Fate of Quadratic Band Crossing under quasiperiodic modulation

Abstract

We study the fate of two-dimensional quadratic band crossing topological phases under a one-dimensional quasiperiodic modulation. By employing numerically exact methods, we fully characterize the phase diagram of the model in terms of spectral, localization and topological properties. Unlike in the presence of regular disorder, the quadratic band crossing is stable towards the application of the quasiperiodic potential and most of the topological phase transitions occur through a gap closing and reopening mechanism, as in the homogeneous case. With a sufficiently strong quasiperiodic potential, the quadratic band crossing point splits into Dirac cones which enables transitions into gapped phases with Chern numbers $C=\pm 1$, absent in the homogeneous limit. This is in sharp contrast with the disordered case, where gapless $C=\pm 1$ phases can arise by perturbing the band crossing with any amount of disorder. In the quasiperiodic case, we find that the $C=\pm 1$ phases can only become gapless for a very strong potential. Only in this regime, the subsequent quasiperiodic-induced topological transitions into the trivial phase mirror the well-known ``levitation and annihilation'' mechanism in the disordered case.

arXiv comment11 pages, 4 figures

References in corpus (70)

• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Classification of topological quantum matter with symmetries
• Experimental realisation of the topological Haldane model
• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• The Kernel Polynomial Method
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Graphene Bilayers with a Twist
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Topological Anderson Insulator
• Localization and delocalization of light in photonic moire lattices
• Theory of the topological Anderson insulator
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets - Quantum Hall Effect from Metal -
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Band Structure Engineering of 2D Materials using Patterned Dielectric Superlattices
• Exponential localization in one-dimensional quasiperiodic optical lattices
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Flat Bands Under Correlated Perturbations
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
• Localization in a quantum spin Hall system
• Real-space calculation of the conductivity tensor for disordered topological matter
• Anomalous mobility edges in one-dimensional quasiperiodic models
• The dependence of topological Anderson insulator on the type of disorder
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Experimental Demonstration of Dynamic Topological Pumping Across Incommensurate Bilayered Acoustic Metamaterials
• Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes
• Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice
• Flatband Engineering of Mobility Edges
• Four-Dimensional Higher-Order Chern Insulator and Its Acoustic Realization
• Renormalization group study of interaction-driven quantum anomalous Hall and quantum spin Hall phases in quadratic band crossing systems
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Coupling-Matrix Approach to the Chern Number Calculation in Disordered Systems
• Two-dimensional Thouless pumping of light in photonic moiré lattices
• Magic-angle semimetals
• Topological states in quasicrystals
• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Strain induced quasi-unidimensional channels in twisted moiré lattices
• Instabilities of quadratic band crossing points
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• The topological Anderson insulator phase in the Kane-Mele model
• Emergent Localization in Dodecagonal Bilayer Quasicrystals
• Anderson localization and topological transition in Chern insulators
• Moire Localization in Two Dimensional Quasi-Periodic Systems
• Experimental observation of intrinsic light localization in photonic icosahedral quasicrystals
• Magic-Angle Semimetals with Chiral Symmetry
• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• The fate of interaction-driven topological insulators under disorder
• Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Quasidisorder Induced Topology
• From topological phase to Anderson localization in a two-dimensional quasiperiodic system
• One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene

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