Multifractality and quantum-to-classical crossover in the Coulomb anomaly at the Mott-Anderson metal-insulator transition

Abstract

We study the interaction driven localization transition, which a recent experiment in Ga_{1-x}Mn_xAs As has shown to come along with multifractal behavior of the local density of states (LDoS) and the intriguing persistence of critical correlations close to the Fermi level. We show that the bulk of these phenomena can be understood within a Hartree-Fock treatment of disordered, Coulomb-interacting spinless fermions. A scaling analysis of the LDoS correlation demonstrates multifractality with correlation dimension d_2=1.57, which is significantly larger than at a non-interacting Anderson transition. At the interaction-driven transition the states at the Fermi level become critical, while the bulk of the spectrum remains delocalized up to substantially stronger interactions. The mobility edge stays close to the Fermi energy in a wide range of disorder strength, as the interaction strength is further increased. The localization transition is concomitant with the quantum-to-classical crossover in the shape of the pseudo-gap in the tunneling density of states, and with the proliferation of metastable HF solutions that suggest the onset of a glassy regime with poor screening properties.

significantly extended version

References in corpus (5)

• Anderson Transitions
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Mean field theory for the three-dimensional Coulomb glass
• Quantum charge glasses of itinerant fermions with cavity-mediated long-range interactions
• Multifractality at Anderson transitions with Coulomb interaction

Cited by in corpus (32)

• Marginal Stability in Structural, Spin and Electron Glasses
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Derivation of exact flow equations from the self-consistent parquet relations
• Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class
• Slow Dynamics of the Electron-Glasses; the Role of Disorder
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Multifractality and electron-electron interaction at Anderson transitions
• Critical exponent of metal-insulator transition in doped semiconductors: the relevance of the Coulomb interaction
• Metal oxide resistive switching: evolution of the density of states across the metal-insulator transition
• Self-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films
• Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction
• Tunneling into the localized phase near Anderson transitions with Coulomb interaction
• Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition
• Multifractality of ab initio wave functions in doped semiconductors
• Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors
• Quantum criticality at the Anderson transition: a TMT perspective
• Dielectric response of Anderson and pseudogapped insulators
• Generalized surface multifractality in 2D disordered systems
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Hartree-Fock study of an Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents
• Electron-phonon cooling power in Anderson insulators
• Coherent Forward Scattering Peak and Multifractality
• Mesoscopic fluctuations of the local density of states in interacting electron systems
• Selective final state spectroscopy and multifractality in two-component ultracold Bose-Einstein condensates: a numerical study
• Boundary multifractality in the spin quantum Hall symmetry class with interaction
• Interaction induced spatial correlations in a Disordered Glass
• Understanding disorder-induced zero-bias anomalies in systems with short-range interactions: An atomic-limit perspective
• Quantum Coulomb glass on the Bethe lattice
• Fluctuation driven transitions in localized insulators: Intermittent metallicity and path chaos precede delocalization
• Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions
• Half metals at intermediate energy scales in Anderson-type insulators
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe