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Motivated by recent experimental progress in high-resolution scanningtunneling microscopy (STM) techniques, we propose to investigate the localquasiparticle density of states around a unitary impurity in the heavy fermionsuperconductor CeCoIn$_{5}$. Based on the T-matrix approach we obtain a sharpnearly zero-energy resonance state (ZERS) in the strong impurity potentialscattering localized around the impurity, and find qualitative differences inthe spatial pattern of the tunneling conductance modulated by the nodalstructure of the superconducting gap. These unique features may be used as aprobe of the superconducting gap symmetry and in combination with the furtherSTM measurements, may help to confirm the $d_{x^{2}-y^{2}}$ pairing inCeCoIn$_{5}$ at ambient pressure.

Spatial modulation of a unitary impurity-induced resonances in superconducting CeCoIn$_{5}$