Figure 1

Quantum dot with an interface between a normal metal ($N$) and a superconductor ($S$, shaded region). Andreev reflection at the NS interface converts a normal current (carried by electron and hole excitations $e$ and $h$) into a supercurrent (carried by Cooper pairs). The conductance $G$ is the ratio of the current $I$ into the grounded superconductor and the voltage $V$ applied to the quantum dot via an $N$-mode point contact to a normal metal electrode (narrow opening at the left). The system is in a topologically nontrivial state if it supports a quasibound state at the Fermi level. This is possible if spin-rotation symmetry is broken by spin-orbit coupling. In the configuration shown in the figure (with a single NS interface), time-reversal symmetry should be broken to prevent the opening of an excitation gap in the quantum dot. In the presence of time-reversal symmetry a second NS interface, with a $\pi$ phase difference, can be used to close the gap.Reuse & Permissions

Figure 2

Probability distribution of the conductance in the CRE, for channel numbers $N=1,\hspace{0.5em}2,\hspace{0.5em}3,\hspace{0.5em}4$ and topological charges $Q=-1$ (red solid curves) and $Q=+1$ (blue dashed curves). In the lower panel the thick vertical lines indicate a $\delta$-function distribution.Reuse & Permissions

Figure 3

Same as described in the caption to Fig. 2 but for the T-CRE.Reuse & Permissions

Figure 4

Comparison of the probability distribution of the electrical conductance as predicted by RMT (dashed curves) and as resulting from numerical simulation of the model Hamiltonian (5.1) (solid histograms). The simulation is for the disordered normal-metal–superconductor junction shown in the inset. The number of propagating modes in the normal region is $N=2$ (lower panel) and $N=3$ (upper panel), while the red and blue curves are for topological quantum number $Q=-1$ and $Q=+1$, respectively. The disorder strength is fixed at $U_0=130$ $E_{\mathrm{so}}$ for $N=2$ and $U_0=100$ $E_{\mathrm{so}}$ for $N=3$. The values used for Fermi energy and Zeeman energy (in units of $E_{\mathrm{so}}$) are as follows. For $N=2$: $E_F=12$, $E_Z=3.8$ ($Q=1$) and $E_F=13$, $E_Z=9$ ($Q=-1$). For $N=3$: $E_F=19$, $E_Z=3.8$ ($Q=1$) and $E_F=19$, $E_Z=8$ ($Q=-1$).Reuse & Permissions