Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene

Abstract

We numerically investigate critically delocalized wavefunctions in models of 2D Dirac fermions, subject to vector potential disorder. These describe the surface states of 3D topological superconductors, and can also be realized through long-range correlated bond randomness in artificial materials like molecular graphene. A frozen regime can occur for strong disorder in these systems, wherein a single wavefunction presents a few localized peaks separated by macroscopic distances. Despite this rarefied spatial structure, we find robust correlations between eigenstates at different energies, at both weak and strong disorder. The associated level statistics are always approximately Wigner-Dyson. The system shows generalized Chalker (quantum critical) scaling, even when individual states are quasilocalized in space. We confirm analytical predictions for the density of states and multifractal spectra. For a single Dirac valley, we establish that finite energy states show universal multifractal spectra consistent with the integer quantum Hall plateau transition. A single Dirac fermion at finite energy can therefore behave as a Quantum Hall critical metal. For the case of two valleys and non-abelian disorder, we verify predictions of conformal field theory. Our results for the non-abelian case imply that both delocalization and conformal invariance are topologically-protected for multivalley topological superconductor surface states.

17 pages, 15 figures, published version

References in corpus (17)

• The electronic properties of graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Quantum transport of massless Dirac fermions in graphene
• Electron fractionalization in two-dimensional graphenelike structures
• Electron transport in disordered graphene
• Ergodicity breaking in a model showing many-body localization
• Theoretical Studies of Superconductor-Insulator Transitions
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory
• Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
• The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition

Cited by in corpus (26)

• A random matrix model with localization and ergodic transitions
• Thouless energy and multifractality across the many-body localization transition
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Topological states on fractal lattices
• Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems
• Magic-Angle Semimetals with Chiral Symmetry
• Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid
• Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor
• Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone
• Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems
• Surface transport coefficients for three-dimensional topological superconductors
• Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
• Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors
• Critical Percolation Without Fine Tuning on the Surface of a Topological Superconductor
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry
• Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons
• Two-dimensional conductors with interactions and disorder from particle-vortex duality
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models
• Stability of topologically protected slow light against disorder
• Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene
• Band-center metal-insulator transition in bond-disordered graphene
• Random Magnetic Field and the Dirac Fermi Surface
• Randomly twisted bilayer graphene -- the cascade transitions