Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides

Abstract

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.

Published version

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Cited by in corpus (9)

• Moiré Band Engineering in Twisted Trilayer WSe2
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Parafermions in Moiré Minibands
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Magnetic Hofstadter cascade in a twisted semiconductor homobilayer
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates
• Robustness of real-space topology in moiré systems