Designing Flat Bands and Pseudo-Landau Levels in GaAs with Patterned Gates
arXiv:2412.04547 · doi:10.1103/ghyq-sz16
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.
arXiv comment14 pages, 6 figures. Version before proofreading. For published version please see DOI
References in corpus (50)
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Berry Phase Effects on Electronic Properties
- 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
- Superfluidity in topologically nontrivial flat bands
- Fractional Chern insulators in magic-angle twisted bilayer graphene
- Origin of band gaps in graphene on hexagonal boron nitride
- Electrostatic effects, band distortions and superconductivity in twisted graphene bilayers
- Generic Miniband Structure of Graphene on a Hexagonal Substrate
- MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
- Non-Abelian gauge potentials in graphene bilayers
- Band Structure Engineering of 2D Materials using Patterned Dielectric Superlattices
- Exact Landau Level Description of Geometry and Interaction in a Flatband
- Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
- Spontaneous Strains and Gap in Graphene on Boron Nitride
- Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach
- Charge-transfer insulation in twisted bilayer graphene
- Superconductivity in a two-dimensional Electron Gas
- Moiré band model and band gaps of graphene on hexagonal boron nitride
- Topological and stacked flat bands in bilayer graphene with a superlattice potential
- From laterally modulated two-dimensional electron gas towards artificial graphene
- 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
- Superconductivity from repulsive interactions in the two dimensional electron gas
- Topological Insulating States in Laterally Patterned Ordinary Semiconductors
- Heterostructure bilayer graphene-hBN: Interplay between misalignment, interlayer asymmetry, and trigonal warping
- Gate-tunable two-dimensional superlattices in graphene
- Engineering high quality graphene superlattices via ion milled ultra-thin etching masks
- Gate-tunable flat bands in van der Waals patterned dielectric superlattices
- Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
- Artificial Graphene: Unconventional Superconductivity in a Honeycomb Superlattice
- Approximate solutions to Mathieu's equation
- 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
- Narrow bands, electrostatic interactions and band topology in graphene stacks
- 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
- Tuning the topological insulator states of 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