Tunable ferroelectricity and anisotropic electric transport in monolayer $\ensuremath{\beta}$-GeSe

Tunable ferroelectricity and anisotropic electric transport in monolayer $β$ -GeSe

Shan Guan, Chang Liu, Yunhao Lu, Yugui Yao, and Shengyuan A. Yang

Phys. Rev. B 97, 144104 – Published 10 April 2018

Abstract

Low-dimensional ferroelectricity has attracted tremendous attention due to its huge potential in device applications. Here, based on first-principles calculations, we predict the existence of spontaneous in-plane electrical polarization and ferroelectricity in monolayer $β$ -GeSe, a polymorph of GeSe with a boat conformation newly synthesized in experiment. The magnitude of the polarization is about $0.16 n C / m$ , which is comparable to that of monolayer SnTe studied in recent experiment, and the intrinsic Curie temperature is estimated to be above 200 K. Interestingly, owing to its puckered structure, the physical properties of $β$ -GeSe can be easily controlled by strain. The Curie temperature can be raised above room temperature by applying a 1% tensile strain, and the magnitude of polarization can be largely increased by strains in either the armchair or zigzag direction. Furthermore, we find that for the case with electron doping, applying strain can readily tune the anisotropic electric transport with the preferred conducting direction rotated by $90^{\circ}$ , which is connected to a strain-induced Lifshitz transition. The ratio between the effective masses along the two in-plane directions can undergo a dramatic change of two orders of magnitude even by a 2% strain. Our result reveals monolayer $β$ -GeSe is a promising platform for exploring ferroelectricity in two dimensions and for nanoscale mechanoelectronic device applications.

Received 13 December 2017
Revised 7 March 2018

DOI:https://doi.org/10.1103/PhysRevB.97.144104

Physics Subject Headings (PhySH)

Electronic structure Fermi surface Ferroelectricity

Density functional theory Monte Carlo methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shan Guan^1,2, Chang Liu^1,3, Yunhao Lu⁴, Yugui Yao^1,*, and Shengyuan A. Yang^2,†

¹Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
²Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
³Kunming Institute of Physics, Kunming 650223, China
⁴State Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China

^*ygyao@bit.edu.cn
^†shengyuan_yang@sutd.edu.sg

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Vol. 97, Iss. 14 — 1 April 2018

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Figure 1
(a) Top view of the crystal structure of monolayer $β$ -GeSe. The shaded area marks the unit cell. $a$ and $b$ are the two lattice constants. (b)–(d) Side views of the three states. State A in (c) is for the undistorted structure with centrosymmetry. B and $B^{'}$ are for the two degenerate ferroelectric structures. They can be considered to be distorted from A, during which the centrosymmetry is broken. In (b) and (d), the red arrows indicate the electric polarization direction. $d_{ℓ}$ and $d_{r}$ are the displacements between the two pairs of neighboring atoms in the unit cell. (e) Free-energy contour plot for monolayer $β$ -GeSe versus the displacements ( $d_{ℓ}, d_{r}$ ).
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Figure 2
(a) The calculated phonon spectrum for monolayer $β$ -GeSe with the undistorted centrosymmetric structure [phase A in Fig. 1]. A pronounced soft optical phonon mode $λ$ at $Γ$ can be observed. (b) Schematics showing the top and side views of the phonon eigenvector corresponding to mode $λ$ in (a).
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Figure 3
(a) Double-well potential of monolayer $β$ -GeSe versus polarization. $E_{B}$ and $P_{S}$ mark the potential barrier and the spontaneous polarization, respectively. The red line represents the fitting curve of the Landau model [the first three terms in Eq. (1)]. (b) The dipole-dipole interaction of monolayer $β$ -GeSe using mean-field theory. The red line represents a fitting curve by the harmonic approximation. (c) Temperature dependence of the polarization in $β$ -GeSe obtained with the MC simulations. Here, we show the results for the unstrained case and for the $1 %$ biaxially strained case. The red line is a heuristic fit in the vicinity of the Curie temperatures $T_{C}$ (see the main text). (d) The barrier $E_{B}$ and (e) the polarization $P_{S}$ as functions of the applied (three types of) strain. (f) Schematic of the evolution of the lattice structure under a tensile strain in the zigzag direction.
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Figure 4
(a) Electronic band structure for monolayer $β$ -GeSe without strain. (b) Two-dimensional Brillouin zone for monolayer $β$ -GeSe. $X^{'}$ indicates the location of the CBM for the unstrained case. (c) Plot of the band structure in (a) along a different path, such that the dispersion around the CBM can be clearly seen. Band structures for monolayer $β$ -GeSe (d) with $- 2 %$ strain, (e) with $+ 2 %$ strain, and (f) with $+ 7 %$ strain. Here, the applied strain is the uniaxial strain along the zigzag direction.
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Figure 5
(a) Electron effective mass of monolayer $β$ -GeSe according to the spatial direction (a) for the unstrained case and (b) for the $+ 2 %$ strained case. (c) The band gap and the ratio $m_{a}^{*} / m_{z}^{*}$ (plotted in log scale) plotted as functions of strain. Shaded regions I, II, and III denote the three different cases of the CBM configuration (see the main text). (d) Equienergy contours for the conduction band under $- 2 %, + 2 %$ , and $+ 7 %$ applied strains, corresponding to the three regions in (c). Here, the energy values are referenced to the CBM energy. In these plots, the applied strain is the uniaxial strain along the zigzag direction.
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Figure 6
Schematic of strain-induced rotation of electrical conduction anisotropy in monolayer $β$ -GeSe.
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Physical Review B

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Tunable ferroelectricity and anisotropic electric transport in monolayer $β$ -GeSe

Shan Guan, Chang Liu, Yunhao Lu, Yugui Yao, and Shengyuan A. Yang

Phys. Rev. B 97, 144104 – Published 10 April 2018

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Physical Review B

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Tunable ferroelectricity and anisotropic electric transport in monolayer β-GeSe

Shan Guan, Chang Liu, Yunhao Lu, Yugui Yao, and Shengyuan A. Yang

Phys. Rev. B 97, 144104 – Published 10 April 2018

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Tunable ferroelectricity and anisotropic electric transport in monolayer $β$ -GeSe