Spin-orbit-induced chirality of Andreev states in Josephson junctions

Abstract

We study Josephson junctions (JJs) in which the region between the two superconductors is a multichannel system with Rashba spin-orbit coupling (SOC) where a barrier or a quantum point contact (QPC) is present. These systems might present unconventional Josephson effects such as Josephson currents for zero phase difference or critical currents that depend on the current direction. Here, we discuss how the spin polarizing properties of the system in the normal state affect the spin characteristics of the Andreev bound states inside the junction. This results in a strong correlation between the spin of the Andreev states and the direction in which they transport Cooper pairs. While the current-phase relation for the JJ at zero magnetic field is qualitatively unchanged by SOC, in the presence of a weak magnetic field, a strongly anisotropic behavior and the mentioned anomalous Josephson effects follow. We show that the situation is not restricted to barriers based on constrictions such as QPCs and should generically arise if in the normal system the direction of the carrier's spin is linked to its direction of motion.

Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires

“…As a result, the phase difference ϕ 0 at the minimum of ground-state energy is deviated from 0 or π , as shown in Fig. 6(a), and the ϕ 0 state is realized [32,[53][54][55]. The phase difference ϕ 0 is almost liner to the magnetic field first, and jumps to ϕ 0 ≈ π like the 0-π transition.…”

“…The dc Josephson current with SO interaction in the normal region was investigated theoretically by a lot of groups, for normal metal with magnetic impurities [32], two-dimensional electron gas (2DEG) in semiconductor heterostructures [33][34][35][36][37][38][39], open quantum dots [40], quantum dots with tunnel barriers [41][42][43][44][45][46][47], carbon nanotubes [48], quantum wires or nanowires [49][50][51][52], quantum point contacts [53,54], topological insulators [55], and others [56]. The SO interaction breaks the spin degeneracy of Andreev levels when the time-reversal symmetry is broken by the phase difference ϕ = 0 even in the absence of magnetic field [40,56].…”

“…Then, the anomalous Josephson current is obtained [32,35,36,43,47,49,[52][53][54][55]. The anomalous current flows in the so-called ϕ 0 state in which the free energy has a minimum at ϕ = ϕ 0 ( =0,π ) [57].…”

“…Krive et al derived the anomalous current for long junctions with a single conduction channel [49]. Reynoso et al found the anomalous current through a quantum point contact in the 2DEG for L ξ [53,54]. They discussed an influence of spin polarization induced around the quantum point contact with SO interaction [59] on the Josephson current.…”

Singularities in the Andreev spectrum of a multiterminal Josephson junction

“…With symmetry broken, the Josephson current is not an odd function of the phase difference. This is called the anomalous Josephson effect [10][11][12][13][14] .…”