Odd-frequency Cooper-pair amplitude around a vortex core in a chiral $p$-wave superconductor in the quantum limit

Odd-frequency Cooper-pair amplitude around a vortex core in a chiral $p$ -wave superconductor in the quantum limit

Takeshi Daino, Masanori Ichioka, Takeshi Mizushima, and Yukio Tanaka

Phys. Rev. B 86, 064512 – Published 9 August 2012

Abstract

Solving the Bogoliubov–de Gennes equation, we study the spatial structure of odd-frequency $s$ -wave Cooper-pair amplitudes at each quantized energy level of vortex bound states in chiral $p$ -wave superconductors. For zero-energy Majorana states, the odd-frequency $s$ -wave pair amplitude has the same spatial structure as that of the local density of states even in an atomic length scale. This relation also holds in finite energy bound states for single vortex winding antiparallel to the chirality, but not for parallel vortex winding. The double winding vortex case is also studied.