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, 9 (4), 044201
eCollection

Superconductivity in Compensated and Uncompensated Semiconductors

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Superconductivity in Compensated and Uncompensated Semiconductors

Youichi Yanase et al. Sci Technol Adv Mater.

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 Tc 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.

Keywords: diamond; localization; semiconductor; superconductivity.

Figures

Figure 1
Figure 1
DOS in the normal state (solid line). We assume nc=nimp=0.02 and U=0. The dashed (dash-dotted) line shows the partial DOS at the boron (carbon) sites. The calculation is carried out on 213 sites and 50 samples are taken for the random average.
Figure 2
Figure 2
Schematic phase diagram of the uncompensated semiconductors describing the crossover from the host band to the impurity band. The solid line shows the transition temperature of superconductivity, Tc. The dashed line shows the transition temperature in the mean field theory, TcMF. The shaded region indicates the pseudogap state induced by the incoherent Cooper pairs. The up arrow (UMI) shows the virtual quantum metal–insulator transition in absence of the superconductivity. Down arrows indicate our interpretation on the B-doped diamond, SiC, and Si (see section 4).
Figure 3
Figure 3
A typical spacial dependence of the superconducting susceptibility formula image for (a) Uimp=3, (b) Uimp=4.0, and (c) Uimp=6.1. We assume nc=nimp=0.02, T=0.002, and U=−1. The calculation is carried out in the 11×11×11 lattice. The results on the 11×11 plane at z=1 are shown.
Figure 4
Figure 4
Doping dependence of the Fourier transformed correlation function formula image in the crossover regime. We show the formula image along formula image for nc=nimp=0.01, 0.02, 0.04, 0.08, 0.125 from the bottom to the top. We fix Uimp=4.6, U=−1, and T=0.002.
Figure 5
Figure 5
DOS for nc=nimp=0.01, 0.02, 0.04, 0.08, 0.125 from the bottom to the top. We assume Uimp=4.6, U=−1, and T=0.002.
Figure 6
Figure 6
Schematic figure of the doping dependence in the crossover regime. We show the magnitude of the superconducting gap (pseudogap) Δ divided by γ=1.73 for a comparison with the Tc.
Figure 7
Figure 7
Averaged superconducting susceptibility for various carrier concentration nc. The impurity concentration is fixed to be nimp=0.02. We assume Uimp=4.6, U=−1, and T=0.002.

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