Anomalous proximity effect and theoretical design for its realization

We discuss the stability of zero-energy states appearing in a dirty normal metal attached to a superconducting thin film with Dresselhaus [110] spin-orbit coupling under an in-plane Zeeman field. The Dresselhaus superconductor preserves an additional chiral symmetry and traps more than one zero-energy state at its edges. All the zero-energy states at an edge belong to the same chirality in large Zeeman fields due to the effective $p$-wave pairing symmetry. The pure chiral nature of the wave function enables the zero-energy states to penetrate the dirty normal metal while retaining their high degree of degeneracy. We prove the perfect Andreev reflection into the dirty normal metal at zero energy.

Figure 1

Schematic image of the NS junction of a Dresselhaus superconductor. The superconductor proximitizes the InSb thin film, which is grown along the [110] crystal direction.

Figure 2

The differential conductance is plotted as a function of the bias voltage for several lengths of disordered segment $L$ in units of $a_0$. In (a), the Zeeman potential $V_{ex}=1.2t$ is chosen that is larger than a critical value of $V_c=0.92t$. The number of propagating channels $N_c$ is 5. In (b), we choose $V_{ex}=0.5t<V_c$ leading to $N_c=6$.

Figure 3

Schematic image of ZESs at two edges of an isolating Dresselhaus superconductor for $V_{ex}>V_c$. The number of the ZESs at either edge is equal to $N_c$. All of the ZESs at the left (right) edge have $\lambda =-1$ $\left(\lambda =1\right)$.