Unified approach to cyclotron and plasmon resonances in a periodic 2DEG hosting the Hofstadter butterfly

TL;DR

This paper develops a theoretical framework to analyze cyclotron and plasmon resonances in a modulated 2DEG, revealing signatures of the Hofstadter butterfly in the excitation spectra.

Contribution

It introduces a real-time excitation approach that captures all collective modes in a modulated 2DEG under magnetic field, extending beyond linear response.

Findings

Identification of Hofstadter butterfly signatures in excitation spectra

Analysis of collective modes due to lateral confinement and magnetic field

Extension of response analysis beyond linear regime

Abstract

We present theoretical calculations for the cyclotron resonance and various magnetoplasmon modes of a Coulomb interacting two-dimensional GaAs electron gas (2DEG) modulated as a lateral superlattice of quantum dots subjected to an external perpendicular constant magnetic field. We use a real-time excitation approach based on the Liouville-von Neumann equation for the density operator, that can go beyond linear response delivering information of all longitudinal and transverse collective modes of interest to the same order. We perform an extensive analysis of the coexisting collective modes due to the lateral confinement and the magnetic field for a different number of electrons in each dot. In the limit of vanishing dot modulation of the 2DEG we find signs of the structure of the Hofstadter butterfly in the excitation spectra.