Fractal defect states in the Hofstadter butterfly
arXiv:2102.12153 · doi:10.1103/PhysRevB.104.035305
Abstract
We investigate the electronic properties in the Bloch electron on a square lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to the system creates a defect energy level in every single innumerable fractal energy gap in the Hofstadter butterfly. The wavefunctions of different defect levels have all different localization lengths depending on their fractal generations, and they can be described by a single universal function after an appropriate fractal scaling. We also show that each defect state has its own characteristic orbital magnetic moment, which is exactly correlated to the gradient of the energy level in the Hofstadter diagram. Probing the spatial nature of the defect-localized states provides a powerful way to elucidate the fractal nature of the Hofstadter butterfly.
arXiv comment10 pages, 10 figures
References in corpus (36)
- Berry Phase Effects on Electronic Properties
- Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
- Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
- Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
- Cloning of Dirac fermions in graphene superlattices
- Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
- Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
- Spectral signatures of many-body localization with interacting photons
- Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
- Hofstadter butterfly and integer quantum Hall effect in three dimensions
- Hofstadter Topology: Non-crystalline Topological Materials at High Flux
- Floquet topological phase transition in - lattice
- Virtual Topological Insulators with Real Quantized Physics
- Real-Space Imaging of Alternate Localization and Extension of Quasi Two-Dimensional Electronic States at Graphite Surfaces in Magnetic Fields
- Population dynamics in Floquet realisation of Harper-Hofstadter Hamiltonian
- Hofstadter's Butterfly in Quantum Geometry
- Acoustic characterization of Hofstadter butterfly with resonant scatterers
- Landau levels in the case of two degenerate coupled bands: kagome lattice tight-binding spectrum
- Adittional levels between Landau bands due to vacancies in graphene: towards a defect engineering
- Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices
- Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene
- Hofstadter butterflies and magnetically induced band gap quenching in graphene antidot lattices
- Revealing Hofstadter Spectrum for Graphene in a Periodic Potential
- Self-similar occurrence of massless Dirac particles in graphene under magnetic field
- Spectral functions of a time-periodically driven Falicov-Kimball model: real-space Floquet DMFT study
- Genesis of the Floquet Hofstadter butterfly
- Impurity bound states as detectors of topological band structures revisited
- Two-dimensional electron gas in a uniform magnetic field in the presence of a delta-impurity
- Hofstadter's Butterfly and Langlands Duality
- Magnonic Floquet Hofstadter Butterfly
- Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves
- Quantum Hall Effect and Langlands Program
- Effects of large disorder on the Hofstadter butterfly
- Translational symmetry breaking and the disintegration of the Hofstadter butterfly
- Impurity induced current in a Chern insulator
- Quantum Hall Effect of Massless Dirac Fermions and Free Fermions in Hofstadter's Butterfly
Cited by in corpus (7)
- Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
- Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
- Topological Effects in Two-Dimensional Quantum Emitter Systems
- Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from -root topology in decorated square lattices
- Investigating global and topological order of states by local measurement and classical communication: Study on SPT phase diagrams by quantum energy teleportation
- Level-spectra Statistics in Planar Fractal Tight-Binding Models
- Vortical Quantum Memory