Spontaneous symmetry breaking and coherence in two-dimensional electron-hole and exciton systems

TL;DR

This paper reviews how spontaneous symmetry breaking in 2D electron-hole and exciton systems under strong magnetic fields leads to new ground states, collective excitations, and quantum coherence phenomena, with implications for quantum Hall effects and Bose-Einstein condensation.

Contribution

It provides a comprehensive review of symmetry breaking, collective excitations, and coherence phenomena in 2D electron-hole and exciton systems, including experimental insights and theoretical models.

Findings

Identification of Nambu-Goldstone modes due to symmetry breaking

Observation of Higgs-like gapped excitations in the spectrum

Conditions for spontaneous coherence in double quantum well systems

Abstract

The spontaneous breaking of the continuous symmetries of the two-dimensional(2D) electron-hole systems in a strong perpendicular magnetic field leads to the formation of new ground states and determines the energy spectra of the collective elementary excitations appearing over these ground states. In this review the main attention is given to the electron-hole systems forming coplanar magnetoexcitons in the Bose-Einstein condensation(BEC) ground state with the wave vector k=0, taking into account the excited Landau levels, when the exciton-type elementary excitations coexist with the plasmon-type oscillations. At the same time properties of the two-dimensional electron gas(2DEG) spatially separated as in the case of double quantum wells(DQWs) from the 2D hole gas under conditions of the fractional quantum Hall effect(FQHE) are of great interest because they can influence the quantum states of the coplanar magnetoexcitons when the distance between the DQW layers diminishes. We also consider in this review the bilayer electron systems under conditions of the FQHE with the one half filling factor for each layer and with the total filling factor for two layers equal to unity because the coherence between the electron states in two layers is equivalent to the formation of the quantum Hall excitons(QHExs) in a coherent macroscopic state. The breaking of the global gauge symmetry as well as of the continuous rotational symmetries leads to the formation of the gapless Nambu-Goldstone(NG) modes while the breaking of the local gauge symmetry gives rise to the Higgs phenomenon characterized by the gapped branches of the energy spectrum. The conditions in which the spontaneous coherence could appear in a system of indirect excitons in a double quantum well structures are discussed. The experimental attempts to achieve these conditions, the main results and the accumulated knowledge are reviewed.