<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> </mml:math> -vector precession induced pumping in topological <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -wave superconductors

Time-reversal-invariant $p$-wave superconductors (SCs) are characterized by their $\mathbit{d}$ vectors, whose orientations could be manipulated by a tiny magnetic field. We study in this paper the adiabatic pumping process induced by periodically rotating the $\mathbit{d}$ vector in a topological $p$-wave SC, which is coupled to two normal leads. If the $\mathbit{d}$ vector rotates nearly within a plane, the pumped spin $2{S}_{z}/\ensuremath{\hbar}$ 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 $2{S}_{z}/\ensuremath{\hbar}$ will 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 find a sharp resonance phenomenon near the phase transition when the $p$-wave $\mathbit{d}$ vector is adiabatically rotating, which may help experimentally distinguish the topological SCs from trivial ones.