Tunneling into the localized phase near Anderson transitions with Coulomb interaction

Abstract

We study the tunneling density of states (TDOS) of a disordered electronic system with Coulomb interaction on the insulating side of the Anderson localization transition. The average TDOS shows a critical behavior at high energies, with a crossover to a soft Coulomb gap $\Delta$ at low energies. We demonstrate that the single-particle excitations experience a localization transition (which belongs to the noninteracting universality class) at an energy $E=\pm E_c$. The mobility edge $E_c$ scales with the distance ${\mu }_c-\mu$ from the interacting critical point according to $E_c\propto ({\mu }_c-\mu {)}^{\nu z}$, where $\nu$ and $z$ are the localization-length and the dynamical critical exponents. Local TDOS shows strong fluctuations and long-range correlations which reflect the multifractality associated with interacting and noninteracting fixed points as well the localization of low-energy excitations.

14 pages, 5 figures; to appear in Physical Review B

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Cited by in corpus (10)

• Multifractality and electron-electron interaction at Anderson transitions
• 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
• Entanglement entropy and particle number cumulants of disordered fermions
• Dielectric response of Anderson and pseudogapped insulators
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Mesoscopic fluctuations of the local density of states in interacting electron systems
• Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model
• Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states
• Information Bounds on phase transitions in disordered systems