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Register a new userMapping of spin lifetimes to electronic states in n-type GaAs near the metal-insulator transition
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The longest spin lifetimes in bulk n-GaAs exceed 100 ns for doping concentrations near the metal-insulator transition (J.M. Kikkawa, D.D. Awschalom, Phys. Rev. Lett. 80, 4313 (1998)). The respective electronic states have yet not been identified. We therefore investigate the energy dependence of spin lifetimes in n-GaAs by time-resolved Kerr rotation. Spin lifetimes vary by three orders of magnitude as a function of energy when occupying donor and conduction band states. The longest spin lifetimes (>100 ns) are assigned to delocalized donor band states, while conduction band states exhibit shorter spin lifetimes. The occupation of localized donor band states is identified by short spin lifetimes (~300 ps) and a distinct Overhauser shift due to dynamic nuclear polarization.
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We start by analyzing experimental data of Spinelli [A. Spinelli, M. A. Torija, C. Liu, C. Jan, and C. Leighton, Phys. Rev. B 81, 155110 (2010)] for conductivity of $n$-type bulk crystals of SrTiO$_3$ (STO) with broad electron concentration $n$ range of $4times 10^{15}$ - $4 times10^{20} $ cm$^{-3}$, at low temperatures. We obtain good fit of the conductivity data, $sigma(n)$, by the Drude formula for $n geq n_c simeq 3 times 10^{16} $ cm$^{-3}$ assuming that used for doping insulating STO bulk crystals are strongly compensated and the total concentration of background charged impurities is $N = 10^{19}$ cm$^{-3}$. At $n< n_c$, the conductivity collapses with decreasing $n$ and the Drude theory fit fails. We argue that this is the metal-insulator transition (MIT) in spite of the very large Bohr radius of hydrogen-like donor state $a_B simeq 700$ nm with which the Mott criterion of MIT for a weakly compensated semiconductor, $na_B^3 simeq 0.02$, predicts $10^{5}$ times smaller $n_c$. We try to explain this discrepancy in the framework of the theory of the percolation MIT in a strongly compensated semiconductor with the same $N=10^{19}$ cm$^{-3}$. In the second part of this paper, we develop the percolation MIT theory for films of strongly compensated semiconductors. We apply this theory to doped STO films with thickness $d leq 130$ nm and calculate the critical MIT concentration $n_c(d)$. We find that, for doped STO films on insulating STO bulk crystals, $n_c(d)$ grows with decreasing $d$. Remarkably, STO films in a low dielectric constant environment have the same $n_c(d)$. This happens due to the Rytova-Keldysh modification of a charge impurity potential which allows a larger number of the film charged impurities to contribute to the random potential.
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