Localization and Superconductivity in Doped Semiconductors

TL;DR

This paper explores the interplay between localization and superconductivity in heavily doped semiconductors, revealing a crossover from host to impurity band superconductivity and associated phenomena like pseudogap formation.

Contribution

It provides a microscopic theoretical framework describing the superconductor-insulator transition and the crossover in doped semiconductors, incorporating inhomogeneity and fluctuations.

Findings

Superconductor-insulator transition coincides with the crossover from host to impurity band.

Enhancement of Cooper pairing occurs in the crossover regime.

Localization leads to incoherent pairs and pseudogap formation above T_c.

Abstract

Motivated by the discovery of superconductivity in boron-doped (B-doped) diamond, we investigate the localization and superconductivity in heavily doped semiconductors. The competition between Anderson localization and s-wave superconductivity is investigated from the microscopic point of view. The effect of microscopic inhomogeneity and the thermal fluctuation in superconductivity are taken into account using the self-consistent 1-loop-order theory with respect to superconducting fluctuation. The crossover from superconductivity in the host band to that in the impurity band is described on the basis of the disordered three-dimensional attractive Hubbard model for binary alloys. We show that superconductor-insulator transition (SIT) accompanies the crossover. We point out an enhancement of Cooper pairing in the crossover regime. Further localization of the electron wave function gives rise to incoherent Cooper pairs and the pseudogap above T_c. A global phase diagram is drawn for host band superconductivity, impurity band superconductivity, Anderson localization, Fermi liquid state, and pseudogap state. A theoretical interpretation is proposed for superconductivity in the doped diamond, SiC, and Si.