Superconducting excitations -- Bogoliubov quasiparticles -- are the quantum mechanical mixture of negatively charged electron (-e) and positively charged hole (+e). We propose a new observable for Angular Resolved Photoemission Spectroscopy (ARPES) studies that is the manifestation of the particle-hole entanglement of the superconducting quasiparticles. We call this observable a {\em Bogoliubov angle}. This angle measures the relative weight of particle and hole amplitude in the superconducting (Bogoliubov) quasiparticle. We show how this quantity can be measured by comparing the ratio of spectral intensities at positive and negative energies.
We performed high-resolution angle-resolved photoemission spectroscopy on triple-layered high-Tc cuprate Bi2Sr2Ca2Cu3O10+delta. We have observed the full energy dispersion (electron and hole branches) of Bogoliubov quasiparticles and determined the coherence factors above and below EF as a function of momentum from the spectral intensity as well as from the energy dispersion based on BCS theory. The good quantitative agreement between the experiment and the theoretical prediction suggests the basic validity of BCS formalism in describing the superconducting state of cuprates.
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 Bogoliub…
We use the Bogoliubov-de Gennes formalism to analyze the ground state phases of harmonically trapped two-species fermion mixtures with unequal masses. In the weakly attracting limit and around unitarity, we find that the superfluid order parameter is spatially modulated around the trap center, and that its global maximum occurs at a finite distance away from the trap center where the mixture is locally unpolarized. As the attraction strength increases towards the molecular limit, the spatial modulations gradually disappear while the Bardeen-Cooper-Schrieffer (BCS) type nonmodulated superfluid …
Low-lying one-particle anomalous excitations are studied for Gutzwiller projected strongly correlated BCS states. It is found that the one-particle anomalous excitations are highly coherent, and the numerically calculated spectrum can be reproduced quantitatively by a renormalized BCS theory, thus strongly indicating that the nature of low-lying excitations described by the projected BCS states is essentially understood within a renormalized Bogoliubov quasi-particle picture. This finding resembles a well known fact that a Gutzwiller projected Fermi gas is a Fermi liquid. The present results a…
Numerical study of momentum-dependent gap function is presented to make clear the origin of superconductivity in copper oxides. We claim that antinodal region with pronounced nesting feature of the Fermi contour gives rise to superconducting pairing with large momentum under screened Coulomb repulsion. Such a pairing results in both spatial checkerboard pattern of the superconducting state below Tc and a gapped state of incoherent pairs in a broad temperature range above Tc. We explain the momentum dependence of the coherent spectral weight detected in angle-resolved photoemission spectroscopy…
We have performed high-resolution angle-resolved photoemission spectroscopy on YBa2Cu3O7-delta (Y123; delta = 0.06; Tc = 92 K). By accurately determining the Fermi surface and energy band dispersion, we solve long-standing controversial issues as to the anomalous electronic states of Y-based high-Tc cuprates. We unambiguously identified surface-bilayer-derived bonding and antibonding bands, together with their bulk counterparts. The surface bands are highly overdoped (hole concentration x = 0.29), showing no evidence for the gap opening or the dispersion anomaly in the antinodal region, while …
We show that in the presence of a pseudogap, the spectral function in the superconducting state of the underdoped cuprates exhibits additional Bogoliubov quasiparticle peaks at both positive and negative energy which are revealed by the particle-hole asymmetry of the pseudogapped energy bands. This provides direct information on the unoccupied band via measurement of the occupied states. When sufficiently close, these Bogoliubov peaks will appear to merge with existing peaks leading to the anomalous observation, seen in experiment, that the carrier spectral density broadens with reduced temper…
Super-high resolution laser-based angle-resolved photoemission measurements have been performed on a high temperature superconductor Bi_2Sr_2CaCu_2O_8. The band back-bending characteristic of the Bogoliubov-like quasiparticle dispersion is clearly revealed at low temperature in the superconducting state. This makes it possible for the first time to experimentally extract the complex electron self-energy and the complex gap function in the superconducting state. The resultant electron self-energy and gap function exhibit features at ~54 meV and ~40 meV, in addition to the superconducting gap-in…
Quasiparticle interference (QPI) by means of scanning tunneling microscopy/spectroscopy (STM/STS), angle resolved photoemission spectroscopy (ARPES), and multi-orbital tight bind- ing calculations are used to investigate the band structure and superconducting order parameter of LiFeAs. Using this combination we identify intra- and interband scattering vectors between the hole (h) and electron (e) bands in the QPI maps. Discrepancies in the band dispersions inferred from previous ARPES and STM/STS are reconciled by recognizing a difference in the $k_z$ sensitivity for the two probes. The observ…
Nanoscale inhomogeneity seems to be a central feature of the d-wave superconductivity in the cuprates. Such a feature can strongly affect the local density of states (LDOS) and the spectral weight functions. Within the Bogoliubov-de Gennes formalism we examine various inhomogeneous configurations of the superconducting order parameter to see which ones better agree with the experimental data. Nanoscale large amplitude oscillations in the order parameter seem to fit the LDOS data for the underdoped cuprates. The one-particle spectral function for a general inhomogeneous configuration exhibits a…
Using inhomogeneous Bogoliubov-de Gennes formalism we study superconducting properties of bundles of single wall carbon nanotubes, consisting of a mixture of metallic and semiconducting nanotubes, having different critical transition temperatures. We investigate how the averaged superconducting order parameter and the critical transition temperature depend on the fraction of semiconducting carbon nanotubes in the bundle.
We analyze evolution of the single particle excitation spectrum of the underdoped cuprate superconductors near the anti-nodal region, considering temperatures below and and above the phase transition. We inspect the phenomenological self-energy that reproduces the angle-resolved-photoemission-spectroscopy (ARPES) data and we show that above the critical temperature, such procedure implies a transfer of the spectral weight from the Bogoliubov-type quasiparticles towards the in-gap damped states. We also discuss some possible microscopic arguments explaining this process.
In copper- and iron-based unconventional superconductors, the Bogoliubov quasiparticles interact with a spin resonance at momentum $(π,π)$. This interaction is revealed by specific signatures in the quasiparticle spectroscopies, like kinks in photoemission and dips in tunneling. We study these signatures, as they appear inside and around a vortex core in the local density of states (LDOS), a property accessible experimentally by scanning tunneling spectroscopy. Our model retains the whole nonlocal structure of the self-energy in space and time and is therefore not amenable to a Hamiltonian tre…
Angle-resolved photoemission on underdoped La$_{1.895}$Sr$_{0.105}$CuO$_4$ reveals that in the pseudogap phase, the dispersion has two branches located above and below the Fermi level with a minimum at the Fermi momentum. This is characteristic of the Bogoliubov dispersion in the superconducting state. We also observe that the superconducting and pseudogaps have the same d-wave form with the same amplitude. Our observations provide direct evidence for preformed Cooper pairs, implying that the pseudogap phase is a precursor to superconductivity.
Hybridization of Bogoliubov-quasiparticles between adjacent CuO$_2$ layers in the triple-layer cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ studied by ARPES
High-resolution angle-resolved photoemission experiments reveal subtle modifications of the surface electronic structure of VSe2. Most remarkably, we show that superconductivity can be induced in VSe2 by the right selection of substrate and growth parameters. Evidence for the superconducting state comes from the simultaneous detection of spectral kink, quasiparticle peak, Fermi gap, and their evolution with the temperature. The observation of Bogoliubov-like back-bending bands at low temperatures, signaling electron-hole pairing, further supports the presence of superconductivity in this syste…
We develop an analytical tool to extract bulk electronic properties of unconventional superconductors through inelastic neutron scattering (INS) spectra. Since the spin excitation spectrum in the superconducting (SC) state originates from Bogoliubov quasiparticle scattering associated with Fermi surface nesting, its energy-momentum relation--the so called `hour-glass' feature--can be inverted to reveal the Fermi momentum dispersion of the single-particle spectrum as well as the corresponding SC gap function. The inversion procedure is analogous to the quasiparticle interference (QPI) effect in…
Usually the superconducting pairing is considered to modify electronic states only in a narrow momentum range close to the Fermi surface. Here we present a direct experimental observation of fusion of Bogoliubov dispersion branches originating from the antipodal Fermi crossings by means of angle-resolved photoemission spectroscopy (ARPES). Uncommon discernibility and brightness of bogoliubons' fusion stems from comparability of the superconducting gap magnitude and the distance from the Fermi level to the band's top, and strong electron scattering on a mode with similar energy. Such similarity…
Many complex electronic systems exhibit so-called pseudogaps, which are poorly-understood suppression of low-energy spectral intensity in the absence of an obvious gap-inducing symmetry. Here we investigate the superconductor $Ba_{1-x}K_{x}BiO_{3}$ near optimal doping, where unconventional transport behavior and evidence of pseudogap(s) have been observed above the superconducting transition temperature $T_{c}$, and near an insulating phase with long-range lattice distortions. Angle-resolved photoemission spectroscopy (ARPES) reveals a dispersive band with vanishing quasiparticle weight and "t…
Using a scenario of a hybridized mixture of localized bipolarons and conduction electrons, we demonstrate for the latter the simultaneous appearance of a pseudogap and of strong incoherent contributions to their quasi-particle spectrum which arise from phonon shake-off effects. This can be traced back to temporarily fluctuating local lattice deformations, giving rise to a double-peak structure in the pair distribution function, which should be a key feature in testing the origin of these incoherent contributions, recently seen in angle-resolved photoemission spectroscopy (ARPES).
Motivated by recent experimental reports of significant spin-orbit coupling (SOC) and a sign-changing order-parameter in the Li$_{1-x}$Fe$_x$(OHFe)$_{1-y}$Zn$_y$Se superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states - $s$-wave, $d$-wave and helical $p$-wave - can have a fully gapped density of states (DOS) consistent with angle-resolved photoemission spectroscopy (ARPES) experiments and, due to spin-orbit coupling, are a mixture of spin singlet and tri…
We study the quasiparticle spectrum of 2D topological $s$-wave superconductors with the Zeeman magnetic field and the Rashba spin-orbit coupling in the presence of spatial inhomogeneity. Solving the real-space Bogoliubov-de Gennes equations, we focus on the excitations within the superconducting gap amplitude, i.e., the appearance of mid-gap states. Two kinds of potential functions, line-type (a chain of impurities) and point-type (a single impurity) ones are examined to take spatial inhomogeneity into account. The line setting shows a link of the mid-gap states with the gapless surface modes …
