Designing Flat Bands and Pseudo-Landau Levels in GaAs with Patterned Gates

TL;DR

This paper presents an analytical and numerical study of how patterned gates induce flat bands and pseudo-Landau levels in 2DEGs, revealing complex quantum geometries and interaction effects.

Contribution

It introduces an exact analytical solution method for the Schrödinger equation with superlattice potentials and explores the resulting electronic phases in patterned 2DEGs.

Findings

Emergence of narrow bands and pseudo-Landau levels due to superlattice potential

Nontrivial Berry curvature when inversion symmetry is broken

Interaction effects influence quantum geometry and phase competition

Abstract

We investigate the electronic properties of two-dimensional electron gases (2DEGs) subjected to a periodic patterned gate. By incorporating the superlattice (SL) potential induced by patterning into the Schrodinger equation, we develop a methodology for obtaining exact analytical solutions. These solutions enable us to construct a comprehensive phase diagram illustrating the emergence of narrow bands and pseudo-Landau levels driven by the SL potential. To complement the analytical approach, we employ a standard plane-wave formalism to track the evolution of the band structure as the SL strength increases. By breaking the inversion symmetry of the SL potential, we found a nontrivial Berry curvature. Furthermore, we introduce a self-consistent Hartree screening to account for the interplay between the SL potential and electronic interactions. Our findings not only reveal the emergence of a non-trivial quantum geometry and a competition between SL strength and electron-electron interactions, but also highlight the value of exact analytical solutions for understanding and engineering electronic phases in patterned 2DEG systems.