Impurity-induced Shiba bound state in the BCS-BEC crossover regime of two-dimensional Fermi superfluid

For a two-dimensional ultra-cold Fermi superfluid with an effective static magnetic impurity, we theoretically investigated the variation of the Yu-Shiba-Rusinov (YSR) bound state in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover regime. Within the framework of mean-field theory, analytical results of the YSR bound state energy were obtained as a function of the interaction parameters. First, when the background Fermi superfluid system stays in the weakly interacting BCS regime, we found that the YSR bound state energy is linearly dependent on the gap parameter with its coefficient slightly different from previous results. Second, we discovered re-entrance phenomena for the YSR state and an upper bound of the strength of the interaction between the paired atoms. By carefully analyzing the bound state energy as a function of the interaction parameters, we obtained a phase diagram showing the existence of the YSR state. Finally, we concluded that the re-entrance phenomena and the critical point can be easily experimentally detected through measurement of radio-frequency spectroscopy and density of states using current experimental techniques.