# Bound states in a superfluid vortex: A detailed study along the BCS-BEC crossover

## TL;DR

This paper provides a comprehensive theoretical analysis of vortex bound states across the BCS-BEC crossover in superfluids, revealing their evolution with coupling strength and temperature, and offering criteria to identify superfluid phases.

## Contribution

It presents a systematic study using Bogoliubov-de Gennes equations to analyze vortex bound states throughout the BCS-BEC crossover at all temperatures.

## Key findings

- Bound states decrease from BCS to BEC side
- Bound states are absent in the BEC regime
- A scaling relation links bound states to vortex properties

## Abstract

The bound states that can occur in a superfluid vortex have recently called for attention owing to the capability of detecting them experimentally. However, a detailed theoretical account for the presence of these vortex bound states is still lacking, for all temperatures in the superfluid phase and couplings along the BCS-BEC crossover. Here, we fill this gap and present a systematic theoretical study based on the Bogoliubov-de~Gennes equations for the bound states that occur over the two characteristic (inner and outer) spatial ranges in which the extension of a superfluid vortex can be partitioned. It is found that the total number of bound states decreases from the BCS (weak-coupling) side of the crossover toward the intermediate-coupling region where they are still present, whereas the bound states disappear upon entering the BEC (strong-coupling) side. A scaling relation is also obtained that connects the number of bound states in the inner spatial range of the vortex to the depth and width of the vortex itself. A criterion is finally provided in terms of the local density of states, to distinguish where a given fermionic superfluid is located in the coupling-temperature phase diagram of the BCS-BEC crossover.