Quantum Hall effect in ac driven graphene: from half-integer to integer case

TL;DR

This paper investigates how an ac electric field modifies the quantum Hall effect in graphene, revealing transitions from half-integer to integer plateaus and the emergence of a zero Hall plateau at high field strengths.

Contribution

It introduces a theoretical framework showing how ac fields induce new Hall plateaus and restore integer quantum Hall effect in graphene, supported by tight-binding and low-energy Hamiltonian analyses.

Findings

New integer Hall plateaus appear with increasing ac field.

A zero Hall plateau emerges at high ac field strength.

Disorder effects do not qualitatively alter the driven QHE features.

Abstract

We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $\sigma_{xy} = \pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at $\sigma_{xy} = \pm n(4e^2/h)$ starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with $\sigma_{xy} = 0$ can be realized at the band center, hence restoring fully a conventional integer QHE with particle-hole symmetry. Within a low-energy Hamiltonian for Dirac cones merging, we show a very good agreement with the tight-binding calculations for the Hall plateau transitions. We also obtain the band structure for driven graphene ribbons to provide a further understanding on the appearance of the new Hall plateaus, showing a trivial insulator behavior for the $\sigma_{xy} = 0$ state. In the presence of disorder, we numerically study the disorder-induced destruction of the quantum Hall states in a finite driven sample and find that qualitative features known in the undriven disordered case are maintained.