Bogoliubov angle and visualization of particle-hole mixture in superconductors

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.

arXiv comment16 pages, latex file, 9 eps figures

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• Quantum Interference of Impurity Bound States in Bi${}_2$Sr${}_2$Ca(Cu${}_{1-x}$Zn${}_x$)${}_2$O${}_{8+\delta }$ Probed by Scanning Tunneling Spectroscopy
• Unconventional particle-hole mixing in the systems with strong superconducting fluctuations
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• Momentum-resolved spectroscopy of superconductivity with the quantum twisting microscope
• The k-space Origins of Scattering in Bi2Sr2CaCu2O8+x
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• "Half-Bogoliubons" as the intermediate states for the phase coherence in underdoped cuprates