Tunneling, dissipation, and superfluid transition in quantum Hall bilayers

TL;DR

This paper investigates how dissipation and tunneling influence phase transitions in bilayer quantum Hall systems at total filling factor one, revealing a critical dissipation level that determines whether the system becomes a quantum Hall state or exhibits superfluidity.

Contribution

It introduces an effective quantum dissipative XY model to describe the system's dynamics and identifies a critical dissipation threshold affecting phase behavior.

Findings

Existence of a critical dissipation $\sigma_c$ that determines the phase outcome.

For $\sigma > \sigma_c$, tunneling induces a quantum Hall state.

For $\sigma < \sigma_c$, the system undergoes a superfluid transition.

Abstract

We study bilayer quantum Hall systems at total Landau level filling factor $\nu=1$ in the presence of interlayer tunneling and coupling to a dissipative normal fluid. Describing the dynamics of the interlayer phase by an effective quantum dissipative XY model, we show that there exists a critical dissipation $\sigma_c$ set by the conductance of the normal fluid. For $\sigma > \sigma_c$, interlayer tunnel splitting drives the system to a $\nu=1$ quantum Hall state. For $\sigma <\sigma_c$, interlayer tunneling is irrelevant at low temperatures, the system exhibits a superfluid transition to a collective quantum Hall state supported by spontaneous interlayer phase coherence. The resulting phase structure and the behavior of the in-plane and tunneling currents are studied in connection to experiments.