Quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene

TL;DR

This paper investigates phase transitions in ABC-trilayer graphene's Landau levels, revealing a transition from quantum Hall liquid to charge density wave states driven by orbital splitting, with observable re-entrant quantum Hall effects.

Contribution

It demonstrates the existence of quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene and characterizes their dependence on Landau level orbital splitting.

Findings

Phase transition from quantum Hall liquid to charge density wave at specific filling factors.

Re-entrant integer quantum Hall effect observed near the transition points.

Transition driven by Landau level orbital splitting.

Abstract

ABC-stacked trilayer graphene's chiral band structure results in three ($n=0,1,2$) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction driven states of the 12-fold degenerate (including spin and valley) N=0 Landau level. In particular, at many filling factors $\nu_{T} =\pm5,\pm4,\pm2,\pm1$ a quantum phase transition from a quantum Hall liquid state to a triangular charge density wave occurs as a function of the single-particle induced LL orbital splitting $\Delta_{LL}$. This phase transition should be characterized by a re-entrant integer quantum Hall effect with the Hall conductivity corresponding to the {\it adjacent} interaction driven integer quantum Hall plateau.