Local Chern marker of smoothly confined Hofstadter fermions

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.

arXiv comment6 pages, 6 figures

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Cited by in corpus (7)

• Local Topological Markers in Odd Dimensions
• Local marker for interacting topological insulators
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• 1D quasicrystals and topological markers
• Superfluid transition temperature and fluctuation theory of spin-orbit and Rabi-coupled fermions with tunable interactions
• Flow of unitary matrices: Real-space winding numbers in one and three dimensions
• Regularized universal topological markers for Dirac systems