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

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.

14 pages, 6 figures. Version before proofreading. For published version please see DOI

References in corpus (27)

• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Origin of band gaps in graphene on hexagonal boron nitride
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Spontaneous Strains and Gap in Graphene on Boron Nitride
• Moiré band model and band gaps of graphene on hexagonal boron nitride
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Electronic structure of spontaneously strained graphene on hexagonal Boron Nitride
• The Ginzburg-Landau theory of flat band superconductors with quantum metric
• Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
• Band structure and gaps of triangular graphene superlattices
• Engineering high quality graphene superlattices via ion milled ultra-thin etching masks
• Multilayer graphene with a superlattice potential
• Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions
• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Gate-tunable topological phases in superlattice modulated bilayer graphene
• Signature of Correlated Insulator in Electric Field Controlled Superlattice
• Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
• Observation of flat bands in gated semiconductor artificial graphene
• Superconductivity in Engineered Two-Dimensional Electron Gases
• Chiral excitonics in monolayer semiconductors on patterned dielectric
• Lateral 2D superlattices in GaAs heterostructures with independent control of carrier density and modulation potential
• Formation of artificial Fermi surfaces with a triangular superlattice on a conventional two dimensional electron gas
• Patterned bilayer graphene as a tunable, strongly correlated system
• Designing Band Structures by Patterned Dielectric Superlattices