Superconductivity in compensated and uncompensated semiconductors

Abstract

We investigate the localization and superconductivity in heavily doped semiconductors. The crossover from the 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. The microscopic inhomogeneity and the thermal superconducting fluctuation are taken into account using the self-consistent 1-loop order theory. The superconductor-insulator transition accompanies the crossover from the host band to the impurity band. We point out an enhancement of the critical temperature T c around the crossover. Further localization of electron wave functions leads to the localization of Cooper pairs and induces the pseudogap. We find that both the doping compensation by additional donors and the carrier increase by additional acceptors suppress the superconductivity. A theoretical interpretation is proposed for the superconductivity in the boron-doped diamond, SiC, and Si.

Superconductor–insulator transition in impurity band systems

“…3. We have calculated the correlation function of SC order parameter and found that the long range correlation of the superconductivity is suppressed as increasing the impurity potential for U imp 45:5 [21]. According to these results, we obtain the schematic figure for the phase diagram in Fig.…”

“…The SC correlation develops in the ''dirty region'' which includes many impurities while the SC correlation is suppressed in the ''clean region'' [21]. This spatial dependence is opposite to that in high-T c cuprates [22].…”

“…The crossover form the Wigner-Dyson statistics in the metallic state to the Poisson statistics in the insulating state is clearly shown. According to the scaling analysis of the inverse participation ratio, we find that the metal-insulator transition occurs around U imp ¼ 4:6 [21].…”

“…Before closing this section, we note that the transition temperature T ¼ 0:002, which we assumed for U imp $4:6, is not high enough to induce the pseudogap in the host band. If we assume a large pairing interaction g ¼ À9:2 so that T c $0:002 for U imp ¼ 0, the SC fluctuation is negligible [21].…”

Superconductivity in carrier-doped silicon carbide

“…Theoretically, the superconductivity in doped semiconductors can be interpreted in terms of degree of randomness caused by the impurity band, which is related to E A [17,18,42]. When E A is large (acceptor level is deep), the randomness caused by the impurity band is large.…”