Topological Phases of Fermionic Ladders with Periodic Magnetic Fields

TL;DR

This paper explores how periodic synthetic magnetic fields in fermionic ladder systems can induce topological phases, revealing complex band structures and edge states through numerical analysis.

Contribution

It introduces a novel scheme using periodic magnetic fields to realize topological phases in fermionic ladders, extending previous uniform flux studies.

Findings

Identification of topological band structures and edge states.

Observation of non-zero Chern numbers and Hofstadter-like spectra.

Complete phase diagram of non-interacting fermionic ladders.

Abstract

In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting many-body states were observed. Motivated by these experiments, we extend the uniform synthetic magnetic field to a periodic case and show that a commensurate synthetic magnetic field offers an alternative scheme to realize topological phases in many-body systems of ultra-cold Fermi gases in ladder-like optical lattices. Using the exact diagonalization, we numerically determine the topological band structure, edge states, non-zero Chern numbers, Hofstadter-like-butterfly spectrum, and a complete phase diagram of non-interacting fermionic ladders.