Magic continuum in twisted bilayer square lattice with staggered flux

TL;DR

This paper develops a continuum model for twisted bilayer staggered-flux square lattices, revealing a 'magic continuum' with exponentially reduced Dirac velocity and flat bands, akin to phenomena in twisted bilayer graphene.

Contribution

It introduces a general continuum framework for twisted bilayer staggered-flux square lattices, identifying a magic regime with flat bands and zero-energy states, extending understanding of moiré physics.

Findings

Exponential reduction of Dirac velocity in the magic continuum

Emergence of flat bands near half filling

Band structure remains gapless due to symmetry constraints

Abstract

We derive the general continuum model for a bilayer system of staggered-flux square lattices, with arbitrary elastic deformation in each layer. Applying this general continuum model to the case where the two layers are rigidly rotated relative to each other by a small angle, we obtain the band structure of the twisted bilayer staggered-flux square lattice. We show that this band structure exhibits a "magic continuum" in the sense that an exponential reduction of the Dirac velocity and bandwidths occurs in a large parameter regime. We show that the continuum model of the twisted bilayer system effectively describes a massless Dirac fermion in a spatially modulating magnetic field, whose renormalized Dirac velocity can be exactly calculated. We further give an intuitive argument for the emergence of flattened bands near half filling in the magic continuum and provide an estimation of the large number of associated nearly-zero-energy states. We also show that the entire band structure of the twisted bilayer system is free of band gaps due to symmetry constraints.