Robust translational invariance in topological bands against lattice potentials and disorders

TL;DR

This paper demonstrates that magnetic translational invariance in Landau levels can persist despite lattice potentials and disorder, revealing robustness in quantum Hall systems and implications for anyonic excitations.

Contribution

It reveals that continuous magnetic translational symmetry can survive in Landau levels with superlattice potentials, even in the presence of disorder, due to interplay of length scales.

Findings

Magnetic translational invariance persists in Landau levels with superlattice potentials.

In the lowest Landau level, symmetry is robust when superlattice spacing is below the magnetic length.

The dynamics of anyonic excitations are resilient against long-wavelength disorder.

Abstract

We theoretically show that the continuous magnetic translational invariance within the Hilbert (sub-)space of a single Landau level (LL) can persist even in the presence of a superlattice electrostatic potential modulation, while such invariance is broken in the full real-space Hilbert space. This is due to the interplay of the superlattice constant and the fundamental length scale of the quantum Hall fluids. In particular for the lowest LL (LLL), when the spacing of superlattice is below the magnetic length, continuous magnetic translational symmetry is very robust. For the fractional quantum Hall phases, the continuous translational symmetry is preserved when the superlattice spacing is below the corresponding fundamental lengths which we can now quantitatively define, which is different from the length scale from the quantum metric. Moreover, our analysis implies that the dynamics of the anyonic excitations can be robust against the long wavelength part of the disorder, and we discuss the related experimental ramifications.