Impurity effect on Bogoliubov Fermi surfaces: Analysis based on iron-based superconductors

TL;DR

This work analyzes impurity effects on Bogoliubov Fermi surfaces using a realistic FeSe-derived tight-binding model with a time-reversal breaking inter-band pairing. By computing Green's functions and self-energies within the (self-consistent) Born approximation, it reveals that impurity scattering induces an off-diagonal, odd-frequency bogolon pairing component that yields a finite zero-energy peak in the local density of states, of about 1% of the clean DOS in the Born limit. The peak height depends on the impurity type (non-magnetic vs magnetic) but is largely insensitive to impurity density in the Born regime, and self-consistent treatment can enhance the peak for certain BFS directions. The results connect BFS physics to observable spectral features in Fe(Se,S) and provide a quantitative framework for impurity effects in BFS systems more broadly.

Abstract

The effect of impurities on a superconductor with Bogoliubov Fermi surfaces (BFSs) is studied using a realistic tight-binding model. Based on the band structure composed of $d$-orbitals in tetragonal FeSe, whose S-doped sample is a potential material for BFS, we construct the superconducting state by introducing a time-reversal broken pair potential in terms of the band index. We further consider the effect of impurities on the BFS, where the impurity potential is defined as a local potential for the original $d$-orbitals. The self-energy is calculated using the (self-consistent) Born approximation, which shows an enhancement of the single-particle spectral weight on the Fermi surface. This is consistent with the previous phenomenological theory and is justified by the present more detailed calculation based on the FeSe-based material.

Figures (6)

• Figure 1: Schematic table for the mechanism of odd-frequency pairing of bogolons and its comparison with the $s$-wave superconductor. The second row ('Clean') shows the frequency dependence of the Cooper pairs in the clean limit. The third row ('Dirty') shows that of the dirty superconductor. The pairs that remain after the impurity average is indicated in the fourth row.
• Figure 2: Flow of the calculation. The normal part is discussed in Sec. \ref{['sec:bfs']}-A, while Sec. \ref{['sec:bfs']}-B and -C deal with the superconductivity part. We list the notations of the Hamiltonians, the eigenenergies and vectors for each part as shown in the figure. We discuss the impurity effect in Sec. \ref{['sec:imp']}.
• Figure 3: (a) Normal Fermi surfaces (gray) and BFSs (red). The magnified view of the BFSs are shown in (b). (c) Zero-energy spectral function for clean limit. The horizontal axis labeled as $k_\parallel$ is path shown by the arrows in (b), in which the beginning of the path is shown by black point. The characteristic $\bm k$ points are indicated by green circles in (b), and the corresponding $\bm k$ points are shown by the same symbols in (b). The number of $k_\parallel$ mesh in (c) is $88$ on the BFSs. The energy unit is taken as $\mathrm{eV}$.
• Figure 4: Comparison between different kinds of impurities. (a) Energy dependence of the density of states, (b) Wave-vector dependent spectral function on the BFSs. The horizontal axis of (b) is taken in the same way as Fig. \ref{['fig:fermi']} (c).
• Figure 5: Self-energies of bogolon obtained by the Born approximation for (a) normal part, (b) anomalous part, and (c) the ratio of the normal and anomalous parts. The horizontal axis is taken in the same way as Fig. \ref{['fig:fermi']} (c).