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

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