$\boldsymbol{d}$-vector precession induced pumping in topological $p$-wave superconductors

TL;DR

This paper investigates how adiabatic rotation of the $oldsymbol{d}$-vector in topological $p$-wave superconductors induces quantized spin pumping and reveals a resonance near topological phase transitions, aiding experimental identification.

Contribution

It demonstrates the quantized spin pumping induced by $oldsymbol{d}$-vector rotation and identifies a resonance phenomenon at topological phase transitions in $p$-wave superconductors.

Findings

Nearly quantized spin pumping at $2$ over one cycle.

Peaks in charge and spin pumping at $1$ when lead is fully spin-polarized.

Resonance near topological phase transition with mixed pairing components.

Abstract

Time-reversal invariant $p$-wave superconductors (SCs) are characterized by their $\boldsymbol{d}$-vectors, whose orientations could be manipulated by a tiny magnetic field. We study in this paper the adiabatic pumping process induced by periodically rotating $\boldsymbol{d}$-vector in a topological $p$-wave SC, which is coupled to two normal leads. If $\boldsymbol{d}$-vector rotates nearly within a plane, the pumped spin $2S_z/\hbar$ over one cycle is nearly quantized at $2$ without net charge pumping. When the pumping lead is fully spin-polarized, both the pumped charge $Q/e$ and spin $2S_z/\hbar$ would peak nearly at $1$. When a mixing $s$-wave pairing component is taken into account, a topological phase transition can be driven by modulating the ratio between the pairing components. We found a sharp resonance phenomenon near the phase transition when the $p$-wave $\boldsymbol{d}$-vector is adiabatically rotating, which may help experimentally distinguish the topological SCs from trivial ones.