# Fulde-Ferrell States in Inverse Proximity Coupled Magnetically-Doped Topological Heterostructures

## TL;DR

This paper demonstrates that inverse proximity effect in magnetically doped topological insulator-superconductor heterostructures can induce Fulde-Ferrell pairing in the superconductor, with the phase depending on film thickness and coupling strength.

## Contribution

It reveals how inverse proximity effect induces FF pairing in conventional superconductors coupled to topological insulators, highlighting the influence of film thickness and coupling strength.

## Key findings

- FF pairing can be induced by inverse proximity effect.
- Crossover from FF to BCS pairing with increasing superconductor thickness.
- Transport signatures can distinguish the FF phase.

## Abstract

We study the superconducting properties of the thin film BCS superconductor proximity coupled to a magnetically doped topological insulator(TI). Using the mean field theory, we show that Fulde-Ferrell(FF) pairing can be induced in the conventional superconductor by having inverse proximity effect(IPE). This occurs when the IPE of the TI to the superconductor is large enough that the normal band of the superconductor possesses 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.