Abstract
We propose to use a one-dimensional system consisting of identical fermions in a periodically driven lattice immersed in a Bose gas, to realise topological superfluid phases with Chern numbers larger than 1. The bosons mediate an attractive induced interaction between the fermions, and we derive a simple formula to analyse the topological properties of the resulting pairing. When the coherence length of the bosons is large compared to the lattice spacing and there is a significant next-nearest neighbour hopping for the fermions, the system can realise a superfluid with Chern number ±2. We show that this phase is stable in a large region of the phase diagram as a function of the filling fraction of the fermions and the coherence length of the bosons. Cold atomic gases offer the possibility to realise the proposed system using well-known experimental techniques.
Highlights
Until fairly recently, only a few topological phases were known to exist in nature [1,2,3,4]
The aim of this paper is to show how the character of the topological invariant of a generalised Kitaev model can be realised in an experimentally realistic system consisting of identical fermions in a 1D lattice immersed in a 1D Bose gas
We demonstrate that the system can realise a phase with Chern number ±2, when the coherence length of the bosons is large and the fermions has a significant next-nearest neighbour hopping
Summary
Only a few topological phases were known to exist in nature [1,2,3,4]. The Kitaev wire has, in addition to a particle–hole symmetry, a timereversal symmetry which squares to be one It follows that it belongs to class BDI in the classification scheme of topogical insulators and superfluids. This class has a topological invariant in 1D [18,19,20], and it allows the existence of multiple orthogonal Majorana edge states. In order to bring out this character of the topological invariant and the associated multiplicity of Majorana states, one needs to generalise the Kitaev model to include long range pairing and hopping This has been demonstrated in several models where the long range nature has been introduced by hand [21,22,23]
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