# Berry phase in superconducting multiterminal quantum dots

## TL;DR

This paper investigates the non-trivial Berry phase in superconducting multiterminal quantum dots, revealing how it affects Floquet spectra and can be detected via tunneling spectroscopy, with implications for quantum transport.

## Contribution

It introduces a Floquet-based model to analyze Berry phases in superconducting quantum dots and predicts observable spectral shifts linked to the Berry phase.

## Key findings

- Berry phase takes values 0 or π at zero energy level
- Floquet spectra are shifted by half a period due to Berry phase
- Spectral shift observable in tunneling density of states

## Abstract

We report on the study of the non-trivial Berry phase in superconducting multiterminal quantum dots biased at commensurate voltages. Starting with the time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model in the Floquet space, and we solve these equations in the semiclassical limit. We observe that the parameter space defined by the contact transparencies and quartet phase splits into two components with a non-trivial Berry phase. We use the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if the quantum dot level sits at zero energy, then the Berry phase takes the values $\varphi_B=0$ or $\varphi_B=\pi$. We demonstrate that this non-trivial Berry phase can be observed by tunneling spectroscopy in the Floquet spectra. Consequently, the Floquet-Wannier-Stark ladder spectra of superconducting multiterminal quantum dots are shifted by half-a-period if $\varphi_B=\pi$. Our numerical calculations based on Keldysh Green's functions show that this Berry phase spectral shift can be observed from the quantum dot tunneling density of states.