Global Phase Diagram of nu = 2 Quantum Hall Bilayers in Tilted Magnetic Field

TL;DR

This paper maps the phase diagram of a nu=2 quantum Hall bilayer system under tilted magnetic fields, revealing topologically connected canted phases and a quantum critical point, advancing understanding of phase transitions in such systems.

Contribution

It provides a detailed theoretical analysis of the global phase diagram of nu=2 quantum Hall bilayers with tilted magnetic fields, identifying topological connections and critical points.

Findings

Identification of symmetric, ferromagnetic, and canted phases.

Discovery of a topologically connected transition between two canted phases.

Existence of a quantum critical point at the end of the first order transition line.

Abstract

We consider a bilayer quantum Hall system at total filling fraction nu=2 in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. Using an "unrestricted Hartree Fock," previously discussed by Burkov and MacDonald (Phys Rev B 66 115323 2002), we examine the zero temperature global phase diagrams that would be accessed experimentally by changing the in-plane field and the bias voltage between the layers while keeping the tunneling between the two layers fixed. In accordance with previous work, we find symmetric and ferromagnetic phases as well as a first order transition between two canted phases with spontaneously broken U(1) symmetry. We find that these two canted phases are topologically connected in the phase diagram and, reminiscent of a first order liquid-gas transition, the first order transition line between these two phases ends in a quantum critical point. We develop a physical picture of these two phases and describe in detail the physics of the transition.