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Impurity eﬀects on the Quasi-particle spectrum in the Fulde-Ferrell-Larkin-Ovchinnikov state of a d -wave superconductor

In a d -wave superconductor (d-SC), a unitary impurity can induce a near-zero-energy resonant peak in the local tunneling density of states (LTDOS) due to the sign change of the order parameter (OP) on the Fermi Surface. If a d-SC is quasi-two-dimensional, a large parallel magnetic ﬁeld can drive it into the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with an OP also changing sign in the real space like a checkerboard pattern. This “double sign change” leads to very subtle eﬀects by a unitary impurity on the LTDOS for two locally stable locations of the impurity.