Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides,Physical Review B

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Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
Physical Review B ( IF 3.2 ) Pub Date : 2024-09-09 , DOI: 10.1103/physrevb.110.115114
Kryštof Kolář ₁ , Kang Yang ₁ , Felix von Oppen ₁ , Christophe Mora _{2,

3}

Affiliation

We study the topological bands in twisted bilayer transition metal dichalcogenides in an external magnetic field. We first focus on a paradigmatic model of

{WSe}_{2}

, which can be described in an adiabatic approximation as particles moving in a periodic potential and an emergent periodic magnetic field with nonzero average. We understand the magnetic-field-dependent spectra of

{WSe}_{2}

based on the point net zero flux, at which the external field cancels the average emergent field. At this point, the band structure interpolates between the tightly bound and nearly free (weak periodic potential) paradigms as the twist angle increases. For small twist angles, the energy levels in a magnetic field mirror the Hofstadter butterfly of the Haldane model. For larger twist angles, the isolated Chern band at zero flux evolves from nearly free bands at the point of net zero flux. We also apply our framework to a realistic model of twisted bilayer

{MoTe}_{2}

, which has recently been suggested to feature higher Landau-level analogs. We show that at negative unit flux per unit cell, the bands exhibit remarkable similarity to a backfolded parabolic dispersion, even though the adiabatic approximation is inapplicable. This backfolded parabolic dispersion naturally explains the similarity of the Chern bands at zero applied flux to the two lowest Landau levels, offering a simple picture supporting the emergence of non-Abelian states in twisted bilayer

{MoTe}_{2}

. We propose the study of magnetic-field-dependent band structures as a versatile method to investigate the nature of topological bands and identify Landau-level analogs.

中文翻译：

扭曲过渡金属二硫化物中陈能带的霍夫施塔特谱

我们研究了外部磁场中扭曲双层过渡金属二硫属化物的拓扑能带。我们首先关注一个范式模型

{WSe}_{2}

，它可以用绝热近似描述为在周期性势和涌现的具有非零平均值的周期性磁场中运动的粒子。我们了解磁场相关的光谱

{WSe}_{2}

基于点净零通量，在该点处外部场抵消了平均出现场。此时，随着扭转角的增加，能带结构在紧密束缚和近乎自由（弱周期势）范式之间插值。对于小扭转角，磁场中的能级反映霍尔丹模型的霍夫施塔特蝴蝶。对于较大的扭转角，零通量处的孤立陈氏带从净零通量点处的几乎自由带演变而来。我们还将我们的框架应用于扭曲双层的现实模型