Numerical studies of the fractional quantum Hall effect in systems with tunable interactions

TL;DR

This paper reviews numerical studies on the fractional quantum Hall effect in various two-dimensional systems with tunable interactions, highlighting methods to control phase transitions and stabilize fragile states.

Contribution

It introduces recent numerical analyses of how external fields and screening can tune interactions in graphene, bilayer graphene, and topological insulators for quantum Hall studies.

Findings

Tunable interactions enable controlled phase transitions.

External fields and dielectric screening modify effective electron interactions.

Manipulation of interactions can stabilize exotic quantum Hall states.

Abstract

The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional, and even non-Abelian, statistics of quasiparticles. One of the main limitations of the experimental systems based on GaAs has been the lack of tunability of the effective interactions between two-dimensional electrons, which made it difficult to stabilize some of the more fragile states, or induce phase transitions in a controlled manner. Here we review the recent studies that have explored the effects of tunability of the interactions offered by alternative two-dimensional systems, characterized by non-trivial Berry phases and including graphene, bilayer graphene and topological insulators. The tunability in these systems is achieved via external fields that change the mass gap, or by screening via dielectric plate in the vicinity of the device. Our study points to a number of different ways to manipulate the effective interactions, and engineer phase transitions between quantum Hall liquids and compressible states in a controlled manner.