Local Electronic Structure around a Single Impurity as a Test of Pairing Symmetry in (K,Tl)Fe$_{x}$Se$_{\rm 2}$ Superconductors

TL;DR

This study investigates how a single impurity affects local electronic states in (K,Tl)Fe$_x$Se$_2$ superconductors to determine their pairing symmetry, using theoretical models and proposing STM experiments for validation.

Contribution

It demonstrates that impurity-induced resonance states are unique to $d_{x^2-y^2}$-wave pairing among considered symmetries, providing a method to identify pairing symmetry in these superconductors.

Findings

Only $d_{x^2-y^2}$-wave pairing produces impurity resonance states.

Intra-gap states are far from the Fermi energy.

Resonance features are robust against inter-band scattering.

Abstract

We have studied the effect of a single nonmagnetic impurity in the recently discovered (K,Tl)Fe$_x$Se$_2$ superconductors, within both a toy two-band model and a more realistic five-band model. We have found that, out of five types of pairing symmetry under consideration, only the $d_{x^2-y^2}$-wave pairing gives rise to impurity resonance states. The intra-gap states have energies far away from the Fermi energy. The existence of these intra-gap states is robust against the presence or absence of inter-band scattering. However, the inter-band scattering does tune the relative distribution of local density of states at the resonance states. All these features can readily be accessed by STM experiments, and are proposed as a means to test pairing symmetry of the new superconductors.