Emergent Localization in Dodecagonal Bilayer Quasicrystals

Abstract

A new type of long-range ordering in the absence of translational symmetry gives rise to drastic revolution of our common knowledge in condensed matter physics. Quasicrystal, as such unconventional system, became a plethora to test our insights and to find exotic states of matter. In particular, electronic properties in quasicrystal have gotten lots of attention along with their experimental realization and controllability in twisted bilayer systems. In this work, we study how quasicrystalline order in bilayer systems can induce unique localization of electrons without any extrinsic disorders. We focus on dodecagonal quasicrystal that has been demonstrated in twisted bilayer graphene system in recent experiments. In the presence of small gap, we show the localization generically occurs due to non-periodic nature of quasicrystal, which is evidenced by the inverse participation ratio and the energy level statistics. We understand the origin of such localization by approximating the dodecagonal quasicrystals as an impurity scattering problem.

4 pages, 5 figures

References in corpus (24)

• Moire bands in twisted double-layer graphene
• Localization of interacting fermions at high temperature
• Graphene bilayer with a twist: electronic structure
• The many-body localization phase transition
• Localization of Dirac electrons by Moire patterns in graphene bilayers
• Continuum Model of the Twisted Bilayer
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Optical Absorption in Twisted Bilayer Graphene
• Modeling disorder in graphene
• Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
• Dirac Electrons in a Dodecagonal Graphene Quasicrystal
• Numerical studies of confined states in rotated bilayers of graphene
• Fluctuations of the inverse participation ratio at the Anderson transition
• Quasicrystalline 30° Twisted Bilayer Graphene as an Incommensurate Superlattice with Strong Interlayer Coupling
• Localization and Kosterlitz-Thouless Transition in Disordered Graphene
• Low energy theory of disordered graphene
• Aharonov-Bohm spectral features and coherence lengths in carbon nanotubes
• Interlayer interaction in general incommensurate atomic layers
• Quasicrystalline electronic states in 30${}^{\circ }$ rotated twisted bilayer graphene
• Electronic states and quantum transport in double-wall carbon nanotubes
• Anderson localization of electron states in graphene in different types of disorder
• Local sublattice-symmetry breaking in rotationally faulted multilayer graphene
• Anderson localization transitions with and without random potentials
• Nature of single-particle states in disordered graphene

Cited by in corpus (26)

• Dodecagonal bilayer graphene quasicrystal and its approximants
• 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
• Moire Localization in Two Dimensional Quasi-Periodic Systems
• Twistronics in graphene-based van der Waals structures
• Charge 4e superconductivity and chiral metal in the $45^{\circ }$-twisted bilayer cuprates and similar bilayers
• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Pressure and electric field dependence of quasicrystalline electronic states in 30${}^{\circ }$ twisted bilayer graphene
• Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
• High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems
• Electronic structure of 30° twisted double bilayer graphene
• Surfactant-Mediated Epitaxial Growth of Single-Layer Graphene in an Unconventional Orientation on SiC
• Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems
• Macroscopically degenerate localized zero-energy states of quasicrystalline bilayer systems in strong coupling limit
• Quasiperiodic pairing in graphene quasicrystals
• Progress on band structure engineering of twisted bilayer and two-dimensional moiré heterostructures
• Making Chiral Topological Superconductivities from Non-topological Superconductivities Through the Twist
• The low energy excitation spectrum of magic-angle semimetals
• Interaction-induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices
• Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: application to electronic structure and optical responses
• Quasiperiodic Quadrupole Insulators
• Fate of Quadratic Band Crossing under quasiperiodic modulation
• Energy Spectrum Theory of Incommensurate Systems