Multifractality and electron-electron interaction at Anderson transitions

Abstract

Mesoscopic fluctuations and correlations of the local density of states are studied near metal-insulator transitions in disordered interacting electronic systems. We show that the multifractal behavior of the local density of states survives in the presence of Coulomb interaction. We calculate the spectrum of multifractal exponents in $2+\epsilon$ spatial dimensions for symmetry classes characterized by broken (partially or fully) spin-rotation invariance and show that it differs from that in the absence of interaction. We also estimate the multifractal exponents at the Anderson metal-insulator transition in 2D systems with preserved spin-rotation invariance. Our results for multifractal correlations of the local density of states are in qualitative agreement with recent experimental findings.

19 pages, 3 figures. arXiv admin note: text overlap with arXiv:1305.2888

References in corpus (13)

• The electronic properties of graphene
• Anderson Transitions
• Disorder-Induced Inhomogeneities of the Superconducting State Close to the Superconductor-Insulator Transition
• Topological delocalization of two-dimensional massless Dirac fermions
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Entanglement entropy and multifractality at localization transitions
• Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions
• Scanning Tunneling Microscopy and Spectroscopy of Graphene on Insulating Substrates
• Probing electron-electron interaction in quantum Hall systems with scanning tunneling spectroscopy

Cited by in corpus (15)

• Exotic Multifractal Conductance Fluctuations in Graphene
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Superconductor-insulator transitions: Phase diagram and magnetoresistance
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems
• Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction
• Dephasing catastrophe in $4-\epsilon$ dimensions: A possible instability of the ergodic (many-body-delocalized) phase
• Multifractally-enhanced superconductivity in two-dimensional systems with spin-orbit coupling
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Generalized surface multifractality in 2D disordered systems
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Mesoscopic fluctuations of the local density of states in interacting electron systems
• Two-loop renormalization of the Finkel'stein theory: The specific heat
• Boundary multifractality in the spin quantum Hall symmetry class with interaction