Dynamic equation for quantum Hall bilayers with spontaneous interlayer coherence: The low-density limit

TL;DR

This paper derives a microscopic dynamic equation for exciton condensates in quantum Hall bilayers at low density, revealing collective excitations, vortex properties, and effects of layer curvature on exciton behavior.

Contribution

It provides a novel microscopic derivation of the condensate wave function dynamics in low-density quantum Hall bilayers under magnetic and electric fields.

Findings

Dispersion law for collective excitations derived

Electric charge of vortices calculated

Critical interlayer spacing estimated

Abstract

The bilayer systems exhibit the Bose-Einstein condensation of excitons that emerge due to Coulomb pairing of electrons belonging to one layer with the holes belonging to the other layer. Here we present the microscopic derivation of the dynamic equation for the condensate wave function at a low density of electron-hole ($e-h$) pairs in a strong magnetic field perpendicular to the layers and an electric field directed along the layers. From this equation we obtain the dispersion law for collective excitations of the condensate and calculate the electric charge of the vortex in the exciton condensate. The critical interlayer spacing, the excess of which leads to a collapse of the superfluid state, is estimated. In bilayer systems with curved conducting layers, the effective mass of the $e-h$ pair becomes the function of the $e-h$ pair coordinates, the regions arise, where the energy of the $e-h$ pair is lowered (exciton traps), and lastly $e-h$ pairs can gain the polarization in the basal plane. This polarization leads to the appearance of quantized vortices even at zero temperature.