Magnetoresistance of two-dimensional $p\text{−}\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{10.3}{\mathrm{Ga}}_{10.7}\mathrm{As}$ structures in the vicinity of metal-insulator transition: Effect of superconducting leads

Experimental and theoretical studies on transport in semiconductor samples with superconducting electrodes are reported. We focus on the samples close to metal-insulator transition. In metallic samples, a peak of negative magnetoresistance at fields lower than critical magnetic field of the leads was observed. This peak is attributed to restoration of a single-particle tunneling emerging with suppression of superconductivity. The experimental results allow us to estimate tunneling transparency of the boundary between superconductor and metal. In contrast, for the insulating samples no such a peak was observed. We explain this behavior as related to properties of transport through the contact between superconductor and hopping conductor. This effect can be used to discriminate between weak localization and strong localization regimes.

Figure 1

Temperature dependences of the conductivity for three samples: samples 1,2 are in the weak localization regime, sample 3 is in the strong localization regime. Sample 1: wells $\left(10\mathrm{nm}\right)$ and barriers are doped (the bulk Be concentration is $6\times {10}^{17}{\mathrm{cm}}^{-3}$), sample 2: only wells $\left(15\mathrm{nm}\right)$ are doped (bulk Be concentration is ${10}^{18}{\mathrm{cm}}^{-3}$), 3: wells $\left(15\mathrm{nm}\right)$ and barriers doped (bulk Be concentration is $4\times {10}^{17}{\mathrm{cm}}^{-3}$).

Figure 2

High-field magnetoresistance at different temperatures for sample 1 (weak localization regime).

Figure 3

Low-field magnetoresistance at different temperatures: (a) for sample 1 (weak localization regime), (b) for sample 3 (strong localization regime).

Figure 4

Temperature dependence of negative magnetoresistance peak magnitude for sample 1 (experiment and theory). Theoretical fitting equation $\Delta R∕R_0=\mathbf{(}1∕\{R_N∕R_T+{[\Delta \left(T\right)∕\Delta \left(0\right)]}^2{R}_N∕R_A\}-1\mathbf{)}{R}_N∕R_0$. Where $R_T$, $R_A$, $R_N$ are the single-particle tunneling, Andreev and normal state contact resistances, respectively. The fitting parameters are $R_N∕R_0\approx 4.2$, $R_N∕R_A\approx 0.33$.