Bogoliubov angle and visualization of particle-hole mixture in superconductors

TL;DR

This paper introduces the Bogoliubov angle, a new observable for STM that visualizes the particle-hole mixture in superconductors, enabling local measurement of quasiparticle composition and superconducting correlations.

Contribution

It proposes the Bogoliubov angle as a novel local measurement tool for particle-hole admixture in superconductors using STM, enhancing understanding of superconducting states and correlations.

Findings

Defines the Bogoliubov angle as a measure of particle-hole mixture.

Suggests measuring the angle via tunneling current ratios at different biases.

Potentially applicable to normal state and pseudogap regimes.

Abstract

Superconducting excitations --Bogoliubov quasiparticles -- are the quantum mechanical mixture of negatively charged electron (-e) and positively charged hole (+e). Depending on the applied voltage bias in STM one can sample the particle and hole content of such a superconducting excitation. Recent Scanning Tunneling Microscope (STM) experiments offer a unique insight into the inner workings of the superconducting state of superconductors. We propose a new observable quantity for STM studies that is the manifestation of the particle-hole dualism of the quasiparticles. We call it a {\em Bogoliubov angle}. This angle measures the relative weight of particle and hole amplitude in the superconducting (Bogoliubov) quasiparticle. We argue that this quantity can be measured locally by comparing the ratio of tunneling currents at positive and negative biases. This Bogoliubov angle allows one to measure directly the energy and position dependent particle-hole admixture 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.