Interplay between superconductivity and spin-dependent fields in nanowire-based systems

Abstract

The interplay between superconductivity, spin-orbit coupling, and Zeeman or exchange field, is studied theoretically in two different setups: a single wire in which all these fields coexist, and a double wire system in which superconducting pairing and the spin-dependent fields are spatially separated. We first explore a magnetoelectric effect, namely the appearance of anomalous charge supercurrents. We determine the conditions under which such currents are allowed by symmetry and express them in terms of the SU(2) electric and magnetic fields. In leading order in the strength of the fields we find that in the single wire setup such currents may appear only when the Zeeman field has both, a longitudinal and transverse component with respect to the spin-orbit field. In contrast, in the two wire setup a parallel component to the SOC can generate the anomalous current, which is allowed by symmetry. We confirm these findings by calculating explicitly the current in both setups together with the self-consistent superconducting order parameter. The latter shows in the ground-state a spatial modulation of the phase that leads to currents that compensate the anomalous current, such that in both cases the ground state corresponds to a total zero-current state. However, in the two wire setup this zero-current state consists of two finite currents flowing in each of the wires in opposite direction.

Nonsinusoidal current-phase relations in semiconductor-superconductor-ferromagnetic insulator devices

“…However, it is not observed in the homogeneous case as the combination of various spin-rotation symmetrybreaking effects is necessary for its manifestation [71]. This can occur, for instance, due to finite spin-splitting with a non-zero component in both the junction direction and the transverse one [72], or multiple modes that can hybridize [73]. The presence of anomalous currents in similar systems has been considered in Refs.…”

Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling

“…Namely, SOC induces a mixing between singlet and triplet correlations [16]. Breaking timereversal symmetry in these superconductors may lead to the formation of modulated helical phases [17][18][19], as well as to various superconducting magnetoelectric effects, such as inducing supercurrents with a static magnetization and vice versa [20][21][22][23][24][25]. These effects are completely analogous to SGE and ISGE in the normal state, respectively [26].…”

A Unified Description of Spin Transport, Weak Antilocalization and Triplet Superconductivity in Systems with Spin-Orbit Coupling

“…Namely, SOC induces a mixing between singlet and triplet correlations 11 . Breaking timereversal symmetry in these superconductors may lead to the formation of modulated helical phases, [12][13][14] as well as to various superconducting magnetoelectric effects, such as inducing supercurrents with a static magnetization and vice-versa [15][16][17][18][19][20] . These effects are completely analogous to SGE/IEE and ISGE/EE in the normal state, respectively 21 .…”