# Quantum phase diagram of Shiba impurities from bosonization

## TL;DR

This paper uses bosonization to analyze the quantum phase diagram of classical Shiba impurities, revealing how geometry and dimensionality influence phase transitions and proposing a new parity-preserving transition in a nanodevice.

## Contribution

It introduces a bosonization-based analysis of Shiba impurities in different dimensions, uncovering new effects of geometry and proposing a novel

## Key findings

- Quantum phase diagram is affected by geometry and dimensionality.
- A new parity-preserving, spin-changing
- Theoretical prediction of a

## Abstract

A characteristic feature of Shiba impurities is the existence of a spin- and parity-changing quantum phase transition (known as "0-$\pi$" transition) which has been observed in scanning tunneling microscopy (STM) and transport experiments. Using the Abelian bosonization technique, here we analyze the ground-state properties and the quantum phase diagram of a classical (i.e., Ising-like) Shiba impurity. In particular, we analyze the cases of an impurity in a three- and a one-dimensional superconductor. Within the bosonization framework, the ground-state properties are determined by simple soliton-like solutions of the classical equations of motion of the bosonic fields, whose topological charge is related to the spin and parity quantum numbers. Our results indicate that the quantum phase diagram of the superconductor can be strongly affected by geometrical and dimensional effects. Exploiting this fact, in the one-dimensional case we propose an experimental superconducting nanodevice in which a novel parity-preserving, spin-changing "0-0" transition is predicted.