# Local Chern marker of smoothly confined Hofstadter fermions

## TL;DR

This paper investigates topological phases in a confined Hofstadter model with interactions, demonstrating the persistence of topological states under various trap geometries and revealing interaction-induced phase transitions and magnetic edge states.

## Contribution

It introduces a local spin Chern marker for confined Hofstadter fermions and explores the effects of interactions on topological phases and magnetic edges.

## Key findings

- Topologically non-trivial phases are observable in all trap geometries.
- Interactions induce a topological phase transition depending on filling.
- Strong interactions lead to magnetic edge states.

## Abstract

The engineering of topological non-trivial states of matter, using cold atoms, has made great progress in the last decade. Driven by experimental successes, it has become of major interest in the cold atom community. In this work we investigate the time-reversal invariant Hofstadter model with an additional confining potential. By calculating a local spin Chern marker we find that topologically non-trivial phases can be observed in all considered trap geometries. This holds also for spin-orbit coupled fermions, where the model exhibits a quantum spin Hall regime at half filling. Using dynamical mean-field theory, we find that interactions compete against the confining potential and induce a topological phase transition depending on the filling of the system. Strong interactions furthermore yield a magnetic edge, which is localized through the interplay of the density distribution and the underlying topological band structure.