Magic-angle Twisted Bilayer Systems with Quadratic-Band-Touching: Exactly Flat Bands with High-Chern Number

Abstract

Studies of twisted moiré systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature stable quadratic-band-touching points and find exotic physics different from previously studied twisted moiré systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number ($C=\pm 2$). We further consider the effect of Coulomb interactions in such magic-angle twisted systems and find that the ground state supports the quantum anomalous Hall effect with quantized Hall conductivity $2\frac{e^2}{hc}$ at certain filling. Furthermore, the possible physical realization of such twisted bilayer systems will be briefly discussed.

4.6 pages + references + supplemental, 4 figures

References in corpus (11)

• The electronic properties of graphene
• Fractional quantum Hall states at zero magnetic field
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Orbital superfluidity in the $P$-band of a bipartite optical square lattice
• Topological flat band models with arbitrary Chern numbers
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
• Quantum anomalous Hall effect from inverted charge transfer gap
• TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe${}_2$
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model

Cited by in corpus (2)

• Topological exact flat bands in two dimensional materials under periodic strain
• Symmetries as the guiding principle for flattening bands of Dirac fermions