Bilayer Quantum Hall Ferromagnet in a Periodic Potential

TL;DR

This paper models the effects of a strong periodic potential on a bilayer quantum Hall system at total filling of ν_T=1, revealing ground state transitions and suppression of superfluid-like properties, offering insights into disorder effects.

Contribution

It introduces a model using a periodic potential to study nonperturbative disorder effects in the bilayer quantum Hall system, highlighting topological transitions and mode softening.

Findings

Ground state transitions alter pseudospin topological content

Emergence of a nearly gapless mode near transitions

Suppression of Kosterlitz-Thouless transition temperature

Abstract

The bilayer quantum Hall system at a total filling of $\nu_T=1$ has long resisted explanation in terms of a true counterflow superfluid, though many experimental features can be seen to be "almost" that of a superfluid. It is widely believed that quenched disorder is the root cause of this puzzle. Here we model the nonperturbative effects of disorder by investigating the $\nu=1$ bilayer in a strong periodic potential. Our model assumes that fermions are gapped and real spins are fully polarized, and concentrates on the pseudospin variable (the layer index), with the external potential coupling to the topological (Pontryagin) density of the pseudospin. We find that as the potential strength increases, there are ground state transitions in which the topological content of the pseudospin configuration changes. These transitions are generically weakly first-order, with a new quadratically dispersing mode (in addition to the linearly dispersing Goldstone mode) sometimes becoming nearly gapless near the transition. We show that this leads to strong suppressions of both the Kosterlitz-Thouless transition temperature and the interlayer tunneling strength, which we treat perturbatively. We discuss how these results might extend to the case of true disorder.