Bogoliubov angle and visualization of particle-hole mixture in superconductors

Abstract

Superconducting excitations---Bogoliubov quasiparticles---are the quantum-mechanical mixture of negatively charged electron $(\ensuremath{-}e)$ and positively charged hole $(+e)$. Depending on the applied voltage bias in scanning tunneling microscope (STM), one can sample the particle and hole contents of such a superconducting excitation. Recent STM experiments offer unique insight into the inner workings of the superconducting state of superconductors. We propose an observable quantity for STM studies that is a manifestation of the particle-hole dualism of the quasiparticles. We call it a Bogoliubov angle. This angle measures the relative weight of particle and hole amplitudes in the superconducting (Bogoliubov) quasiparticle. We argue that this quantity can be measured locally by comparing the ratios of tunneling currents at positive and negative biases. This Bogoliubov angle allows one to measure directly the energy and position dependent particle-hole admixtures and therefore visualize robustness of superconducting state locally. It may also allow one to measure the particle-hole admixture of excitations in normal state above critical temperature and thus may be used to measure superconducting correlations in pseudogap state.