The Hofstadter Spectrum and Photoluminescence

TL;DR

This paper investigates the observability of the Hofstadter spectrum in a Wigner crystal via photoluminescence, proposing a new two-layer system geometry to better detect the full spectrum despite lattice distortions.

Contribution

It introduces a novel two-layer system geometry that enables the observation of the complete Hofstadter spectrum despite lattice distortions in a Wigner crystal.

Findings

Only the largest Hofstadter gaps are observable with lattice distortions.

A two-layer system with electrons forming a Wigner crystal and a full Landau level can reveal the full Hofstadter spectrum.

Recombination of electrons and localized holes reflects the entire Hofstadter spectrum.

Abstract

The observability of the Hofstadter spectrum generated by a Wigner crystal using photoluminescence techniques is studied. Itinerant hole geometries are examined, in which a hole may combine directly with electrons in the lattice. It is found that when the effect of lattice distortions of the WC due to interactions with the hole are accounted for, only the largest Hofstadter gaps are observable. To overcome the problems of lattice distortion, a novel geometry is proposed, involving a two layer system with electrons in one layer forming a WC and in the other a full Landau level. It is found that recombination of electrons in the full Landau level with {\it localized} holes reflects the full Hofstadter spectrum of the lattice.