Vol.07 No.01(2018), Article ID:23871,5 pages
10.12677/CMP.2018.71006

Topological Flat Band and Quantum Hall Effect in the Triangular Lattice

Le Gong, Hao Wei*, Xiangru Tao

School of Physics Science and Technology, Xinjiang University, Urumqi Xinjiang

Received: Feb. 2nd, 2018; accepted: Feb. 18th, 2018; published: Feb. 27th, 2018

ABSTRACT

We use the tight-bonding model to study the topological flat band in a triangular lattice. Under a staggered magnetic field with zero total flux through the unit cell, the topological nearly flat band with a large band gap and nonzero Chern number can be obtained by manipulating the next nearest neighbor hopping and staggered flux. This topological flat band carries a high Chern number C = 2, which can yield an integer quantum Hall effect.

Keywords:Topological Flat Band, Staggered Flux, Quantum Hall Effect

1. 引言

2. 模型和方法

$H=±t\sum _{〈ij〉}\left({e}^{i{\varphi }_{ij}}{c}_{i}^{†}{c}_{j}+H.c.\right)±{t}^{\prime }\sum _{〈〈ij〉〉}\left({c}_{i}^{†}{c}_{j}+H.c.\right)$ (1)

${\sigma }_{xy}\left(E\right)=\frac{i{e}^{2}\hslash }{S}\sum _{{\epsilon }_{m}E}\frac{2\mathrm{Im}〈m|{\upsilon }_{x}|n〉〈n|{\upsilon }_{y}|m〉}{{\left({\epsilon }_{m}-{\epsilon }_{n}\right)}^{2}}$ (2)

Figure 1. The three-band triangular-lattice model, which contains three independent sites (A, B, C)

3. 结果与讨论

4. 结论

Figure 2. (a) and (b) The flatness ratio of the band gap to the bandwidth versus magnetic flux and next nearest neighbor hopping; (c) and (d) The flatness ratio of the band gap to the bandwidth versus next nearest neighbor hopping at a fixed magnetic flux

Figure 3. (a) and (b) Energy dispersion of nanoribbon in triangular lattice; (c) The Hall conductance

Topological Flat Band and Quantum Hall Effect in the Triangular Lattice[J]. 凝聚态物理学进展, 2018, 07(01): 43-47. http://dx.doi.org/10.12677/CMP.2018.71006

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