Fractional quantum Hall states at zero magnetic field

TL;DR

This paper proposes a method to flatten topologically non-trivial bands in lattice models, enabling the realization of fractional quantum Hall states at zero magnetic field through engineered band structures and interactions.

Contribution

It introduces a simple prescription for flattening Chern bands using tunable hoppings and demonstrates the emergence of fractional quantum Hall states at zero magnetic field with exact diagonalization.

Findings

Existence of a spectral gap at 1/3 filling

Ground state identified as topological

Hall conductance quantized

Abstract

We present a simple prescription to flatten isolated Bloch bands with non-zero Chern number. We first show that approximate flattening of bands with non-zero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest neighbor hoppings in the Haldane model and, similarly, in the chiral-pi-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.