Physical properties of novel electronic states related to  flat band in twisted two-dimensional quantum materials

Wang Zhong-Rui; Jiang Yu-Hang

doi:10.7498/aps.71.20220064

Abstract

Two-dimensional (2D) materials can exhibit novel quantum phenomena and be easily tuned by the external environment, which has made them one of the most attractive topics in condensed matter physics during the recent decades. The moiré superlattice induced by varied stacking geometry can further renormalize the material band structure, resulting in the electronic flat bands. With the help of external fields, one can tune the electron-electron correlated interaction in these flat bands, even control the overall physical properties. In this paper we review the recent researches of novel properties in twisted 2D materials (graphene and transition metal dichalcogenide heterostructure), involving strong correlation effect, unconventional superconductivity, quantum anomalous Hall effect, topological phase, and electronic crystals. We also discuss some open questions and give further prospects in this field.

Keywords:

Authors and contacts

1.
College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
2.
Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Jiang Yu-Hang, yuhangjiang@ucas.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12074377) and the Fundamental Research Funds for the Central Universities, China.

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References

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Cited By

图 1 (a) 单层石墨烯低能区线性能带结构^[21]; (b) 转角石墨烯形成的莫尔超晶格^[21]; (c) STM观测TBG的示意图与均匀的莫尔斑点^[21]; (d) 转角石墨烯电子能带结构^[3]; (e) 原位解理-转移制备法^[27]; (f) 第一布里渊区中的平带体系^[2]

Figure 1. (a) Low-energy band structure of monolayer graphene^[21]; (b) moiré pattern formed by twisted graphene^[21]; (c) schematics of STM measurement of TBG sample, topography of which shows a uniform moiré pattern^[21]; (d) band structure of twisted graphene^[3]; (e) tear-and-stack technique^[27]; (f) flat band structure in the first Brillouin zone^[2].

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图 2 转角石墨烯体系中平带相关的关联绝缘态　(a) T = 0.3 K时, 魔角石墨烯电导率随载流子浓度的变化^[3]; (b) 从0 T(黑色曲线)到480 mT(红色曲线)不同垂直磁场下纵向电阻随载流子浓度的变化^[25]; (c) 由hBN封装的双栅极ABC-TLG侧向示意图^[29]; (d) ABC-TLG电阻随V_t和V_b的变化(颜色从亮到暗代表电阻从100 kΩ到10 Ω, V_t和V_b分别代表顶部栅压与底部栅压)^[29]; (e) 魔角石墨烯中电荷条纹有序相^[7]; (f) T = 0.3 K, θ = 1.08°时, TMBG的电阻率随电位移场D与载流子浓度的变化^[17]; (g) D < 0时, ν = 1, 2, 3处的关联态性质^[17]

Figure 2. Correlated insulating state of flat band in twisted graphene system: (a) measured conductance of magic-angle graphene as a function of carrier density at T = 0.3 K^[3]; (b) longitudinal resistance against carrier density at different perpendicular magnetic fields from 0 T (black trace) to 480 mT (red trace) ^[25]; (c) schematic cross-sectional view of the dual-gated ABC-TLG device encapsulated by hBN^[29]; (d) ABC-TLG resistance as a function of V_t and V_b (The colour scale is from 10 Ω (dark) to 100 kΩ (bright) in a log scale, V_t and V_b refer to the top and bottom gate voltage)^[29]; (e) stripe charge ordered phase in magic-angle graphene^[7]; (f) resistivity of TMBG plotted against electric displacement field D and carrier density under the condition of T = 0.3 K and θ = 1.08°^[17]; (g) properties of the correlated states at ν= 1, 2, 3 for D < 0^[17].

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图 3 魔角石墨烯非常规超导态　(a), (b) 电阻与温度和载流子浓度的关系, 显示出魔角石墨烯在(a) 半填充^[2]和(b) 整数填充^[25]绝缘态附近的超导圆顶; (c) 三个屏蔽调控的魔角石墨烯电阻与温度和填充因子关系, 在整数填充附近呈现关联绝缘态消失的超导特征^[33]; 利用Dynes方程对(d) s波超导体和(e)节点超导体的准粒子态密度模型进行实验谱学上的模拟^[40]; (f) 过剩电流、超导能隙与温度的关系^[40]; (g) 相对霍尔密度 $ \left|{n}_{\mathrm{H}}-\nu \right| $随载流子浓度和电位移场的变化^[11]

Figure 3. Unconventional superconductivity of magic-angle graphene: (a), (b) Resistance as a function of temperature and carrier density, where shows superconductivity domes around (a) half-filling^[2] and (b) integer-filling^[25] correlated states of magic-angle graphene respectively; (c) colour plot of resistivity versus moiré band filling factor ν and temperature for three screening-controlled magic-angle TBG devices, which shows correlated insulators are completely absent, while superconductivity persists^[33]; Dynes-function fits to the experimental tunneling spectrum using the model quasiparticle density of states for (d) s-wave superconductor and (e) nodal superconductor^[40]; (f) excess current and the superconducting energy gap versus temperature^[40]; (g) subtracted Hall density $ \left|{n}_{\mathrm{H}}-\nu \right| $ as a function of carrier density and electric displacement field^[11].

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图 4 转角石墨烯的量子反常霍尔效应　(a) 30 mK下, 3/4填充魔角石墨烯霍尔电阻随磁场的变化; (b) θ = 1.20°± 0.01°时, 不同温度下3/4填充魔角石墨烯霍尔电阻随磁场的变化^[44]; (c) 魔角石墨烯铁磁性拓扑绝缘性质示意图^[46]; (d) 强关联Chern绝缘体对磁场的量子化响应^[15]; (e) T = 0.3 K, n/n₀ = 3.5时, 纵向电阻R*与平面内磁场B_∥的关系^[48]; (f) Chern绝缘体示意图, 红线对应于(t, s) = (–2, –3/2)和(–3, –1/2)的对称破缺Chern绝缘体(s是布洛赫带填充指数; t是与带隙相关的总Chern数)^[49]

Figure 4. Anomalous Hall Effect of magic-angle graphene: (a) Hall resistance of twisted graphene tested as a function of magnetic fields at 30 mK near three-quarters filling; (b) Hall resistance of twisted graphene tested as a function of magnetic fields at different temperatures near three-quarters filling at θ = 1.20°±0.01°^[44]; (c) schematic of the ferromagnetic topological insulator property of magic-angle graphene^[46]; (d) quantized magnetic-field response of strongly correlated Chern insulating phases^[15]; (e) in-plane field B_∥ dependence of longitudinal R*, at n/n₀= 3.5, at T = 0.3 K^[48]; (f) schematic of Chern insulator states, with red lines corresponding to SBCIs with (t, s) = (–2, –3/2) and (–3, –1/2)( s is the Bloch band filling index; t is the total Chern number associated with a given gap) ^[49].

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图 5 (a)—(c) 不同转角双层WSe₂的STS分析^[60]; (d)—(f) WSe₂/WS₂异质结莫尔超晶格重构^[52]

Figure 5. (a)–(c) STS of twisted bilayer-WSe₂ with different twisted angles^[60]; (d)–(f) moiré superlattice reconstruction of WSe₂/WS₂ heterostructure^[52].

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图 6 (a) 转角WSe₂异质结示意图与莫尔超晶格平带结构^[64]; (b) 电阻随温度和载流子浓度变化的相图(D = 0.45 V/nm, θ = 5.1°, 顶部栅压V_tg = –12.25 V)^[64]; (c), (d) 转角与电位移场共同调制的关联绝缘态^[64]; (e) WS₂/WSe₂异质结器件结构示意图^[67]; (f) 2.8—140 K时的关联绝缘态以及晶格填充情况的蒙特卡罗模拟^[67]

Figure 6. (a) Schematic of the twisted bilayer-WSe₂ sample and the moiré superlattice flat bands structure ^[64]; (b) resistance color plotted against temperature and carrier density (D = 0.45 V/nm, θ = 5.1°, top gate V_tg = –12.25 V)^[64]; (c), (d) angle and electric displacement field dependence of the correlated insulating states^[64]; (e) schematic of the WS₂/WSe₂ device structure ^[67]; (f) correlated insulating states at a temperature range from 2.8 K to 140 K and spatial filling patterns gained from Monte Carlo simulation^[67]

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图 7 4%晶格错配WSe₂/WS₂ 莫尔超晶格　(a) 光学各向异性测量示意图^[68]; (b) 1/2填充时电子条纹的结构域图^[68]; (c) WSe₂/WS₂ 异质结示意图及广义Wigner晶格^[18]; (d) 双层MoSe₂中Wigner晶体的量子与温度相变^[20]; (e) 不同栅压下Se/W 莫尔位点的dI/dV谱, 显示出 STM针尖在莫尔周期里的局部放电现象(蓝色箭头表示充放电时表面色散特征)^[53]

Figure 7. 4% mismatch WSe₂/WS₂ moiré superlattice: (a) Schematics of optical anisotropy measurement^[68]; (b) electronic stripe domain patterns at half filling^[68]; (c) schematic of correlated states and generalized Wigner crystal states in a WSe₂/WS₂ moiré superlattice^[18]; (d) MoSe₂ bilayer Wigner crystals’ quantum and thermal phase transitions^[20]; (e) gate-dependent dI/dV spectra measured at the Se/W moiré sites, showing local discharging of moiré site induced by the STM tip (The blue arrows indicate surface dispersion characteristics during charge and discharge)^[53].

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