Broken Symmetry Ground States in \nu=2 Bilayer Quantum Hall Systems

TL;DR

This paper investigates the complex phase diagram of a bilayer quantum Hall system at filling factor 2, revealing broken symmetry states and phase transitions influenced by bias, Zeeman, and tunneling parameters.

Contribution

It introduces a comprehensive variational wavefunction to describe the ground state across all relevant parameters in the bilayer quantum Hall system.

Findings

Broken symmetry states exist near the phase boundary.

Analytic phase diagram intersections are derived.

Differential capacitance is singular at phase boundaries.

Abstract

We report on a study of a bilayer two-dimensional electron gas at Landau level filling factor $\nu=2$. The system exhibits both magnetic and spontaneous interlayer phase coherence broken symmetries. We propose a 3-parameter Slater determinant variational wavefunction which describes the ground state over the full range of bias potential ($\Delta_V$) Zeeman coupling ($\Delta_z$) and interlayer tunneling amplitude ($\Delta_t$) strengths. Broken symmetry states occur inside a volume in this three-dimensional phase diagram near the $\Delta_z^2=\Delta_V^2+\Delta_t^2$ surface. We have obtained analytic results for the intersections of the phase diagram with the $\Delta_t=0$, $\Delta_z=0$, and $\Delta_V=0$, planes and show that the differential capacitance of the bilayer system is singular at the phase boundary.