Specular Andreev Reflection in the Interface of a Two-Dimensional Semiconductor with Rashba Spin-Orbit Coupling and a $d$-Wave Superconductor

We reveal that the recently discovered specular Andreev reflection (SAR) [C. W. J. Beenakker, Phys. Rev. Lett. 97, 067007 (2006)] can occur in semiconductors where the spin-orbit coupling is finite. We demonstrate this finding in the hybrid of a two-dimensional electron gas with Rashba spin-orbit coupling and a superconductor. In the limit of low density or a strong spin-orbit coupling, specular Andreev reflection is finite. We also show that unit electron-hole conversion is possible in a specular Andreev reflection due to the different topological structures of the equal-energy surface between electrons and holes. The SAR in the semiconductor is determined by the relative orientation of wave vector to group velocity, which can be analyzed by ray equations.

Figure 1

(a) Diagrammatic sketch of band structures in the R2DEGs and superconductors. An electron with $\epsilon >0$ intersects both “$+$” and “$-$” branches while a hole with the same energy intersects the “$-$” branch. (b) Various $k$ positions for reflected electrons and holes. (c) All possible reflection processes at a R2DEG/S interface.

Figure 2

SAR coefficients in $s$-wave superconductors as a function of the incident angle for different values of $Z$, ${\Lambda }_{\mathrm{SO}}=0.4$.

Figure 3

SAR coefficients in $d$-wave superconductors as a function of the incident angle for $\beta =0$, $\pi /8$, and $Z=1$, ${\Lambda }_{\mathrm{SO}}=0.4$. The insets are SAR coefficients for the interface potential $Z=0$.

Figure 4

SAR conductance versus bias for different interface potentials. (a) For $s$-wave and (b) for $d$-wave superconductors with $\beta =\pi /8$. The insets show the derivative of the SAR conductance.