Fulde-Ferrell states in inverse proximity-coupled magnetically doped topological heterostructures

We study the superconducting properties of the thin film BCS superconductor proximity coupled to a magnetically doped time-reversal invariant topological insulator (TI). Using mean-field theory, we show that Fulde-Ferrell (FF) pairing can be induced in the conventional superconductor through the inverse proximity effect (IPE). This occurs when the IPE of the TI to the superconductor is large enough that the normal bands of the superconductor possess a proximity induced spin-orbit coupling and magnetization. We find that the energetics of the different pairings are dependent on the coupling strength between the TI and the BCS superconductor and the thickness of the superconductor film. As the thickness of the superconductor film is increased, we find a crossover from the FF pairing to the BCS pairing phase. This is a consequence of the increased number of the superconducting bands, which favor the BCS pairing, implying that the FF phase can only be observed in the thin film limit. In addition, we also propose transport experiments that show distinct signatures of the FF phase.