Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices

TL;DR

This paper classifies topological phase transitions in graphene superlattices under magnetic fields, highlighting the role of van Hove singularities and Chern bands in quantum critical phenomena beyond traditional quantum Hall transitions.

Contribution

It introduces a framework for classifying multiflavor Dirac fermion critical points related to topological phase transitions in graphene superlattices.

Findings

Numerical evidence for transitions involving Chern bands and van Hove singularities.

Identification of nontrivial interplay between band topology and singularities near charge neutrality.

Extension of critical phenomena understanding beyond conventional quantum Hall plateau transitions.

Abstract

We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.