Bose-Einstein condensation and superfluidity of magnetobiexcitons in quantum wells' and graphene superlattices

TL;DR

This paper investigates Bose-Einstein condensation and superfluidity of magnetobiexcitons in layered quantum wells and graphene superlattices under high magnetic fields, deriving effective Hamiltonians and analyzing phase transition conditions.

Contribution

It introduces a unified effective Hamiltonian for magnetoexcitons in superlattices, and studies the stability and superfluid properties of magnetobiexcitons in quantum wells and graphene.

Findings

Derived an effective Hamiltonian for magnetoexcitons in superlattices.

Established the instability of the ground state of interacting magnetoexcitons.

Calculated the superfluid density and Kosterlitz-Thouless transition temperature.

Abstract

We propose the Bose-Einstein condensation (BEC) and superfluidity of quasi-two-dimensional (2D) spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field. The two different Hamiltonians of a dilute gas of magnetoexcitons with a dipole-dipole repulsion in superlattices consisting of both QWs and graphene layers in the limit of high magnetic field have been reduced to one effective Hamiltonian a dilute gas of two-dimensional excitons without magnetic field. Moreover, for $N$ excitons we have reduced the problem of $2N\times 2$ dimensional space onto the problem of $N\times 2$ dimensional space by integrating over the coordinates of the relative motion of an electron (e) and a hole (h). The instability of the ground state of the system of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is established. The stable system of indirect quasi-two-dimensional magnetobiexcitons, consisting of pair of indirect excitons with opposite dipole moments is considered. The density of superfluid component $n_{s}(T)$ and the temperature of the Kosterlitz-Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both QW and graphene realizations.