_2\): from monolayer to bulk. Phys. Rev. B 90(20), 205420 (2014)CrossRef J. Padilha, H. Peelaers, A. Janotti, C. Van de Walle, Nature and evolution of the band-edge states in MoS\(_2\): from monolayer to bulk. Phys. Rev. B 90(20), 205420 (2014)CrossRef
47.
Zurück zum Zitat L. Mattheiss, Band structures of transition-metal-dichalcogenide layer compounds. Phys. Rev. B 8(8), 3719 (1973)CrossRef L. Mattheiss, Band structures of transition-metal-dichalcogenide layer compounds. Phys. Rev. B 8(8), 3719 (1973)CrossRef
48.
Zurück zum Zitat H. Shi, H. Pan, Y.W. Zhang, B.I. Yakobson, Quasiparticle band structures and optical properties of strained monolayer MoS\(_2\) and WS\(_2\). Phys. Rev. B 87(15), 155304 (2013)CrossRef H. Shi, H. Pan, Y.W. Zhang, B.I. Yakobson, Quasiparticle band structures and optical properties of strained monolayer MoS\(_2\) and WS\(_2\). Phys. Rev. B 87(15), 155304 (2013)CrossRef
49.
Zurück zum Zitat Y. Liang, S. Huang, R. Soklaski, L. Yang, Quasiparticle band-edge energy and band offsets of monolayer of molybdenum and tungsten chalcogenides. Appl. Phys. Lett. 103(4), 042106 (2013)CrossRef Y. Liang, S. Huang, R. Soklaski, L. Yang, Quasiparticle band-edge energy and band offsets of monolayer of molybdenum and tungsten chalcogenides. Appl. Phys. Lett. 103(4), 042106 (2013)CrossRef
50.
Zurück zum Zitat D.Y. Qiu, F.H. da Jornada, S.G. Louie, Optical spectrum of MoS\(_2\): many-body effects and diversity of exciton states. Phys. Rev. Lett. 111(21), 216805 (2013)CrossRef D.Y. Qiu, F.H. da Jornada, S.G. Louie, Optical spectrum of MoS\(_2\): many-body effects and diversity of exciton states. Phys. Rev. Lett. 111(21), 216805 (2013)CrossRef
51.
Zurück zum Zitat Z. Zhu, Y. Cheng, U. Schwingenschlögl, Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys. Rev. B 84(15), 153402 (2011)CrossRef Z. Zhu, Y. Cheng, U. Schwingenschlögl, Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys. Rev. B 84(15), 153402 (2011)CrossRef
52.
Zurück zum Zitat S. Bhattacharyya, A.K. Singh, Semiconductor-metal transition in semiconducting bilayer sheets of transition-metal dichalcogenides. Phys. Rev. B 86(7), 075454 (2012)CrossRef S. Bhattacharyya, A.K. Singh, Semiconductor-metal transition in semiconducting bilayer sheets of transition-metal dichalcogenides. Phys. Rev. B 86(7), 075454 (2012)CrossRef
53.
Zurück zum Zitat Q. Liu, L. Li, Y. Li, Z. Gao, Z. Chen, J. Lu, Tuning electronic structure of bilayer MoS\(_2\) by vertical electric field: a first-principles investigation. J. Phys. Chem. C 116(40), 21556 (2012)CrossRef Q. Liu, L. Li, Y. Li, Z. Gao, Z. Chen, J. Lu, Tuning electronic structure of bilayer MoS\(_2\) by vertical electric field: a first-principles investigation. J. Phys. Chem. C 116(40), 21556 (2012)CrossRef
54.
Zurück zum Zitat W. Jin, P.C. Yeh, N. Zaki, D. Zhang, J.T. Sadowski, A. Al-Mahboob, A.M. van der Zande, D.A. Chenet, J.I. Dadap, I.P. Herman et al., Direct measurement of the thickness-dependent electronic band structure of MoS\(_2\) using angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 111(10), 106801 (2013)CrossRef W. Jin, P.C. Yeh, N. Zaki, D. Zhang, J.T. Sadowski, A. Al-Mahboob, A.M. van der Zande, D.A. Chenet, J.I. Dadap, I.P. Herman et al., Direct measurement of the thickness-dependent electronic band structure of MoS\(_2\) using angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 111(10), 106801 (2013)CrossRef
55.
Zurück zum Zitat H.P. Komsa, A.V. Krasheninnikov, Two-dimensional transition metal dichalcogenide alloys: stability and electronic properties. J. Phys. Chem. Lett. 3(23), 3652 (2012)CrossRef H.P. Komsa, A.V. Krasheninnikov, Two-dimensional transition metal dichalcogenide alloys: stability and electronic properties. J. Phys. Chem. Lett. 3(23), 3652 (2012)CrossRef
56.
Zurück zum Zitat A. Kutana, E.S. Penev, B.I. Yakobson, Engineering electronic properties of layered transition-metal dichalcogenide compounds through alloying. Nanoscale 6(11), 5820 (2014)CrossRef A. Kutana, E.S. Penev, B.I. Yakobson, Engineering electronic properties of layered transition-metal dichalcogenide compounds through alloying. Nanoscale 6(11), 5820 (2014)CrossRef
57.
Zurück zum Zitat A. Ramasubramaniam, Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 86(11), 115409 (2012)CrossRef A. Ramasubramaniam, Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 86(11), 115409 (2012)CrossRef
58.
Zurück zum Zitat Z. Gong, G.B. Liu, H. Yu, D. Xiao, X. Cui, X. Xu, W. Yao, Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers. Nat. Commun. 4 (2013). doi:10.1038/ncomms3053 Z. Gong, G.B. Liu, H. Yu, D. Xiao, X. Cui, X. Xu, W. Yao, Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers. Nat. Commun. 4 (2013). doi:10.​1038/​ncomms3053
59.
Zurück zum Zitat H. Ochoa, R. Roldán, Spin-orbit-mediated spin relaxation in monolayer MoS\(_2\). Phys. Rev. B 87(24), 245421 (2013)CrossRef H. Ochoa, R. Roldán, Spin-orbit-mediated spin relaxation in monolayer MoS\(_2\). Phys. Rev. B 87(24), 245421 (2013)CrossRef
60.
Zurück zum Zitat A. Kormányos, V. Zólyomi, N.D. Drummond, P. Rakyta, G. Burkard, V.I. Fal’ko, Monolayer MoS\(_2\): trigonal warping, the \(\Gamma \) valley, and spin-orbit coupling effects. Phys. Rev. B 88(4), 045416 (2013) A. Kormányos, V. Zólyomi, N.D. Drummond, P. Rakyta, G. Burkard, V.I. Fal’ko, Monolayer MoS\(_2\): trigonal warping, the \(\Gamma \) valley, and spin-orbit coupling effects. Phys. Rev. B 88(4), 045416 (2013)
61.
Zurück zum Zitat H. Yu, Y. Wu, G.B. Liu, X. Xu, W. Yao, Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals. Phys. Rev. Lett. 113(15), 156603 (2014) H. Yu, Y. Wu, G.B. Liu, X. Xu, W. Yao, Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals. Phys. Rev. Lett. 113(15), 156603 (2014)
62.
Zurück zum Zitat Y.M. Koroteev, G. Bihlmayer, J. Gayone, E. Chulkov, S. Blügel, P. Echenique, P. Hofmann, Strong spin-orbit splitting on Bi surfaces. Phys. Rev. Lett. 93(4), 046403 (2004)CrossRef Y.M. Koroteev, G. Bihlmayer, J. Gayone, E. Chulkov, S. Blügel, P. Echenique, P. Hofmann, Strong spin-orbit splitting on Bi surfaces. Phys. Rev. Lett. 93(4), 046403 (2004)CrossRef
63.
Zurück zum Zitat D. Wolverson, S. Crampin, A.S. Kazemi, A. Ilie, S.J. Bending, Raman spectra of monolayer, few-layer, and bulk ReSe\(_2\): an anisotropic layered semiconductor. ACS Nano 8(11), 11154 (2014)CrossRef D. Wolverson, S. Crampin, A.S. Kazemi, A. Ilie, S.J. Bending, Raman spectra of monolayer, few-layer, and bulk ReSe\(_2\): an anisotropic layered semiconductor. ACS Nano 8(11), 11154 (2014)CrossRef
64.
Zurück zum Zitat C.H. Chang, X. Fan, S.H. Lin, J.L. Kuo, Orbital analysis of electronic structure and phonon dispersion in MoS\(_2\), MoSe\(_2\), WS\(_2\), and WSe\(_2\) monolayers under strain. Phys. Rev. B 88(19), 195420 (2013)CrossRef C.H. Chang, X. Fan, S.H. Lin, J.L. Kuo, Orbital analysis of electronic structure and phonon dispersion in MoS\(_2\), MoSe\(_2\), WS\(_2\), and WSe\(_2\) monolayers under strain. Phys. Rev. B 88(19), 195420 (2013)CrossRef
65.
Zurück zum Zitat P. Johari, V.B. Shenoy, Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains. ACS Nano 6(6), 5449 (2012)CrossRef P. Johari, V.B. Shenoy, Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains. ACS Nano 6(6), 5449 (2012)CrossRef
66.
Zurück zum Zitat A. Kumar, P.K. Ahluwalia, Mechanical strain dependent electronic and dielectric properties of two-dimensional honeycomb structures of MoX\(_2\) (X=S, Se, Te). Phys. B 419, 66 (2013)CrossRef A. Kumar, P.K. Ahluwalia, Mechanical strain dependent electronic and dielectric properties of two-dimensional honeycomb structures of MoX\(_2\) (X=S, Se, Te). Phys. B 419, 66 (2013)CrossRef
67.
Zurück zum Zitat S. Horzum, H. Sahin, S. Cahangirov, P. Cudazzo, A. Rubio, T. Serin, F. Peeters, Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe\(_2\). Phys. Rev. B 87(12), 125415 (2013)CrossRef S. Horzum, H. Sahin, S. Cahangirov, P. Cudazzo, A. Rubio, T. Serin, F. Peeters, Phonon softening and direct to indirect band gap crossover in strained single-layer MoSe\(_2\). Phys. Rev. B 87(12), 125415 (2013)CrossRef
68.
Zurück zum Zitat Q. Zhang, Y. Cheng, L.Y. Gan, U. Schwingenschlögl, Giant valley drifts in uniaxially strained monolayer MoS\(_2\). Phys. Rev. B 88(24), 245447 (2013)CrossRef Q. Zhang, Y. Cheng, L.Y. Gan, U. Schwingenschlögl, Giant valley drifts in uniaxially strained monolayer MoS\(_2\). Phys. Rev. B 88(24), 245447 (2013)CrossRef
69.
Zurück zum Zitat P. Lu, X. Wu, W. Guo, X.C. Zeng, Strain-dependent electronic and magnetic properties of MoS\(_2\) monolayer, bilayer, nanoribbons and nanotubes. Phys. Chem. Chem. Phys. 14(37), 13035 (2012)CrossRef P. Lu, X. Wu, W. Guo, X.C. Zeng, Strain-dependent electronic and magnetic properties of MoS\(_2\) monolayer, bilayer, nanoribbons and nanotubes. Phys. Chem. Chem. Phys. 14(37), 13035 (2012)CrossRef
70.
Zurück zum Zitat E. Scalise, M. Houssa, G. Pourtois, V. Afanasev, A. Stesmans, Strain-induced semiconductor to metal transition in the two-dimensional honeycomb structure of MoS\(_2\). Nano Res. 5(1), 43 (2012)CrossRef E. Scalise, M. Houssa, G. Pourtois, V. Afanasev, A. Stesmans, Strain-induced semiconductor to metal transition in the two-dimensional honeycomb structure of MoS\(_2\). Nano Res. 5(1), 43 (2012)CrossRef
71.
Zurück zum Zitat N.A. Lanzillo, A.J. Simbeck, S.K. Nayak, Strain engineering the work function in monolayer metal dichalcogenides. J. Phys. Condens. Matter 27(17), 175501 (2015)CrossRef N.A. Lanzillo, A.J. Simbeck, S.K. Nayak, Strain engineering the work function in monolayer metal dichalcogenides. J. Phys. Condens. Matter 27(17), 175501 (2015)CrossRef
72.
Zurück zum Zitat J. Feng, X. Qian, C.W. Huang, J. Li, Strain-engineered artificial atom as a broad-spectrum solar energy funnel. Nat. Photon. 6(12), 866 (2012)CrossRef J. Feng, X. Qian, C.W. Huang, J. Li, Strain-engineered artificial atom as a broad-spectrum solar energy funnel. Nat. Photon. 6(12), 866 (2012)CrossRef
73.
Zurück zum Zitat A. Castellanos-Gomez, R. Roldán, E. Cappelluti, M. Buscema, F. Guinea, H.S. van der Zant, G.A. Steele, Local strain engineering in atomically thin MoS\(_2\). Nano Lett. 13(11), 5361 (2013)CrossRef A. Castellanos-Gomez, R. Roldán, E. Cappelluti, M. Buscema, F. Guinea, H.S. van der Zant, G.A. Steele, Local strain engineering in atomically thin MoS\(_2\). Nano Lett. 13(11), 5361 (2013)CrossRef
74.
Zurück zum Zitat A.P. Nayak, T. Pandey, D. Voiry, J. Liu, S.T. Moran, A. Sharma, C. Tan, C.H. Chen, L.J. Lee, M. Chhowalla et al., Pressure-dependent optical and vibrational properties of monolayer molybdenum disulfide. Nano Lett. 15(1), 346 (2015)CrossRef A.P. Nayak, T. Pandey, D. Voiry, J. Liu, S.T. Moran, A. Sharma, C. Tan, C.H. Chen, L.J. Lee, M. Chhowalla et al., Pressure-dependent optical and vibrational properties of monolayer molybdenum disulfide. Nano Lett. 15(1), 346 (2015)CrossRef
75.
Zurück zum Zitat A.P. Nayak, S. Bhattacharyya, J. Zhu, J. Liu, X. Wu, T. Pandey, C. Jin, A.K. Singh, D. Akinwande, J.F. Lin, Pressure-induced semiconducting to metallic transition in multilayered molybdenum disulphide. Nat. Commun. 5 (2014). doi:10.1038/ncomms4731 A.P. Nayak, S. Bhattacharyya, J. Zhu, J. Liu, X. Wu, T. Pandey, C. Jin, A.K. Singh, D. Akinwande, J.F. Lin, Pressure-induced semiconducting to metallic transition in multilayered molybdenum disulphide. Nat. Commun. 5 (2014). doi:10.​1038/​ncomms4731
76.
Zurück zum Zitat J. Xiao, M. Long, X. Li, Q. Zhang, H. Xu, K.S. Chan, Effects of van der waals interaction and electric field on the electronic structure of bilayer MoS\(_2\). J. Phys. Condens. Matter 26(40), 405302 (2014)CrossRef J. Xiao, M. Long, X. Li, Q. Zhang, H. Xu, K.S. Chan, Effects of van der waals interaction and electric field on the electronic structure of bilayer MoS\(_2\). J. Phys. Condens. Matter 26(40), 405302 (2014)CrossRef
77.
Zurück zum Zitat K. Dolui, C.D. Pemmaraju, S. Sanvito, Electric field effects on armchair MoS\(_2\) nanoribbons. ACS Nano 6(6), 4823 (2012)CrossRef K. Dolui, C.D. Pemmaraju, S. Sanvito, Electric field effects on armchair MoS\(_2\) nanoribbons. ACS Nano 6(6), 4823 (2012)CrossRef
78.
Zurück zum Zitat A.M. van der Zande, J. Kunstmann, A. Chernikov, D.A. Chenet, Y. You, X. Zhang, P.Y. Huang, T.C. Berkelbach, L. Wang, F. Zhang et al., Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist. Nano Lett. 14(7), 3869 (2014)CrossRef A.M. van der Zande, J. Kunstmann, A. Chernikov, D.A. Chenet, Y. You, X. Zhang, P.Y. Huang, T.C. Berkelbach, L. Wang, F. Zhang et al., Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist. Nano Lett. 14(7), 3869 (2014)CrossRef
79.
Zurück zum Zitat T. Jiang, H. Liu, D. Huang, S. Zhang, Y. Li, X. Gong, Y.R. Shen, W.T. Liu, S. Wu, Valley and band structure engineering of folded MoS\(_2\) bilayers. Nat. Nanotech. 9(10), 825 (2014)CrossRef T. Jiang, H. Liu, D. Huang, S. Zhang, Y. Li, X. Gong, Y.R. Shen, W.T. Liu, S. Wu, Valley and band structure engineering of folded MoS\(_2\) bilayers. Nat. Nanotech. 9(10), 825 (2014)CrossRef
80.
Zurück zum Zitat S. Huang, X. Ling, L. Liang, J. Kong, H. Terrones, V. Meunier, M.S. Dresselhaus, Probing the interlayer coupling of twisted bilayer MoS\(_2\) using photoluminescence spectroscopy. Nano Lett. 14(10), 5500 (2014)CrossRef S. Huang, X. Ling, L. Liang, J. Kong, H. Terrones, V. Meunier, M.S. Dresselhaus, Probing the interlayer coupling of twisted bilayer MoS\(_2\) using photoluminescence spectroscopy. Nano Lett. 14(10), 5500 (2014)CrossRef
81.
Zurück zum Zitat K. Liu, L. Zhang, T. Cao, C. Jin, D. Qiu, Q. Zhou, A. Zettl, P. Yang, S.G. Louie, F. Wang, Evolution of interlayer coupling in twisted molybdenum disulfide bilayers. Nat. Commun. 5 (2014). doi:10.1038/ncomms5966 K. Liu, L. Zhang, T. Cao, C. Jin, D. Qiu, Q. Zhou, A. Zettl, P. Yang, S.G. Louie, F. Wang, Evolution of interlayer coupling in twisted molybdenum disulfide bilayers. Nat. Commun. 5 (2014). doi:10.​1038/​ncomms5966
82.
Zurück zum Zitat M. Koshino, T. Habe, Spin-dependent refraction at the atomic step of transition-metal dichalcogenides. Phys. Rev. B 91, 201407 (2015)CrossRef M. Koshino, T. Habe, Spin-dependent refraction at the atomic step of transition-metal dichalcogenides. Phys. Rev. B 91, 201407 (2015)CrossRef
83.
Zurück zum Zitat M. Kan, J. Wang, X.W. Li, S. Zhang, Y. Li, Y. Kawazoe, Q. Sun, P. Jena, Structures and phase transition of a MoS\(_2\) monolayer. J. Phys. Chem. C 118(3), 1515 (2014)CrossRef M. Kan, J. Wang, X.W. Li, S. Zhang, Y. Li, Y. Kawazoe, Q. Sun, P. Jena, Structures and phase transition of a MoS\(_2\) monolayer. J. Phys. Chem. C 118(3), 1515 (2014)CrossRef
84.
Zurück zum Zitat L. Britnell, R.M. Ribeiro, A. Eckmann, R. Jalil, B.D. Belle, A. Mishchenko, Y.J. Kim, R.V. Gorbachev, T. Georgiou, S.V. Morozov et al., Strong light-matter interactions in heterostructures of atomically thin films. Science 340(6138), 1311 (2013)CrossRef L. Britnell, R.M. Ribeiro, A. Eckmann, R. Jalil, B.D. Belle, A. Mishchenko, Y.J. Kim, R.V. Gorbachev, T. Georgiou, S.V. Morozov et al., Strong light-matter interactions in heterostructures of atomically thin films. Science 340(6138), 1311 (2013)CrossRef
85.
Zurück zum Zitat A. Carvalho, R. Ribeiro, A.C. Neto, Band nesting and the optical response of two-dimensional semiconducting transition metal dichalcogenides. Phys. Rev. B 88(11), 115205 (2013)CrossRef A. Carvalho, R. Ribeiro, A.C. Neto, Band nesting and the optical response of two-dimensional semiconducting transition metal dichalcogenides. Phys. Rev. B 88(11), 115205 (2013)CrossRef
86.
Zurück zum Zitat G.F. Bassani, G.P. Parravicini, Electronic States and Optical Transitions in Solids (Pergamon Press, Oxford, 1975) G.F. Bassani, G.P. Parravicini, Electronic States and Optical Transitions in Solids (Pergamon Press, Oxford, 1975)
87.
Zurück zum Zitat D. Kozawa, R. Kumar, A. Carvalho, K.K. Amara, W. Zhao, S. Wang, M. Toh, R.M. Ribeiro, A.C. Neto, K. Matsuda, et al., Photocarrier relaxation pathway in two-dimensional semiconducting transition metal dichalcogenides. Nat. Commun. 5 (2014). doi:10.1038/ncomms5543 D. Kozawa, R. Kumar, A. Carvalho, K.K. Amara, W. Zhao, S. Wang, M. Toh, R.M. Ribeiro, A.C. Neto, K. Matsuda, et al., Photocarrier relaxation pathway in two-dimensional semiconducting transition metal dichalcogenides. Nat. Commun. 5 (2014). doi:10.​1038/​ncomms5543
88.
Zurück zum Zitat M. Bernardi, M. Palummo, J.C. Grossman, Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials. Nano Lett. 13(8), 3664 (2013)CrossRef M. Bernardi, M. Palummo, J.C. Grossman, Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials. Nano Lett. 13(8), 3664 (2013)CrossRef
89.
Zurück zum Zitat G. Eda, S.A. Maier, Two-dimensional crystals: managing light for optoelectronics. ACS Nano 7(7), 5660 (2013)CrossRef G. Eda, S.A. Maier, Two-dimensional crystals: managing light for optoelectronics. ACS Nano 7(7), 5660 (2013)CrossRef
90.
Zurück zum Zitat O. Lopez-Sanchez, E. Alarcon Llado, V. Koman, A. Fontcuberta i Morral, A. Radenovic, A. Kis. Light generation and harvesting in a van der Waals heterostructure. ACS Nano 8(3), 3042 (2014) O. Lopez-Sanchez, E. Alarcon Llado, V. Koman, A. Fontcuberta i Morral, A. Radenovic, A. Kis. Light generation and harvesting in a van der Waals heterostructure. ACS Nano 8(3), 3042 (2014)
91.
Zurück zum Zitat X. Liu, T. Galfsky, Z. Sun, F. Xia, E.C. Lin, Y.H. Lee, S. Kéna-Cohen, V.M. Menon, Strong light-matter coupling in two-dimensional atomic crystals. Nat. Photonics 9(1), 30 (2015)CrossRef X. Liu, T. Galfsky, Z. Sun, F. Xia, E.C. Lin, Y.H. Lee, S. Kéna-Cohen, V.M. Menon, Strong light-matter coupling in two-dimensional atomic crystals. Nat. Photonics 9(1), 30 (2015)CrossRef
92.
Zurück zum Zitat H.P. Komsa, A.V. Krasheninnikov, Effects of confinement and environment on the electronic structure and exciton binding energy of MoS\(_2\) from first principles. Phys. Rev. B 86(24), 241201 (2012)CrossRef H.P. Komsa, A.V. Krasheninnikov, Effects of confinement and environment on the electronic structure and exciton binding energy of MoS\(_2\) from first principles. Phys. Rev. B 86(24), 241201 (2012)CrossRef
93.
Zurück zum Zitat G. Onida, L. Reining, A. Rubio, Electronic excitations: density-functional versus many-body Green’s-function approaches. Rev. Mod. Phys. 74(2), 601 (2002)CrossRef G. Onida, L. Reining, A. Rubio, Electronic excitations: density-functional versus many-body Green’s-function approaches. Rev. Mod. Phys. 74(2), 601 (2002)CrossRef
94.
Zurück zum Zitat R. Coehoorn, C. Haas, J. Dijkstra, C. Flipse, R. De Groot, A. Wold, Electronic structure of MoSe\(_2\), MoS\(_2\), and WSe\(_2\). I. Band-structure calculations and photoelectron spectroscopy. Phys. Rev. B 35(12), 6195 (1987)CrossRef R. Coehoorn, C. Haas, J. Dijkstra, C. Flipse, R. De Groot, A. Wold, Electronic structure of MoSe\(_2\), MoS\(_2\), and WSe\(_2\). I. Band-structure calculations and photoelectron spectroscopy. Phys. Rev. B 35(12), 6195 (1987)CrossRef
95.
Zurück zum Zitat H. Mirhosseini, G. Roma, J. Kiss, C. Felser, First-principles investigation of the bulk and low-index surfaces of MoSe\(_2\). Phys. Rev. B 89(20), 205301 (2014)CrossRef H. Mirhosseini, G. Roma, J. Kiss, C. Felser, First-principles investigation of the bulk and low-index surfaces of MoSe\(_2\). Phys. Rev. B 89(20), 205301 (2014)CrossRef
96.
Zurück zum Zitat H. Peelaers, C.G. Van de Walle, First-principles study of van der Waals interactions in MoS\(_2\) and MoO\(_2\). J. Phys. Condens. Matter 26(30), 305502 (2014)CrossRef H. Peelaers, C.G. Van de Walle, First-principles study of van der Waals interactions in MoS\(_2\) and MoO\(_2\). J. Phys. Condens. Matter 26(30), 305502 (2014)CrossRef
97.
Zurück zum Zitat T. Björkman, A. Gulans, A. Krasheninnikov, R. Nieminen, Are we van der Waals ready? J. Phys. Condens. Matter 24(42), 424218 (2012) T. Björkman, A. Gulans, A. Krasheninnikov, R. Nieminen, Are we van der Waals ready? J. Phys. Condens. Matter 24(42), 424218 (2012)
98.
Zurück zum Zitat J. Harris, Simplified method for calculating the energy of weakly interacting fragments. Phys. Rev. B 31(4), 1770 (1985)CrossRef J. Harris, Simplified method for calculating the energy of weakly interacting fragments. Phys. Rev. B 31(4), 1770 (1985)CrossRef
99.
Zurück zum Zitat H. Rydberg, M. Dion, N. Jacobson, E. Schröder, P. Hyldgaard, S. Simak, D.C. Langreth, B.I. Lundqvist, Van der Waals density functional for layered structures. Phys. Rev. Lett. 91(12), 126402 (2003) H. Rydberg, M. Dion, N. Jacobson, E. Schröder, P. Hyldgaard, S. Simak, D.C. Langreth, B.I. Lundqvist, Van der Waals density functional for layered structures. Phys. Rev. Lett. 91(12), 126402 (2003)
100.
Zurück zum Zitat J. Harris, R. Jones, The surface energy of a bounded electron gas. J. Phys. F 4(8), 1170 (1974) J. Harris, R. Jones, The surface energy of a bounded electron gas. J. Phys. F 4(8), 1170 (1974)
101.
Zurück zum Zitat D.C. Langreth, J.P. Perdew, The exchange-correlation energy of a metallic surface. Solid State Commun. 17(11), 1425 (1975)CrossRef D.C. Langreth, J.P. Perdew, The exchange-correlation energy of a metallic surface. Solid State Commun. 17(11), 1425 (1975)CrossRef
102.
Zurück zum Zitat T. Olsen, K.S. Thygesen, Random phase approximation applied to solids, molecules, and graphene-metal interfaces: from van der Waals to covalent bonding. Phys. Rev. B 87(7), 075111 (2013) T. Olsen, K.S. Thygesen, Random phase approximation applied to solids, molecules, and graphene-metal interfaces: from van der Waals to covalent bonding. Phys. Rev. B 87(7), 075111 (2013)
103.
Zurück zum Zitat S. Grimme, Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comput. Chem. 25(12), 1463 (2004)CrossRef S. Grimme, Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comput. Chem. 25(12), 1463 (2004)CrossRef
104.
Zurück zum Zitat S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27(15), 1787 (2006) S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27(15), 1787 (2006)
105.
Zurück zum Zitat S. Grimme, J. Antony, S. Ehrlich, H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132(15), 154104 (2010)CrossRef S. Grimme, J. Antony, S. Ehrlich, H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132(15), 154104 (2010)CrossRef
106.
Zurück zum Zitat J. Klimeš, D.R. Bowler, A. Michaelides, Van der Waals density functionals applied to solids. Phys. Rev. B 83(19), 195131 (2011) J. Klimeš, D.R. Bowler, A. Michaelides, Van der Waals density functionals applied to solids. Phys. Rev. B 83(19), 195131 (2011)
107.
Zurück zum Zitat K. Berland, P. Hyldgaard, Exchange functional that tests the robustness of the plasmon description of the van der Waals density functional. Phys. Rev. B 89(3), 035412 (2014) K. Berland, P. Hyldgaard, Exchange functional that tests the robustness of the plasmon description of the van der Waals density functional. Phys. Rev. B 89(3), 035412 (2014)
108.
Zurück zum Zitat G. Román-Pérez, J.M. Soler, Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes. Phys. Rev. Lett. 103(9), 096102 (2009) G. Román-Pérez, J.M. Soler, Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes. Phys. Rev. Lett. 103(9), 096102 (2009)
109.
Zurück zum Zitat T. Björkman, A. Gulans, A.V. Krasheninnikov, R.M. Nieminen, Van der Waals bonding in layered compounds from advanced density-functional first-principles calculations. Phys. Rev. Lett. 108(23), 235502 (2012) T. Björkman, A. Gulans, A.V. Krasheninnikov, R.M. Nieminen, Van der Waals bonding in layered compounds from advanced density-functional first-principles calculations. Phys. Rev. Lett. 108(23), 235502 (2012)
110.
Zurück zum Zitat O.A. Vydrov, T. Van Voorhis, Nonlocal van der Waals density functional: the simpler the better. J. Chem. Phys. 133(24), 244103 (2010) O.A. Vydrov, T. Van Voorhis, Nonlocal van der Waals density functional: the simpler the better. J. Chem. Phys. 133(24), 244103 (2010)
111.
Zurück zum Zitat M. Dion, H. Rydberg, E. Schröder, D.C. Langreth, B.I. Lundqvist, Van der Waals density functional for general geometries. Phys. Rev. Lett. 92(24), 246401 (2004) M. Dion, H. Rydberg, E. Schröder, D.C. Langreth, B.I. Lundqvist, Van der Waals density functional for general geometries. Phys. Rev. Lett. 92(24), 246401 (2004)
112.
Zurück zum Zitat K. Lee, É.D. Murray, L. Kong, B.I. Lundqvist, D.C. Langreth, Higher-accuracy van der Waals density functional. Phys. Rev. B 82(8), 081101 (2010) K. Lee, É.D. Murray, L. Kong, B.I. Lundqvist, D.C. Langreth, Higher-accuracy van der Waals density functional. Phys. Rev. B 82(8), 081101 (2010)
113.
Zurück zum Zitat J. He, K. Hummer, C. Franchini, Stacking effects on the electronic and optical properties of bilayer transition metal dichalcogenides MoS\(_2\), MoSe\(_2\), WS\(_2\), and WSe\(_2\). Phys. Rev. B 89(7), 075409 (2014)CrossRef J. He, K. Hummer, C. Franchini, Stacking effects on the electronic and optical properties of bilayer transition metal dichalcogenides MoS\(_2\), MoSe\(_2\), WS\(_2\), and WSe\(_2\). Phys. Rev. B 89(7), 075409 (2014)CrossRef
114.
Zurück zum Zitat Y. Zhao, X. Luo, H. Li, J. Zhang, P.T. Araujo, C.K. Gan, J. Wu, H. Zhang, S.Y. Quek, M.S. Dresselhaus et al., Interlayer breathing and shear modes in few-trilayer MoS\(_2\) and WSe\(_2\). Nano Lett. 13(3), 1007 (2013)CrossRef Y. Zhao, X. Luo, H. Li, J. Zhang, P.T. Araujo, C.K. Gan, J. Wu, H. Zhang, S.Y. Quek, M.S. Dresselhaus et al., Interlayer breathing and shear modes in few-trilayer MoS\(_2\) and WSe\(_2\). Nano Lett. 13(3), 1007 (2013)CrossRef
115.
Zurück zum Zitat N. Marzari, A.A. Mostofi, J.R. Yates, I. Souza, D. Vanderbilt, Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84(4), 1419 (2012) N. Marzari, A.A. Mostofi, J.R. Yates, I. Souza, D. Vanderbilt, Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84(4), 1419 (2012)
116.
Zurück zum Zitat A. Savin, R. Nesper, S. Wengert, T.F. Fässler, The electron localization function. Angew. Chem. Int. Ed. 36(17), 1808 (1997)CrossRef A. Savin, R. Nesper, S. Wengert, T.F. Fässler, The electron localization function. Angew. Chem. Int. Ed. 36(17), 1808 (1997)CrossRef
117.
Zurück zum Zitat A.V. Kolobov, P. Fons, J. Tominaga, S.R. Ovshinsky, Vacancy-mediated three-center four-electron bonds in GeTe-Sb\(_2\)Te\(_3\) phase-change memory alloys. Phys. Rev. B 87, 165206 (2013) A.V. Kolobov, P. Fons, J. Tominaga, S.R. Ovshinsky, Vacancy-mediated three-center four-electron bonds in GeTe-Sb\(_2\)Te\(_3\) phase-change memory alloys. Phys. Rev. B 87, 165206 (2013)
118.
Zurück zum Zitat E.R. Johnson, S. Keinan, P. Mori-Sanchez, J. Contreras-Garcia, A.J. Cohen, W. Yang, Revealing noncovalent interactions. J. Am. Chem. Soc. 132(18), 6498 (2010)CrossRef E.R. Johnson, S. Keinan, P. Mori-Sanchez, J. Contreras-Garcia, A.J. Cohen, W. Yang, Revealing noncovalent interactions. J. Am. Chem. Soc. 132(18), 6498 (2010)CrossRef
119.
Zurück zum Zitat A. Otero-de-la Roza, E.R. Johnson, J. Contreras-Garcia, Revealing non-covalent interactions in solids: NCI plots revisited. J. Phys. Chem. Chem. Phys. 14, 12165 (2012) A. Otero-de-la Roza, E.R. Johnson, J. Contreras-Garcia, Revealing non-covalent interactions in solids: NCI plots revisited. J. Phys. Chem. Chem. Phys. 14, 12165 (2012)
120.
Zurück zum Zitat A. Otero-de-la Roza, E.R. Johnson, V. Luaña, Critic2: A program for real-space analysis of quantum chemical interactions in solids. Comput. Phys. Commun. 185(3), 1007 (2014) A. Otero-de-la Roza, E.R. Johnson, V. Luaña, Critic2: A program for real-space analysis of quantum chemical interactions in solids. Comput. Phys. Commun. 185(3), 1007 (2014)
121.
Zurück zum Zitat R.F.W. Bader, Atoms in Molecules: A Quantum Theory (Clarendon Press, Oxford, 1990) R.F.W. Bader, Atoms in Molecules: A Quantum Theory (Clarendon Press, Oxford, 1990)
122.
Zurück zum Zitat E. Kadantsev, MoS\(_2\): materials, physics, and devices, in Chapter 2: Electronic Structure of Exfoliated MoS\(_2\), ed. by Z.M. Wang, pp. 37–51 (Springer Science and Business Media, Berlin, 2014) E. Kadantsev, MoS\(_2\): materials, physics, and devices, in Chapter 2: Electronic Structure of Exfoliated MoS\(_2\), ed. by Z.M. Wang, pp. 37–51 (Springer Science and Business Media, Berlin, 2014)
123.
Zurück zum Zitat W. Li, M. Guo, G. Zhang, Y.W. Zhang, Gapless MoS\(_2\) allotrope possessing both massless Dirac and heavy fermions. Phys. Rev. B 89(20), 205402 (2014)CrossRef W. Li, M. Guo, G. Zhang, Y.W. Zhang, Gapless MoS\(_2\) allotrope possessing both massless Dirac and heavy fermions. Phys. Rev. B 89(20), 205402 (2014)CrossRef
124.
Zurück zum Zitat S. Najmaei, Z. Liu, W. Zhou, X. Zou, G. Shi, S. Lei, B.I. Yakobson, J.C. Idrobo, P.M. Ajayan, J. Lou, Vapour phase growth and grain boundary structure of molybdenum disulphide atomic layers. Nat. Mater. 12(8), 754 (2013)CrossRef S. Najmaei, Z. Liu, W. Zhou, X. Zou, G. Shi, S. Lei, B.I. Yakobson, J.C. Idrobo, P.M. Ajayan, J. Lou, Vapour phase growth and grain boundary structure of molybdenum disulphide atomic layers. Nat. Mater. 12(8), 754 (2013)CrossRef
125.
Zurück zum Zitat A.M. van der Zande, P.Y. Huang, D.A. Chenet, T.C. Berkelbach, Y. You, G.H. Lee, T.F. Heinz, D.R. Reichman, D.A. Muller, J.C. Hone, Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide. Nat. Mater. 12(6), 554 (2013)CrossRef A.M. van der Zande, P.Y. Huang, D.A. Chenet, T.C. Berkelbach, Y. You, G.H. Lee, T.F. Heinz, D.R. Reichman, D.A. Muller, J.C. Hone, Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide. Nat. Mater. 12(6), 554 (2013)CrossRef
126.
Zurück zum Zitat X. Zou, Y. Liu, B.I. Yakobson, Predicting dislocations and grain boundaries in two-dimensional metal-disulfides from the first principles. Nano Lett. 13(1), 253 (2012)CrossRef X. Zou, Y. Liu, B.I. Yakobson, Predicting dislocations and grain boundaries in two-dimensional metal-disulfides from the first principles. Nano Lett. 13(1), 253 (2012)CrossRef
127.
Zurück zum Zitat P. Avouris, Z. Chen, V. Perebeinos, Carbon-based electronics. Nat. Nanotech. 2(10), 605 (2007)CrossRef P. Avouris, Z. Chen, V. Perebeinos, Carbon-based electronics. Nat. Nanotech. 2(10), 605 (2007)CrossRef
128.
Zurück zum Zitat C.C. Liu, W. Feng, Y. Yao, Quantum spin Hall effect in silicene and two-dimensional germanium. Phys. Rev. Lett. 107(7), 076802 (2011) C.C. Liu, W. Feng, Y. Yao, Quantum spin Hall effect in silicene and two-dimensional germanium. Phys. Rev. Lett. 107(7), 076802 (2011)
129.
Zurück zum Zitat W. Zhao, R.M. Ribeiro, G. Eda, Electronic structure and optical signatures of semiconducting transition metal dichalcogenide nanosheets. Acc. Chem. Res. 48(1), 91 (2015)CrossRef W. Zhao, R.M. Ribeiro, G. Eda, Electronic structure and optical signatures of semiconducting transition metal dichalcogenide nanosheets. Acc. Chem. Res. 48(1), 91 (2015)CrossRef
130.
Zurück zum Zitat N. Mott, E. Davis, R. Street, States in the gap and recombination in amorphous semiconductors. Philos. Mag. 32(5), 961 (1975)CrossRef N. Mott, E. Davis, R. Street, States in the gap and recombination in amorphous semiconductors. Philos. Mag. 32(5), 961 (1975)CrossRef
131.
Zurück zum Zitat R. Street, T. Searle, I. Austin, The photoluminescence properties of glasses in the As-Se system. Philos. Mag. 30(5), 1181 (1974)CrossRef R. Street, T. Searle, I. Austin, The photoluminescence properties of glasses in the As-Se system. Philos. Mag. 30(5), 1181 (1974)CrossRef
132.
Zurück zum Zitat R. Street, Luminescence in amorphous semiconductors. Adv. Phys. 25(4), 397 (1976)CrossRef R. Street, Luminescence in amorphous semiconductors. Adv. Phys. 25(4), 397 (1976)CrossRef
133.
Zurück zum Zitat N. Ravindra, S. Auluck, V. Srivastava, On the Penn gap in semiconductors. Phys. Status Solidi B 93(2), K155 (1979) N. Ravindra, S. Auluck, V. Srivastava, On the Penn gap in semiconductors. Phys. Status Solidi B 93(2), K155 (1979)
134.
Zurück zum Zitat K. Shimakawa, L. Střižik, T. Wagner, M. Frumar, Penn gap rule in phase-change memory materials: no clear evidence for resonance bonds. APL Mater. 3(4), 041801 (2015)CrossRef K. Shimakawa, L. Střižik, T. Wagner, M. Frumar, Penn gap rule in phase-change memory materials: no clear evidence for resonance bonds. APL Mater. 3(4), 041801 (2015)CrossRef
135.
Zurück zum Zitat H.L. Liu, C.C. Shen, S.H. Su, C.L. Hsu, M.Y. Li, L.J. Li, Optical properties of monolayer transition metal dichalcogenides probed by spectroscopic ellipsometry. Appl. Phys. Lett. 105(20), 201905 (2014)CrossRef H.L. Liu, C.C. Shen, S.H. Su, C.L. Hsu, M.Y. Li, L.J. Li, Optical properties of monolayer transition metal dichalcogenides probed by spectroscopic ellipsometry. Appl. Phys. Lett. 105(20), 201905 (2014)CrossRef
136.
Zurück zum Zitat C. Zhang, H. Wang, W. Chan, C. Manolatou, F. Rana, Absorption of light by excitons and trions in monolayers of metal dichalcogenide MoS\(_2\): experiments and theory. Phys. Rev. B 89(20), 205436 (2014)CrossRef C. Zhang, H. Wang, W. Chan, C. Manolatou, F. Rana, Absorption of light by excitons and trions in monolayers of metal dichalcogenide MoS\(_2\): experiments and theory. Phys. Rev. B 89(20), 205436 (2014)CrossRef
137.
Zurück zum Zitat A. Beal, J. Knights, W. Liang, Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination. J Phys. C 5(24), 3540 (1972)CrossRef A. Beal, J. Knights, W. Liang, Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination. J Phys. C 5(24), 3540 (1972)CrossRef
138.
Zurück zum Zitat R. Bromley, R. Murray, A. Yoffe, The band structures of some transition metal dichalcogenides. III. Group VIA: trigonal prism materials. J. Phys. Condens. Matter 5(7), 759 (1972) R. Bromley, R. Murray, A. Yoffe, The band structures of some transition metal dichalcogenides. III. Group VIA: trigonal prism materials. J. Phys. Condens. Matter 5(7), 759 (1972)
139.
Zurück zum Zitat W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.H. Tan, G. Eda, Evolution of electronic structure in atomically thin sheets of WS\(_2\) and WSe\(_2\). ACS Nano 7(1), 791 (2012)CrossRef W. Zhao, Z. Ghorannevis, L. Chu, M. Toh, C. Kloc, P.H. Tan, G. Eda, Evolution of electronic structure in atomically thin sheets of WS\(_2\) and WSe\(_2\). ACS Nano 7(1), 791 (2012)CrossRef
140.
Zurück zum Zitat G. Eda, H. Yamaguchi, D. Voiry, T. Fujita, M. Chen, M. Chhowalla, Photoluminescence from chemically exfoliated MoS\(_2\). Nano Lett. 11(12), 5111 (2011)CrossRef G. Eda, H. Yamaguchi, D. Voiry, T. Fujita, M. Chen, M. Chhowalla, Photoluminescence from chemically exfoliated MoS\(_2\). Nano Lett. 11(12), 5111 (2011)CrossRef
141.
Zurück zum Zitat A.R. Klots, A.K.M. Newaz, B. Wang, D. Prasai, H. Krzyzanowska, J. Lin, D. Caudel, N.J. Ghimire, J. Yan, B.L. Ivanov, et al., Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy. Sci. Rep. 4 (2014). doi:10.1038/srep06608 A.R. Klots, A.K.M. Newaz, B. Wang, D. Prasai, H. Krzyzanowska, J. Lin, D. Caudel, N.J. Ghimire, J. Yan, B.L. Ivanov, et al., Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy. Sci. Rep. 4 (2014). doi:10.​1038/​srep06608
142.
Zurück zum Zitat C. Zhang, A. Johnson, C.L. Hsu, L.J. Li, C.K. Shih, Direct imaging of band profile in single layer MoS\(_2\) on graphite: quasiparticle energy gap, metallic edge states, and edge band bending. Nano Lett. 14(5), 2443 (2014)CrossRef C. Zhang, A. Johnson, C.L. Hsu, L.J. Li, C.K. Shih, Direct imaging of band profile in single layer MoS\(_2\) on graphite: quasiparticle energy gap, metallic edge states, and edge band bending. Nano Lett. 14(5), 2443 (2014)CrossRef
143.
Zurück zum Zitat M.H. Chiu, C. Zhang, H.W. Shiu, C.P. Chuu, C.H. Chen, C.Y.S. Chang, C.H. Chen, M.Y. Chou, C.K. Shih, L.J. Li, Determination of band alignment in the single-layer MoS\(_2\)/WSe\(_2\) heterojunction. Nat. Commun. 6 (2015). doi:10.1038/ncomms8666 M.H. Chiu, C. Zhang, H.W. Shiu, C.P. Chuu, C.H. Chen, C.Y.S. Chang, C.H. Chen, M.Y. Chou, C.K. Shih, L.J. Li, Determination of band alignment in the single-layer MoS\(_2\)/WSe\(_2\) heterojunction. Nat. Commun. 6 (2015). doi:10.​1038/​ncomms8666
144.
Zurück zum Zitat M.M. Ugeda, A.J. Bradley, S.F. Shi, H. Felipe, Y. Zhang, D.Y. Qiu, W. Ruan, S.K. Mo, Z. Hussain, Z.X. Shen et al., Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13(12), 1091 (2014)CrossRef M.M. Ugeda, A.J. Bradley, S.F. Shi, H. Felipe, Y. Zhang, D.Y. Qiu, W. Ruan, S.K. Mo, Z. Hussain, Z.X. Shen et al., Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13(12), 1091 (2014)CrossRef
145.
Zurück zum Zitat H. Liu, L. Jiao, F. Yang, Y. Cai, X. Wu, W. Ho, C. Gao, J. Jia, N. Wang, H. Fan et al., Dense network of one-dimensional midgap metallic modes in monolayer MoSe\(_2\) and their spatial undulations. Phys. Rev. Lett. 113(6), 066105 (2014)CrossRef H. Liu, L. Jiao, F. Yang, Y. Cai, X. Wu, W. Ho, C. Gao, J. Jia, N. Wang, H. Fan et al., Dense network of one-dimensional midgap metallic modes in monolayer MoSe\(_2\) and their spatial undulations. Phys. Rev. Lett. 113(6), 066105 (2014)CrossRef
146.
Zurück zum Zitat S.G. Sørensen, H.G. Füchtbauer, A.K. Tuxen, A.S. Walton, J.V. Lauritsen, Structure and electronic properties of in situ synthesized single-layer MoS\(_2\) on a gold surface. ACS Nano 8(7), 6788 (2014)CrossRef S.G. Sørensen, H.G. Füchtbauer, A.K. Tuxen, A.S. Walton, J.V. Lauritsen, Structure and electronic properties of in situ synthesized single-layer MoS\(_2\) on a gold surface. ACS Nano 8(7), 6788 (2014)CrossRef
147.
Zurück zum Zitat M. Yankowitz, D. McKenzie, B.J. LeRoy, Local spectroscopic characterization of spin and layer polarization in WSe\(_2\). Phys. Rev. Lett. 115, 13680 (2015)CrossRef M. Yankowitz, D. McKenzie, B.J. LeRoy, Local spectroscopic characterization of spin and layer polarization in WSe\(_2\). Phys. Rev. Lett. 115, 13680 (2015)CrossRef
148.
Zurück zum Zitat C. Zhang, Y. Chen, A. Johnson, M.Y. Li, L.J. Li, P.C. Mende, R.M. Feenstra, C.K. Shih, Probing critical point energies of transition metal dichalcogenides: surprising indirect gap of single layer WSe\(_2\). Nano Lett. 15, 6494 (2015)CrossRef C. Zhang, Y. Chen, A. Johnson, M.Y. Li, L.J. Li, P.C. Mende, R.M. Feenstra, C.K. Shih, Probing critical point energies of transition metal dichalcogenides: surprising indirect gap of single layer WSe\(_2\). Nano Lett. 15, 6494 (2015)CrossRef
149.
Zurück zum Zitat A.J. Bradley, M.M. Ugeda, F.H. da Jornada, D.Y. Qiu, W. Ruan, Y. Zhang, S. Wickenburg, A. Riss, J. Lu, S.K. Mo et al., Probing the role of interlayer coupling and Coulomb interactions on electronic structure in few-layer MoSe\(_2\) nanostructures. Nano Lett. 15(4), 2594 (2015)CrossRef A.J. Bradley, M.M. Ugeda, F.H. da Jornada, D.Y. Qiu, W. Ruan, Y. Zhang, S. Wickenburg, A. Riss, J. Lu, S.K. Mo et al., Probing the role of interlayer coupling and Coulomb interactions on electronic structure in few-layer MoSe\(_2\) nanostructures. Nano Lett. 15(4), 2594 (2015)CrossRef
150.
Zurück zum Zitat Y.L. Huang, Y. Chen, W. Zhang, S.Y. Quek, C.H. Chen, L.J. Li, W.T. Hsu, W.H. Chang, Y.J. Zheng, W. Chen, et al., Bandgap tunability at single-layer molybdenum disulphide grain boundaries. Nat. Commun. 6 (2015). doi:10.1038/ncomms7298 Y.L. Huang, Y. Chen, W. Zhang, S.Y. Quek, C.H. Chen, L.J. Li, W.T. Hsu, W.H. Chang, Y.J. Zheng, W. Chen, et al., Bandgap tunability at single-layer molybdenum disulphide grain boundaries. Nat. Commun. 6 (2015). doi:10.​1038/​ncomms7298
151.
Zurück zum Zitat H. Yuan, M.S. Bahramy, K. Morimoto, S. Wu, K. Nomura, B.J. Yang, H. Shimotani, R. Suzuki, M. Toh, C. Kloc et al., Zeeman-type spin splitting controlled by an electric field. Nat. Phys. 9(9), 563 (2013)CrossRef H. Yuan, M.S. Bahramy, K. Morimoto, S. Wu, K. Nomura, B.J. Yang, H. Shimotani, R. Suzuki, M. Toh, C. Kloc et al., Zeeman-type spin splitting controlled by an electric field. Nat. Phys. 9(9), 563 (2013)CrossRef
152.
Zurück zum Zitat L. Sun, J. Yan, D. Zhan, L. Liu, H. Hu, H. Li, B.K. Tay, J.L. Kuo, C.C. Huang, D.W. Hewak et al., Spin-orbit splitting in single-layer MoS\(_2\) revealed by triply resonant Raman scattering. Phys. Rev. Lett. 111(12), 126801 (2013) L. Sun, J. Yan, D. Zhan, L. Liu, H. Hu, H. Li, B.K. Tay, J.L. Kuo, C.C. Huang, D.W. Hewak et al., Spin-orbit splitting in single-layer MoS\(_2\) revealed by triply resonant Raman scattering. Phys. Rev. Lett. 111(12), 126801 (2013)
153.
Zurück zum Zitat S.W. Han, G.B. Cha, E. Frantzeskakis, I. Razado-Colambo, J. Avila, Y.S. Park, D. Kim, J. Hwang, J.S. Kang, S. Ryu et al., Band-gap expansion in the surface-localized electronic structure of MoS\(_2\) (0002). Phys. Rev. B 86(11), 115105 (2012)CrossRef S.W. Han, G.B. Cha, E. Frantzeskakis, I. Razado-Colambo, J. Avila, Y.S. Park, D. Kim, J. Hwang, J.S. Kang, S. Ryu et al., Band-gap expansion in the surface-localized electronic structure of MoS\(_2\) (0002). Phys. Rev. B 86(11), 115105 (2012)CrossRef
154.
Zurück zum Zitat P. Zhang, P. Richard, T. Qian, Y.M. Xu, X. Dai, H. Ding, A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 82(4), 043712 (2011)CrossRef P. Zhang, P. Richard, T. Qian, Y.M. Xu, X. Dai, H. Ding, A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 82(4), 043712 (2011)CrossRef
155.
Zurück zum Zitat H. Peelaers, C.G. Van de Walle, Effects of strain on band structure and effective masses in MoS\(_2\). Phys. Rev. B 86(24), 241401 (2012)CrossRef H. Peelaers, C.G. Van de Walle, Effects of strain on band structure and effective masses in MoS\(_2\). Phys. Rev. B 86(24), 241401 (2012)CrossRef
156.
Zurück zum Zitat A. Ayari, E. Cobas, O. Ogundadegbe, M.S. Fuhrer, Realization and electrical characterization of ultrathin crystals of layered transition-metal dichalcogenides. J. Appl. Phys. 101(1), 014507 (2007)CrossRef A. Ayari, E. Cobas, O. Ogundadegbe, M.S. Fuhrer, Realization and electrical characterization of ultrathin crystals of layered transition-metal dichalcogenides. J. Appl. Phys. 101(1), 014507 (2007)CrossRef
157.
Zurück zum Zitat R. Fivaz, E. Mooser, Mobility of charge carriers in semiconducting layer structures. Phys. Rev. 163(3), 743 (1967)CrossRef R. Fivaz, E. Mooser, Mobility of charge carriers in semiconducting layer structures. Phys. Rev. 163(3), 743 (1967)CrossRef
158.
Zurück zum Zitat N. Alidoust, G. Bian, S.Y. Xu, R. Sankar, M. Neupane, C. Liu, I. Belopolski, D.X. Qu, J.D. Denlinger, F.C. Chou, et al., Observation of monolayer valence band spin-orbit effect and induced quantum well states in MoX\(_2\). Nat. Commun. 5 (2014). doi:10.1038/ncomms5673 N. Alidoust, G. Bian, S.Y. Xu, R. Sankar, M. Neupane, C. Liu, I. Belopolski, D.X. Qu, J.D. Denlinger, F.C. Chou, et al., Observation of monolayer valence band spin-orbit effect and induced quantum well states in MoX\(_2\). Nat. Commun. 5 (2014). doi:10.​1038/​ncomms5673
159.
Zurück zum Zitat S. Tongay, J. Zhou, C. Ataca, K. Lo, T.S. Matthews, J. Li, J.C. Grossman, J. Wu, Thermally driven crossover from indirect toward direct bandgap in 2D semiconductors: MoSe\(_2\) versus MoS\(_2\). Nano Lett. 12(11), 5576 (2012)CrossRef S. Tongay, J. Zhou, C. Ataca, K. Lo, T.S. Matthews, J. Li, J.C. Grossman, J. Wu, Thermally driven crossover from indirect toward direct bandgap in 2D semiconductors: MoSe\(_2\) versus MoS\(_2\). Nano Lett. 12(11), 5576 (2012)CrossRef
160.
Zurück zum Zitat H. Rostami, A.G. Moghaddam, R. Asgari, Effective lattice hamiltonian for monolayer MoS\(_2\): tailoring electronic structure with perpendicular electric and magnetic fields. Phys. Rev. B 88(8), 085440 (2013)CrossRef H. Rostami, A.G. Moghaddam, R. Asgari, Effective lattice hamiltonian for monolayer MoS\(_2\): tailoring electronic structure with perpendicular electric and magnetic fields. Phys. Rev. B 88(8), 085440 (2013)CrossRef
161.
Zurück zum Zitat J. Zheng, H. Zhang, S. Dong, Y. Liu, C.T. Nai, H.S. Shin, H.Y. Jeong, B. Liu, K.P. Loh, High yield exfoliation of two-dimensional chalcogenides using sodium naphthalenide. Nat. Commun. 5 (2014). doi:10.1038/ncomms3995 J. Zheng, H. Zhang, S. Dong, Y. Liu, C.T. Nai, H.S. Shin, H.Y. Jeong, B. Liu, K.P. Loh, High yield exfoliation of two-dimensional chalcogenides using sodium naphthalenide. Nat. Commun. 5 (2014). doi:10.​1038/​ncomms3995
162.
Zurück zum Zitat P.C. Yeh, W. Jin, N. Zaki, D. Zhang, J.T. Liou, J.T. Sadowski, A. Al-Mahboob, J.I. Dadap, I.P. Herman, P. Sutter et al., Layer-dependent electronic structure of an atomically heavy two-dimensional dichalcogenide. Phys. Rev. B 91(4), 041407 (2015)CrossRef P.C. Yeh, W. Jin, N. Zaki, D. Zhang, J.T. Liou, J.T. Sadowski, A. Al-Mahboob, J.I. Dadap, I.P. Herman, P. Sutter et al., Layer-dependent electronic structure of an atomically heavy two-dimensional dichalcogenide. Phys. Rev. B 91(4), 041407 (2015)CrossRef
163.
Zurück zum Zitat D. Le, A. Barinov, E. Preciado, M. Isarraraz, I. Tanabe, T. Komesu, C. Troha, L. Bartels, T.S. Rahman, P.A. Dowben, Spin-orbit coupling in the band structure of monolayer WSe\(_2\). J. Phys. Condens. Matter 27(18), 182201 (2015)CrossRef D. Le, A. Barinov, E. Preciado, M. Isarraraz, I. Tanabe, T. Komesu, C. Troha, L. Bartels, T.S. Rahman, P.A. Dowben, Spin-orbit coupling in the band structure of monolayer WSe\(_2\). J. Phys. Condens. Matter 27(18), 182201 (2015)CrossRef
164.
Zurück zum Zitat A. Chernikov, T.C. Berkelbach, H.M. Hill, A. Rigosi, Y. Li, O.B. Aslan, D.R. Reichman, M.S. Hybertsen, T.F. Heinz, Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS\(_2\). Phys. Rev. Lett. 113(7), 076802 (2014) A. Chernikov, T.C. Berkelbach, H.M. Hill, A. Rigosi, Y. Li, O.B. Aslan, D.R. Reichman, M.S. Hybertsen, T.F. Heinz, Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS\(_2\). Phys. Rev. Lett. 113(7), 076802 (2014)
165.
Zurück zum Zitat K. He, N. Kumar, L. Zhao, Z. Wang, K.F. Mak, H. Zhao, J. Shan, Tightly bound excitons in monolayer WSe\(_2\). Phys. Rev. Lett. 113(2), 026803 (2014)CrossRef K. He, N. Kumar, L. Zhao, Z. Wang, K.F. Mak, H. Zhao, J. Shan, Tightly bound excitons in monolayer WSe\(_2\). Phys. Rev. Lett. 113(2), 026803 (2014)CrossRef
166.
Zurück zum Zitat K.F. Mak, K. He, C. Lee, G.H. Lee, J. Hone, T.F. Heinz, J. Shan, Tightly bound trions in monolayer MoS\(_2\). Nat. Mater. 12(3), 207 (2013)CrossRef K.F. Mak, K. He, C. Lee, G.H. Lee, J. Hone, T.F. Heinz, J. Shan, Tightly bound trions in monolayer MoS\(_2\). Nat. Mater. 12(3), 207 (2013)CrossRef
167.
Zurück zum Zitat J.S. Ross, S. Wu, H. Yu, N.J. Ghimire, A.M. Jones, G. Aivazian, J. Yan, D.G. Mandrus, D. Xiao, W. Yao, et al., Electrical control of neutral and charged excitons in a monolayer semiconductor. Nat. Commun. 4 (2013). doi:10.1038/ncomms2498 J.S. Ross, S. Wu, H. Yu, N.J. Ghimire, A.M. Jones, G. Aivazian, J. Yan, D.G. Mandrus, D. Xiao, W. Yao, et al., Electrical control of neutral and charged excitons in a monolayer semiconductor. Nat. Commun. 4 (2013). doi:10.​1038/​ncomms2498
168.
Zurück zum Zitat A. Chernikov, C. Ruppert, H.M. Hill, A.F. Rigosi, T.F. Heinz, Population inversion and giant bandgap renormalization in atomically thin WS\(_2\) layers. Nat. Photonics 9(7), 466 (2015)CrossRef A. Chernikov, C. Ruppert, H.M. Hill, A.F. Rigosi, T.F. Heinz, Population inversion and giant bandgap renormalization in atomically thin WS\(_2\) layers. Nat. Photonics 9(7), 466 (2015)CrossRef
169.
Zurück zum Zitat Y.Y. Hui, X. Liu, W. Jie, N.Y. Chan, J. Hao, Y.T. Hsu, L.J. Li, W. Guo, S.P. Lau, Exceptional tunability of band energy in a compressively strained trilayer MoS\(_2\) sheet. ACS Nano 7(8), 7126 (2013)CrossRef Y.Y. Hui, X. Liu, W. Jie, N.Y. Chan, J. Hao, Y.T. Hsu, L.J. Li, W. Guo, S.P. Lau, Exceptional tunability of band energy in a compressively strained trilayer MoS\(_2\) sheet. ACS Nano 7(8), 7126 (2013)CrossRef
170.
Zurück zum Zitat K. He, C. Poole, K.F. Mak, J. Shan, Experimental demonstration of continuous electronic structure tuning via strain in atomically thin MoS\(_2\). Nano Lett. 13(6), 2931 (2013)CrossRef K. He, C. Poole, K.F. Mak, J. Shan, Experimental demonstration of continuous electronic structure tuning via strain in atomically thin MoS\(_2\). Nano Lett. 13(6), 2931 (2013)CrossRef
171.
Zurück zum Zitat S.B. Desai, G. Seol, J.S. Kang, H. Fang, C. Battaglia, R. Kapadia, J.W. Ager, J. Guo, A. Javey, Strain-induced indirect to direct bandgap transition in multilayer WSe\(_2\). Nano Lett. 14(8), 4592 (2014)CrossRef S.B. Desai, G. Seol, J.S. Kang, H. Fang, C. Battaglia, R. Kapadia, J.W. Ager, J. Guo, A. Javey, Strain-induced indirect to direct bandgap transition in multilayer WSe\(_2\). Nano Lett. 14(8), 4592 (2014)CrossRef
172.
Zurück zum Zitat Y. Lin, X. Ling, L. Yu, S. Huang, A.L. Hsu, Y.H. Lee, J. Kong, M.S. Dresselhaus, T. Palacios, Dielectric screening of excitons and trions in single-layer MoS\(_2\). Nano Lett. 14(10), 5569 (2014)CrossRef Y. Lin, X. Ling, L. Yu, S. Huang, A.L. Hsu, Y.H. Lee, J. Kong, M.S. Dresselhaus, T. Palacios, Dielectric screening of excitons and trions in single-layer MoS\(_2\). Nano Lett. 14(10), 5569 (2014)CrossRef
173.
Zurück zum Zitat S. Manzeli, A. Allain, A. Ghadimi, A. Kis, Piezoresistivity and strain-induced band gap tuning in atomically thin MoS\(_2\). Nano Lett. 15(8), 5330 (2015)CrossRef S. Manzeli, A. Allain, A. Ghadimi, A. Kis, Piezoresistivity and strain-induced band gap tuning in atomically thin MoS\(_2\). Nano Lett. 15(8), 5330 (2015)CrossRef
174.
Zurück zum Zitat M.Y. Tsai, A. Tarasov, Z.R. Hesabi, H. Taghinejad, P.M. Campbell, C. Joiner, A. Adibi, E.M. Vogel. Flexible MoS\(_2\) field-effect transistors for gate-tunable piezoresistive strain sensors. ACS Appl. Mater. Interfaces 7, 12850 (2015) M.Y. Tsai, A. Tarasov, Z.R. Hesabi, H. Taghinejad, P.M. Campbell, C. Joiner, A. Adibi, E.M. Vogel. Flexible MoS\(_2\) field-effect transistors for gate-tunable piezoresistive strain sensors. ACS Appl. Mater. Interfaces 7, 12850 (2015)
Metadaten
Titel
Electronic Band Structure of 2D TMDCs
verfasst von
Alexander V. Kolobov
Junji Tominaga
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-31450-1_6

Neuer Inhalt