Moire Localization in Two Dimensional Quasi-Periodic Systems
arXiv:1905.08277 · doi:10.1103/PhysRevB.100.144202
Abstract
We discuss a two-dimensional system under the perturbation of a Moire potential, which takes the same geometry and lattice constant as the underlying lattices but mismatches up to relative rotation. Such a self-dual model belongs to the orthogonal class of a quasi-periodic system whose features have been evasive in previous studies. We find that such systems enjoy the same scaling exponent as the one-dimensional Aubry-Andre model , which saturates the Harris bound in two-dimensions. Meanwhile, there exist an infinite number of mobility edges different from the typical one-dimensional situation where only a few or no mobility edges show up. An experimental scheme based on optical lattices is discussed. It allows for using lasers of arbitrary wavelengths and therefore is more applicable than the one-dimensional situations requiring laser wavelengths close to certain incommensurate ratios.
arXiv comment7+4 pages, 6 figures, 1 table
References in corpus (31)
- The electronic properties of graphene
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Many body localization and thermalization in quantum statistical mechanics
- Tuning superconductivity in twisted bilayer graphene
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- Anderson localization of a non-interacting Bose-Einstein condensate
- Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Exploring the many-body localization transition in two dimensions
- Commensurate-incommensurate transition for graphene on hexagonal boron nitride
- Continuum Model of the Twisted Bilayer
- Long-time behavior of periodically driven isolated interacting lattice systems
- Electronic structure of turbostratic graphene
- Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
- Quasicrystalline 30° Twisted Bilayer Graphene as an Incommensurate Superlattice with Strong Interlayer Coupling
- Two universality classes for the many-body localization transition
- Mobility Edges in 1D Bichromatic Incommensurate Potentials
- Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
- Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
- Multifractal finite-size-scaling and universality at the Anderson transition
- Quasi Many-body Localization in Translation Invariant Systems
- Critical parameters from generalised multifractal analysis at the Anderson transition
- Many-body localization in disorder-free systems: the importance of finite-size constraints
- Multifractal analysis with the probability density function at the three-dimensional Anderson transition
- Anderson localization transitions with and without random potentials
- Emergent Localization in Dodecagonal Bilayer Quasicrystals
- Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
Cited by in corpus (24)
- Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
- Critical phase dualities in 1D exactly-solvable quasiperiodic models
- Hidden dualities in 1D quasiperiodic lattice models
- Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
- Quasiperiodicity, band topology, and moiré graphene
- Coexistence of localization and transport in many-body two-dimensional Aubry-André models
- Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
- Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
- Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
- Enhanced Superconductivity in Quasi-periodic Crystals
- Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
- Quasidisorder Induced Topology
- Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
- Interaction induced moiré systems in twisted bilayer optical lattices
- Interaction-induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices
- Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice
- Fate of Quadratic Band Crossing under quasiperiodic modulation
- Level spacing distribution of localized phases induced by quasiperiodic potentials
- Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
- Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
- Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene
- Quasiperiodic Quadrupole Insulators
- Localization and Topology in Noncentrosymmetric Superconductors with Disorder
- Localization and topological signatures under periodic twisting