Engineering of properties of low-dimensional materials via inhomogeneous strain

Wang Ya-Xun; Guo Di; Li Jian-Gao; Zhang Dong-Bo

doi:10.7498/aps.71.20220085

Abstract

Low-dimensional material represents a special structure of matter. The exploring of its novel properties is an important frontier subject in the fundamental research of condensed matter physics and material science. Owing to its small length scale in one or two dimensions, low-dimensional materials are usually flexible in structure. This feature together with the prompt electronic response to structural deformations enable us to modulate the material properties via a strain way. The main purpose of this paper is to introduce the recent research progress of obtaining novel physical properties by inhomogeneously straining two-dimensional materials, with focusing on two effects, i.e., pseudomagnetic field effect and the flexoelectric effect. Of course, the influence of inhomogeneous strains on electrons is not limited to these two effects. Fundamentally, an inhomogeneous deformation breaks the symmetry of crystalline structure. This may serve as a start point to delineate the structural-properties relation. First, the symmetry breaking can eliminate the degeneracy of energy levels. Second, the symmetry breaking will also cause the heterogeneity of electronic and phonon properties in different parts of the material.In the paper, we also introduce a special method named the generalized Bloch theorem that is suitable for dealing with the inhomogeneous strain patterns at an atomistic level. From the perspective of atomistic simulation, due to the breaking of translational symmetry, the standard quantum mechanical calculations encounter fundamental difficulties in dealing with an inhomogeneous strain, e.g., bending and torsion. The generalized Bloch method overcomes such an obstacle by considering rotational and/or screw symmetries given by bending and/or torsion in solving the eigenvalue problem. As such, quantum mechanical calculations can be still conducted with a relatively small number of atoms.

Keywords:

Authors and contacts

College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China

Corresponding author: Zhang Dong-Bo, dbzhang@bnu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303400), the National Natural Science Foundation of China (Grant Nos. 11674022, 11874088), and the Fundamental Research Funds for the Central Universities of China (Grant No. 12000-310432101).

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Cited By

图 1 最大应变为50%的应变几何示意图^[46]

Figure 1. Sketch of an example strain geometry with a maximum strain of 50%^[46].

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图 2 在(a)实际磁场B = 9 T, (b)赝磁场B_s = 9 T情况下, 典型能量色散随动量沿输运方向的变化^[46]

Figure 2. Plot of typical energy dispersion as a function of momentum along the transport direction for the case of (a) real magnetic field B = 9 T, (b) pseudomagnetic field B_s = 9 T^[46].

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图 3 STM干涉仪: r表示STM尖端在表面的位置, r₁和r₂表示两个杂质^[62]

Figure 3. STM interferometer: r represents the position of the STM tip on the surface and r₁ and r₂ represent two impurities^[62].

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图 4 在减去B = 0的信号后, 在Ag(111)表面上两个杂质相隔20 nm的情况下模拟得到的STM图像^[62]

Figure 4. Expected STM patterns for two impurities 20 nm apart on the Ag(111) surface after subtraction of the B = 0 signal^[62].

DownLoad: Full-Size Img PowerPoint

图 5 研究材料的结构　(a)石墨烯同素异形体; (b)氮化物XN, X = B, Al, Ga; (c) IV族元素X, X = Si, Ge, Sn的石墨烯类似物; (d)过渡金属二硫族化合物XS₂, X = Cr, Mo, W. (a)—(c)中, h为屈曲高度, (d)中, h₁和h₂为层内距离^[98]

Figure 5. Structures of the studied materials: (a) Graphene allotropes; (b) nitrides XN, X = B, Al, Ga; (c) graphene analogues of group-IV elements X, X = Si, Ge, Sn; (d) transition metal dichalcogenides XS₂, X = Cr, Mo, W. For (a)–(c), h refers to the buckling height, while in (d), h₁ and h₂ refer to intralayer distances^[98].

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图 6 MoS2片的(a)未形变与(b)形变下的原子构型^[98]

Figure 6. Atomic configurations of MoS2 sheet under (a) undeformed and (b) deformed^[98].

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图 7 弯曲悬臂梁中的挠曲电极化^[100]

Figure 7. Flexoelectric polarization induced in a cantilever beam under bending^[100].

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图 8 (a)扭曲形变下的G/hBN横向异质结与(b) 其未应变情况^[118]

Figure 8. The G/hBN lateral heterojunction (a) under twisting deformation and (b) its unstrained state^[118].

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图 9 (a)弯曲形变下的石墨烯与(b)其未应变情况^[118]

Figure 9. Graphene (a) under bending deformation and (b) its unstrained state^[118].

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图 10 170 nm宽zigzag型石墨烯条带在未应变(a)与0.61(°)/nm扭曲率(b)下的能带结构(上图)和态密度(下图)^[126]

Figure 10. Band structures (upper) and density of states (lower) of a 170 nm wide zigzag graphene nanoribbon at (a) no strain and (b) twist rate = 0.61(°)/nm^[126].

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图 11 176 nm宽armchair型石墨烯条带在未应变(a)与0.66(°)/nm扭曲率(b)下的能带结构(上图)和态密度(下图)^[126]

Figure 11. Band structures (upper) and density of states (lower) of a 176 nm wide armchair graphene nanoribbon at (a) no strain and (b) twist rate = 0.66(°)/nm^[126].

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图 12 (a)石墨烯/六方氮化硼横向异质结及其(b)面内弯曲下的结构^[118]

Figure 12. (a) Grapheme/hexagonal boron nitride lateral heterojunction and (b) its structure under in-plane bending^[118].

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图 13 石墨烯/六方氮化硼横向异质结在(a)弯曲0°、(b)弯曲0.3°、(c)弯曲0.6°情况下的电子能带结构^[118]

Figure 13. Electronic band structures of the grapheme/hexagonal boron nitride lateral heterojunction with the bending angle of (a) 0°, (b) 0.3° and (c) 0.6°^[118].

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表 1 IV族原子单层膜的横向挠曲电系数μ_T[e] ^[95]

Table 1. Transversal flexoelectric coefficient μ_T[e] for group IV atomic monolayers^[95].

Zigzag Armchair
LDA PBE LDA PBE

Graphene 0.22 0.22 0.22 0.22
Silicene 0.19 0.19 0.19 0.19
Germanene 0.28 0.28 0.28 0.27
Stanene 0.27 0.26 0.27 0.26

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