Topological Edge States and Fractional Quantum Hall Effect from Umklapp Scattering

TL;DR

This paper demonstrates how resonant Umklapp scattering in anisotropic lattice strips under magnetic fields induces topological edge states and quantum Hall plateaus, revealing new topological phases and transitions.

Contribution

It introduces a novel mechanism for topological edge states via Umklapp scattering, linking lattice effects to quantum Hall phenomena in a new way.

Findings

Resonant Umklapp scattering creates bulk gaps with chiral edge states.

Quantum Hall plateaus occur at known filling factors n/m.

Topological phase transitions support midgap edge states with flat dispersion.

Abstract

We study anisotropic lattice strips in the presence of a magnetic field in the quantum Hall effect regime. At specific magnetic fields, causing resonant Umklapp scattering, the system is gapped in the bulk and supports chiral edge states in close analogy to topological insulators. These gaps result in plateaus for the Hall conductivity exactly at the known fillings n/m (both positive integers and m odd) for the integer and fractional quantum Hall effect. For double strips we find topological phase transitions with phases that support midgap edge states with flat dispersion. The topological effects predicted here could be tested directly in optical lattices.