Visualization of atomic-scale phenomena in superconductors: Application to FeSe

Abstract

We propose a simple method of calculating inhomogeneous, atomic-scale phenomena in superconductors which makes use of the wave function information traditionally discarded in the construction of tight-binding models used in the Bogoliubov-de Gennes equations. The method uses symmetrybased first principles Wannier functions to visualize the effects of superconducting pairing on the distribution of electronic states over atoms within a crystal unit cell. Local symmetries lower than the global lattice symmetry can thus be exhibited as well, rendering theoretical comparisons with scanning tunneling spectroscopy data much more useful. As a simple example, we discuss the geometric dimer states observed near defects in superconducting FeSe.

Extensive impurity-scattering study on the pairing symmetry of monolayer FeSe films onSrTiO3

“…Tunneling spectra were acquired at sample temperature of 5 K using a standard lock-in technique with a bias modulation of 0.4 mV at 937 Hz, unless otherwise specified. been interpreted as perturbation at the Fe site that affects the orbitals on neighboring Se atoms [25]. There are several candidates to induce perturbation at the Fe-site, such as Fe-site vacancies, SeFe antisite defects, Fe-site substitutions, as will be shown below.…”

Interpretation of Scanning Tunneling Quasiparticle Interference and Impurity States in Cuprates

“…Many attempts have been made to calculate these patterns assuming simple tight-binding band structures, d-wave pairing, and methods ranging from single-impurity T matrix[31-37] to many-impurity solutions of the BdG equations [38]. While some similarities between the calculated patterns, the simplified so-called "octet model" [31], and experiment have been reported, there are always serious discrepancies, typically related not so much to the positions of peaks but rather their shapes and intensities.In this paper we revisit these classic unsolved problems using a new method called the BdG-Wannier (BdG+W) approach [39], which combines traditional solutions of the Bogoliubov-de Gennes (BdG) equations with the microscopic Wannier functions obtained from downfolding density functional theory onto a low-energy effective tightbinding Hamiltonian. We show that the local density of states (LDOS) obtained from the continuum Green's function for a simple strong nonmagnetic impurity bound state in the BSSCO material with a d-wave superconducting gap displays excellent agreement with STM conductance maps (Fig.…”

“…This can be understood from the fact that the hybridization of the Cu-d x 2 −y 2 orbital with apical O-p and Bi-p orbitals in the same unit cell is forbidden by symmetry. In order to account for correlation effects at low energies, we use a mass renormalization factor of 1/Z = 3 to scale down all hoppings such that the Fermi velocities approximately match the experimentally observed values [41] and fix the chemical potential to be at optimal doping, (n = 0.85).Next, we solve the inhomogeneous mean field BdG equations for the full Hamiltonian of a superconduc-3 tor in presence of an impurity H = H 0 + H BCS + H imp , where the d-wave pairing interaction Γ RR (details in the Supplemental Material [42]) enters the calculation of the superconducting order parameter via ∆ RR = Γ RR c R ↓ c R↑ and gives rise to the second term H BCS = − R,R ∆ RR c † R↑ c † R ↓ + H.c., while the third term is just a nonmagnetic impurity at lattice position R * , e.g.From the BdG eigenvalues E nσ and eigenvectors u nσ and v nσ we can construct the usual retarded lattice Green's functionand the corresponding continuum Greens function [39,43] by a simple basis transformation from the lattice operators c Rσ to the continuum operators ψ σ (r) = R c Rσ w R (r) where the Wannier functions w R (r) are the matrix elements. A similar transformation has been applied previously to understand neutron[44] and xray [45,46] spectra in the normal state.…”

“…In this paper we revisit these classic unsolved problems using a new method called the BdG-Wannier (BdG+W) approach [39], which combines traditional solutions of the Bogoliubov-de Gennes (BdG) equations with the microscopic Wannier functions obtained from downfolding density functional theory onto a low-energy effective tightbinding Hamiltonian. We show that the local density of states (LDOS) obtained from the continuum Green's function for a simple strong nonmagnetic impurity bound state in the BSSCO material with a d-wave superconducting gap displays excellent agreement with STM conductance maps (Fig.…”

Critical Current Oscillations in the Intrinsic Hybrid Vortex State of SmFeAs(O,F)

“…Depending on the orbitals involved in Cooper pair transport along and perpendicularly to the layers, the OP modulation along c varies in strength and shape. It will be an interesting theoretical challenge to develop a microscopic model based on the Fe-and As-orbitals [21] to derive a more realistic form for the potential V (z). Within the simplistic step-function model, the magnitude of V 0 cannot be quantitatively estimated from transport experiments.…”