Spontaneous Symmetry Breaking and Exotic Quantum Order in Integer Quantum Hall Systems under a Tilted Magnetic Field

TL;DR

This paper investigates quantum phase transitions and spontaneous symmetry breaking in integer quantum Hall systems under a tilted magnetic field, revealing novel phases including a ferroelectric quantum order.

Contribution

It introduces a new theoretical framework predicting spontaneous parity symmetry breaking and ferroelectric order in quantum Hall systems, expanding understanding of many-body quantum phases.

Findings

Prediction of spontaneous parity symmetry breaking

Identification of ferroelectric quantum order

Quantum phase diagrams for experimental regimes

Abstract

We use the microscopic Hartree-Fock approximation to investigate various quantum phase transitions associated with possible spontaneous symmetry breaking induced by a tilted magnetic field in the integral quantum Hall regime of wide parabolic wells and zero width double well (bilayer) systems. We propose a general class of variational wavefunctions that describe several types of parity, spin, and translational symmetry breaking, including spin and charge density wave phases. Zero temperature quantum phase diagrams for these systems are calculated in the parameter regime of experimental interest. We discuss the symmetry properties of our predicted quantum phase diagrams and give a unified picture of these novel many-body phases. A conceptually new aspect of our theory is the predicted possibility for the spontaneous breaking of parity symmetry, which indicates a ``ferroelectric'' quantum order in integer quantum Hall systems and has not been considered in the literature before.