Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions

TL;DR

This paper investigates phase transitions in double-layer quantum Hall systems with spontaneous inter-layer coherence, focusing on vortex charge, excitations, and the critical temperature for Kosterlitz-Thouless transitions.

Contribution

It introduces a pseudospin model for the system, derives an effective action, and estimates critical temperatures based on first-principles and numerical studies.

Findings

Vortices carry fractional charge e/2.

Vortex-antivortex pairs can be neutral or charged.

Critical temperature depends on layer separation.

Abstract

At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. In this paper we explore the rich variety of quantum and finite-temperature phase transitions associated with this broken symmetry. We describe the system using a pseudospin language in which the layer degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With this mapping the spontaneous symmetry breaking is equivalent to that of a spin 1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge. In particular, vortices carry e/2 electrical charge and vortex-antivortex pairs can be neutral or carry charge e. We derive an effective low-energy action and use it to discuss the charged and collective neutral excitations of the system. We have obtained the parameters of the Landau-Ginzburg functional from first-principles estimates and from finite-size exact diagonalization studies. We use these results to estimate the dependence of the critical temperature for the Kosterlitz-Thouless phase transition on layer separation.