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 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.

Electronic structure of cuprate superconductors in a full charge-spin recombination scheme

“…3, the thick solid curve is the momentum distribution curve where the electron coherence factors U 2 k = V 2 k at the electron Fermi energy. It is apparent that the theoretical result captures the qualitative feature of the momentum dependence of the electron spectrum observed experimentally on cuprate superconductors in the SC-state 5,6,[15][16][17][18][19][20][21][22][23] . There are two branches of dispersion centered at the electron Fermi energy, however, two sharp low-energy SC quasiparticle peaks in each energy distribution curve exhibit an evolution of the relative peak height at different momentum positions due to the momentum dependence of the coherence factors.…”

“…Later, the ARPES experimental studies show that in the underdoped and optimally doped regimes, although the antinodal region of the electron Fermi surface is gapped out, leading to the notion that only part of the electron Fermi surface survives as the disconnected Fermi arcs around the nodes [28][29][30][31][32] , the underlying electron Fermi surface determined from the low-energy spectral weight still fulfills Luttinger's theorem in the entire doping range 32 . These ARPES experimental facts [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] on the other hand provide strong evidences supporting the notion of the charge-spin recombination 13,14 . Since the electron Fermi surface is a fundamental property of interacting electron systems, the study of the nature of the electron Fermi surface should be crucial for understanding the electronic structure of cuprate superconductors.…”

“…However, one of the most striking dilemmas is that the SC coherence of the low-energy quasiparticle excitations in cuprate superconductors seems to be described by the standard Bardeen-Cooper-Schrieffer (BCS) formalism [15][16][17][18][19] , although the normal-state is undoubtedly not the standard Landau Fermi-liquid on which the conventional electron-phonon theory is based. Angle-resolved photoemission spectroscopy (ARPES) experiments reveal sharp spectral peaks in the singleparticle excitation spectrum 5,6,[15][16][17][18][19][20][21][22][23] , indicating the presence of quasiparticle-like states, which is also consistent with the long lifetime of the electronic state as it has been determined by the conductivity measurements 10,11 . In particular, as a direct method for probing the electron Fermi surface, the early ARPES measurements indicate that in the entire doping range, the underlying electron Fermi surface satisfies Luttinger's theorem [24][25][26][27] , i.e., the electron Fermi surface with the area is proportional to 1 − δ.…”

Universal disorder in Bi2Sr2CaCu2OAlldredge1, Fujita2, Eisaki3 et al. 2013Phys. Rev. BSelf Cite

“…Of course if there is an LDOS(E) modulation that exists in phase on both sides of zero bias, then it will be canceled out in the Z-map as well. This is why q 5 in the dispersive QPI is suppressed when the ratio map is taken 5,11,49 .…”

Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

“…Due to superconducting coherence factors, the Z-map in fact enhances the intensity of LDOS modulations from QPI, as discussed in Ref. 28. To summarize their argument, since STS tunnels electrons rather than quasiparticles, the strength of the measured conductance at r depends on the magnitude of the hole and electron amplitudes, |u n (r)| 2 and |v n (r)| 2 (n labels the eigenvalue of excitations).…”