Skip to main content
Erschienen in: Journal of Computational Electronics 3/2017

17.07.2017

Tunable electronic properties of multilayer phosphorene and its nanoribbons

verfasst von: S. Soleimanikahnoj, I. Knezevic

Erschienen in: Journal of Computational Electronics | Ausgabe 3/2017

Einloggen

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

search-config
loading …

Abstract

We study the effects of a vertical electric field on the electronic band structure and transport in multilayer phosphorene and its nanoribbons. In phosphorene, at a critical value of the vertical electric field (\(E_\mathrm{c}\)), the band gap closes and the band structure undergoes a massive-to-massless Dirac fermion transition along the armchair direction. This transition is observable in quantum Hall measurements, as the power-law dependence of the Landau-level energy on the magnetic field B goes from \({\sim }(n+1/2)B\) below \(E_\mathrm{c}\), to \({\sim }[(n+1/2)B]^{2/3}\) at \(E_\mathrm{c}\), to \({\sim }[(n+1/2)B]^{1/2}\) above \(E_\mathrm{c}\). In multilayer phosphorene nanoribbons (PNRs), the vertical electric field can be employed to manipulate the midgap energy bands that are associated with edge states, thereby giving rise to new device functionalities. We propose a dual-edge-gate PNR structure that works as a quantum switch.

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!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
The condition for energy levels in a magnetic field B is \(S(E) = 2\pi (n+\frac{1}{2})eB\), where S(E) is the area of constant-energy surface in reciprocal space [56]. Since \(\rho (E) = \frac{\partial S(E)}{\partial E}\), the Landau levels are found to be \(E_n\sim [(n+1/2)B]^{2/3}\) for multilayer phosphorene at the critical electric field.
 
Literatur
1.
Zurück zum Zitat Lu, W., et al.: Plasma-assisted fabrication of monolayer phosphorene and its raman characterization. Nano Res. 7(6), 853 (2014)CrossRef Lu, W., et al.: Plasma-assisted fabrication of monolayer phosphorene and its raman characterization. Nano Res. 7(6), 853 (2014)CrossRef
2.
Zurück zum Zitat Liu, H., et al.: Phosphorene: an unexplored 2d semiconductor with a high hole mobility. ACS Nano 8(4), 4033 (2014)CrossRef Liu, H., et al.: Phosphorene: an unexplored 2d semiconductor with a high hole mobility. ACS Nano 8(4), 4033 (2014)CrossRef
3.
Zurück zum Zitat Zhang, S., et al.: Extraordinary photoluminescence and strong temperature/angle-dependent raman responses in few-layer phosphorene. ACS Nano 8(9), 9590 (2014)CrossRef Zhang, S., et al.: Extraordinary photoluminescence and strong temperature/angle-dependent raman responses in few-layer phosphorene. ACS Nano 8(9), 9590 (2014)CrossRef
4.
Zurück zum Zitat Tran, V., et al.: Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B 89(23), 235319 (2014)CrossRef Tran, V., et al.: Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B 89(23), 235319 (2014)CrossRef
5.
Zurück zum Zitat Jing, Y., et al.: Small molecules make big differences: molecular doping effects on electronic and optical properties of phosphorene. Nanotechnology 26(9), 095201 (2015)CrossRef Jing, Y., et al.: Small molecules make big differences: molecular doping effects on electronic and optical properties of phosphorene. Nanotechnology 26(9), 095201 (2015)CrossRef
6.
Zurück zum Zitat Buscema, M., et al.: Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors. Nano. Lett. 14(6), 3347 (2014)CrossRef Buscema, M., et al.: Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors. Nano. Lett. 14(6), 3347 (2014)CrossRef
7.
Zurück zum Zitat Koenig, S .P., et al.: Electric field effect in ultrathin black phosphorus. Appl. Phys. Lett. 104(10), 103106 (2014)CrossRef Koenig, S .P., et al.: Electric field effect in ultrathin black phosphorus. Appl. Phys. Lett. 104(10), 103106 (2014)CrossRef
8.
Zurück zum Zitat Xia, F., Wang, H., Jia, Y.: Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nat. Commun. 5, 4458 (2014) Xia, F., Wang, H., Jia, Y.: Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nat. Commun. 5, 4458 (2014)
9.
Zurück zum Zitat Çakır, D., Sevik, C., Peeters, F.M.: Significant effect of stacking on the electronic and optical properties of few-layer black phosphorus. Phys. Rev. B 92(16), 165406 (2015)CrossRef Çakır, D., Sevik, C., Peeters, F.M.: Significant effect of stacking on the electronic and optical properties of few-layer black phosphorus. Phys. Rev. B 92(16), 165406 (2015)CrossRef
10.
Zurück zum Zitat Çakır, D., Sahin, H., Peeters, F.M.: Tuning of the electronic and optical properties of single-layer black phosphorus by strain. Phys. Rev. B 90(20), 205421 (2014)CrossRef Çakır, D., Sahin, H., Peeters, F.M.: Tuning of the electronic and optical properties of single-layer black phosphorus by strain. Phys. Rev. B 90(20), 205421 (2014)CrossRef
11.
Zurück zum Zitat Fei, R., Yang, L.: Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Lett. 14(5), 2884 (2014)CrossRef Fei, R., Yang, L.: Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Lett. 14(5), 2884 (2014)CrossRef
12.
Zurück zum Zitat Fei, R., et al.: Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductances in phosphorene. Nano Lett. 14(11), 6393 (2014)CrossRef Fei, R., et al.: Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductances in phosphorene. Nano Lett. 14(11), 6393 (2014)CrossRef
13.
Zurück zum Zitat Yuan, S., Rudenko, A., Katsnelson, M.: Transport and optical properties of single-and bilayer black phosphorus with defects. Phys. Rev. B 91(11), 115436 (2015)CrossRef Yuan, S., Rudenko, A., Katsnelson, M.: Transport and optical properties of single-and bilayer black phosphorus with defects. Phys. Rev. B 91(11), 115436 (2015)CrossRef
14.
Zurück zum Zitat Qin, G., et al.: Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles. Phys. Chem. Chem. Phys. 17(7), 4854 (2015)CrossRef Qin, G., et al.: Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles. Phys. Chem. Chem. Phys. 17(7), 4854 (2015)CrossRef
15.
Zurück zum Zitat Cai, Y., et al.: Giant phononic anisotropy and unusual anharmonicity of phosphorene: interlayer coupling and strain engineering. Adv. Funct. Mater. 25(15), 2230 (2015)CrossRef Cai, Y., et al.: Giant phononic anisotropy and unusual anharmonicity of phosphorene: interlayer coupling and strain engineering. Adv. Funct. Mater. 25(15), 2230 (2015)CrossRef
16.
Zurück zum Zitat Low, T., et al.: Plasmons and screening in monolayer and multilayer black phosphorus. Phys. Rev. Lett. 113(10), 106802 (2014)CrossRef Low, T., et al.: Plasmons and screening in monolayer and multilayer black phosphorus. Phys. Rev. Lett. 113(10), 106802 (2014)CrossRef
17.
Zurück zum Zitat Elahi, M., et al.: Modulation of electronic and mechanical properties of phosphorene through strain. Phys. Rev. B 91(11), 115412 (2015)CrossRef Elahi, M., et al.: Modulation of electronic and mechanical properties of phosphorene through strain. Phys. Rev. B 91(11), 115412 (2015)CrossRef
18.
Zurück zum Zitat Das, S., et al.: Tunable transport gap in phosphorene. Nano Lett. 14(10), 5733 (2014)CrossRef Das, S., et al.: Tunable transport gap in phosphorene. Nano Lett. 14(10), 5733 (2014)CrossRef
19.
Zurück zum Zitat Kim, J., et al.: Observation of tunable band gap and anisotropic dirac semimetal state in black phosphorus. Science 349(6249), 723 (2015)CrossRef Kim, J., et al.: Observation of tunable band gap and anisotropic dirac semimetal state in black phosphorus. Science 349(6249), 723 (2015)CrossRef
20.
Zurück zum Zitat Dutreix, C., Stepanov, E., Katsnelson, M.: Laser-induced topological transitions in phosphorene with inversion symmetry. Phys. Rev. B 93(24), 241404 (2016)CrossRef Dutreix, C., Stepanov, E., Katsnelson, M.: Laser-induced topological transitions in phosphorene with inversion symmetry. Phys. Rev. B 93(24), 241404 (2016)CrossRef
21.
Zurück zum Zitat Liu, Q., et al.: Switching a normal insulator into a topological insulator via electric field with application to phosphorene. Nano Lett. 15(2), 1222 (2015)CrossRef Liu, Q., et al.: Switching a normal insulator into a topological insulator via electric field with application to phosphorene. Nano Lett. 15(2), 1222 (2015)CrossRef
22.
Zurück zum Zitat Low, T., Jiang, Y., Guinea, F.: Topological currents in black phosphorus with broken inversion symmetry. Phys. Rev. B 92(23), 235447 (2015)CrossRef Low, T., Jiang, Y., Guinea, F.: Topological currents in black phosphorus with broken inversion symmetry. Phys. Rev. B 92(23), 235447 (2015)CrossRef
23.
Zurück zum Zitat Carvalho, A., Rodin, A., Neto, A.C.: Phosphorene nanoribbons. Europhys. Lett. (EPL) 108(4), 47005 (2014)CrossRef Carvalho, A., Rodin, A., Neto, A.C.: Phosphorene nanoribbons. Europhys. Lett. (EPL) 108(4), 47005 (2014)CrossRef
24.
Zurück zum Zitat Guo, H., et al.: Phosphorene nanoribbons, phosphorus nanotubes, and van der waals multilayers. J. Phys. Chem. C 118(25), 14051 (2014)CrossRef Guo, H., et al.: Phosphorene nanoribbons, phosphorus nanotubes, and van der waals multilayers. J. Phys. Chem. C 118(25), 14051 (2014)CrossRef
25.
Zurück zum Zitat Ali, M., Keshtan, M., Esmaeilzadeh, M.: Spin filtering in a magnetized zigzag phosphorene nanoribbon. J. Phys. D Appl. Phys. 48(48), 485301 (2015)CrossRef Ali, M., Keshtan, M., Esmaeilzadeh, M.: Spin filtering in a magnetized zigzag phosphorene nanoribbon. J. Phys. D Appl. Phys. 48(48), 485301 (2015)CrossRef
26.
Zurück zum Zitat Peng, X., Copple, A., Wei, Q.: Edge effects on the electronic properties of phosphorene nanoribbons. J. Appl. Phys. 116(14), 144301 (2014)CrossRef Peng, X., Copple, A., Wei, Q.: Edge effects on the electronic properties of phosphorene nanoribbons. J. Appl. Phys. 116(14), 144301 (2014)CrossRef
27.
Zurück zum Zitat Rudenko, A., Yuan, S., Katsnelson, M.: Toward a realistic description of multilayer black phosphorus: from GW approximation to large-scale tight-binding simulations. Phys. Rev. B 92(8), 085419 (2015)CrossRef Rudenko, A., Yuan, S., Katsnelson, M.: Toward a realistic description of multilayer black phosphorus: from GW approximation to large-scale tight-binding simulations. Phys. Rev. B 92(8), 085419 (2015)CrossRef
28.
Zurück zum Zitat Rudenko, A.N., Katsnelson, M.I.: Quasiparticle band structure and tight-binding model for single-and bilayer black phosphorus. Phys. Rev. B 89(20), 201408 (2014)CrossRef Rudenko, A.N., Katsnelson, M.I.: Quasiparticle band structure and tight-binding model for single-and bilayer black phosphorus. Phys. Rev. B 89(20), 201408 (2014)CrossRef
29.
Zurück zum Zitat Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, vol. 1. Wiley, New York (1972) Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, vol. 1. Wiley, New York (1972)
30.
Zurück zum Zitat Zhou, X., et al.: Landau levels and magneto-transport property of monolayer phosphorene. Sci. Rep. 5, 12295 (2015)CrossRef Zhou, X., et al.: Landau levels and magneto-transport property of monolayer phosphorene. Sci. Rep. 5, 12295 (2015)CrossRef
31.
Zurück zum Zitat Jr Pereira, J., Katsnelson, M.: Landau levels of single-layer and bilayer phosphorene. Phys. Rev. B 92(7), 075437 (2015)CrossRef Jr Pereira, J., Katsnelson, M.: Landau levels of single-layer and bilayer phosphorene. Phys. Rev. B 92(7), 075437 (2015)CrossRef
32.
Zurück zum Zitat Ghazaryan, A., Chakraborty, T.: Aspects of anisotropic fractional quantum hall effect in phosphorene. Phys. Rev. B 92(16), 165409 (2015)CrossRef Ghazaryan, A., Chakraborty, T.: Aspects of anisotropic fractional quantum hall effect in phosphorene. Phys. Rev. B 92(16), 165409 (2015)CrossRef
33.
Zurück zum Zitat Harper, P.G.: Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. Lond. Sect. A 68(10), 874 (1955)CrossRefMATH Harper, P.G.: Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. Lond. Sect. A 68(10), 874 (1955)CrossRefMATH
34.
Zurück zum Zitat Thouless, D., et al.: Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49(6), 405 (1982)CrossRef Thouless, D., et al.: Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49(6), 405 (1982)CrossRef
35.
Zurück zum Zitat Wakabayashi, K., et al.: Electronic and magnetic properties of nanographite ribbons. Phys. Rev. B 59(12), 8271 (1999)CrossRef Wakabayashi, K., et al.: Electronic and magnetic properties of nanographite ribbons. Phys. Rev. B 59(12), 8271 (1999)CrossRef
36.
Zurück zum Zitat Wiegmann, P., Zabrodin, A.: Bethe-ansatz for the Bloch electron in magnetic field. Phys. Rev. Lett. 72(12), 1890 (1994)CrossRefMATH Wiegmann, P., Zabrodin, A.: Bethe-ansatz for the Bloch electron in magnetic field. Phys. Rev. Lett. 72(12), 1890 (1994)CrossRefMATH
37.
Zurück zum Zitat Jiang, Z., et al.: Infrared spectroscopy of landau levels of graphene. Phys. Rev. Lett. 98, 197403 (2007)CrossRef Jiang, Z., et al.: Infrared spectroscopy of landau levels of graphene. Phys. Rev. Lett. 98, 197403 (2007)CrossRef
38.
Zurück zum Zitat Yuan, S., et al.: Quantum hall effect and semiconductor-to-semimetal transition in biased black phosphorus. Phys. Rev. B 93(24), 245433 (2016)CrossRef Yuan, S., et al.: Quantum hall effect and semiconductor-to-semimetal transition in biased black phosphorus. Phys. Rev. B 93(24), 245433 (2016)CrossRef
39.
Zurück zum Zitat Hasegawa, Y., et al.: Zero modes of tight-binding electrons on the honeycomb lattice. Phys. Rev. B 74(3), 033413 (2006)CrossRef Hasegawa, Y., et al.: Zero modes of tight-binding electrons on the honeycomb lattice. Phys. Rev. B 74(3), 033413 (2006)CrossRef
40.
Zurück zum Zitat Dietl, P., Piéchon, F., Montambaux, G.: New magnetic field dependence of landau levels in a graphenelike structure. Phys. Rev. Lett. 100(23), 236405 (2008)CrossRef Dietl, P., Piéchon, F., Montambaux, G.: New magnetic field dependence of landau levels in a graphenelike structure. Phys. Rev. Lett. 100(23), 236405 (2008)CrossRef
41.
Zurück zum Zitat Montambaux, G., et al.: Merging of dirac points in a two-dimensional crystal. Phys. Rev. B 80(15), 153412 (2009)CrossRef Montambaux, G., et al.: Merging of dirac points in a two-dimensional crystal. Phys. Rev. B 80(15), 153412 (2009)CrossRef
42.
Zurück zum Zitat Montambaux, G., et al.: A universal hamiltonian for motion and merging of dirac points in a two-dimensional crystal. Eur. Phys. J. B 72(4), 509 (2009)CrossRefMATH Montambaux, G., et al.: A universal hamiltonian for motion and merging of dirac points in a two-dimensional crystal. Eur. Phys. J. B 72(4), 509 (2009)CrossRefMATH
43.
Zurück zum Zitat Park, C.-H., Marzari, N.: Berry phase and pseudospin winding number in bilayer graphene. Phys. Rev. B 84(20), 205440 (2011)CrossRef Park, C.-H., Marzari, N.: Berry phase and pseudospin winding number in bilayer graphene. Phys. Rev. B 84(20), 205440 (2011)CrossRef
44.
Zurück zum Zitat Resta, R.: Manifestations of Berry’s phase in molecules and condensed matter. J. Phys. Condens. Matter 12(9), R107 (2000)CrossRef Resta, R.: Manifestations of Berry’s phase in molecules and condensed matter. J. Phys. Condens. Matter 12(9), R107 (2000)CrossRef
45.
Zurück zum Zitat Zhang, Y., et al.: Experimental observation of the quantum hall effect and berry’s phase in graphene. Nature 438(7065), 201 (2005)CrossRef Zhang, Y., et al.: Experimental observation of the quantum hall effect and berry’s phase in graphene. Nature 438(7065), 201 (2005)CrossRef
46.
Zurück zum Zitat Ramasubramaniam, A., Muniz, A.R.: Ab initio studies of thermodynamic and electronic properties of phosphorene nanoribbons. Phys. Rev. B 90, 085424 (2014)CrossRef Ramasubramaniam, A., Muniz, A.R.: Ab initio studies of thermodynamic and electronic properties of phosphorene nanoribbons. Phys. Rev. B 90, 085424 (2014)CrossRef
47.
Zurück zum Zitat Grujić, M.M., et al.: Tunable skewed edges in puckered structures. Phys. Rev. B 93(24), 245413 (2016)CrossRef Grujić, M.M., et al.: Tunable skewed edges in puckered structures. Phys. Rev. B 93(24), 245413 (2016)CrossRef
48.
Zurück zum Zitat Sisakht, E.T., Zare, M.H., Fazileh, F.: Scaling laws of band gaps of phosphorene nanoribbons: a tight-binding calculation. Phys. Rev. B 91(8), 085409 (2015)CrossRef Sisakht, E.T., Zare, M.H., Fazileh, F.: Scaling laws of band gaps of phosphorene nanoribbons: a tight-binding calculation. Phys. Rev. B 91(8), 085409 (2015)CrossRef
49.
Zurück zum Zitat Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge university press, Cambridge (1997) Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge university press, Cambridge (1997)
50.
Zurück zum Zitat Sancho, M.P.L., et al.: Highly convergent schemes for the calculation of bulk and surface green functions. J. Phys. F Met. Phys. 15(4), 851 (1985)CrossRef Sancho, M.P.L., et al.: Highly convergent schemes for the calculation of bulk and surface green functions. J. Phys. F Met. Phys. 15(4), 851 (1985)CrossRef
51.
Zurück zum Zitat Craciun, M., et al.: Trilayer graphene is a semimetal with a gate-tunable band overlap. Nature Nanotechnol. 4(6), 383 (2009)CrossRef Craciun, M., et al.: Trilayer graphene is a semimetal with a gate-tunable band overlap. Nature Nanotechnol. 4(6), 383 (2009)CrossRef
52.
Zurück zum Zitat Williams, J., et al.: Gate-controlled guiding of electrons in graphene. Nature Nanotechnol. 6(4), 222 (2011)CrossRef Williams, J., et al.: Gate-controlled guiding of electrons in graphene. Nature Nanotechnol. 6(4), 222 (2011)CrossRef
53.
Zurück zum Zitat Li, L., et al.: Black phosphorus field-effect transistors. Nature Nanotechnol. 9, 372 (2014)CrossRef Li, L., et al.: Black phosphorus field-effect transistors. Nature Nanotechnol. 9, 372 (2014)CrossRef
54.
Zurück zum Zitat Ezawa, M.: Topological origin of quasi-flat edge band in phosphorene. New J. Phys. 16(11), 115004 (2014)CrossRef Ezawa, M.: Topological origin of quasi-flat edge band in phosphorene. New J. Phys. 16(11), 115004 (2014)CrossRef
55.
Zurück zum Zitat Choi, W.Y., et al.: Tunneling field-effect transistors (tfets) with subthreshold swing (ss) less than 60 mv/dec. IEEE Electron Device Lett. 28(8), 743 (2007). ISSN 0741-3106CrossRef Choi, W.Y., et al.: Tunneling field-effect transistors (tfets) with subthreshold swing (ss) less than 60 mv/dec. IEEE Electron Device Lett. 28(8), 743 (2007). ISSN 0741-3106CrossRef
56.
Zurück zum Zitat Lifshitz, I., Kosevich, A.: Theory of magnetic susceptibility in metals at low temperatures. Sov. Phys. JETP 2, 636 (1956) Lifshitz, I., Kosevich, A.: Theory of magnetic susceptibility in metals at low temperatures. Sov. Phys. JETP 2, 636 (1956)
Metadaten
Titel
Tunable electronic properties of multilayer phosphorene and its nanoribbons
verfasst von
S. Soleimanikahnoj
I. Knezevic
Publikationsdatum
17.07.2017
Verlag
Springer US
Erschienen in
Journal of Computational Electronics / Ausgabe 3/2017
Print ISSN: 1569-8025
Elektronische ISSN: 1572-8137
DOI
https://doi.org/10.1007/s10825-017-1036-1

Weitere Artikel der Ausgabe 3/2017

Journal of Computational Electronics 3/2017 Zur Ausgabe

Neuer Inhalt