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Bulletin of the American Physical Society

From 2D semimetal to topological Fulde-Ferrell superfluid in fermionic ultracold atoms

Ting Fung Jeffrey Poon, Xiong-Jun Liu

Published Mar 15, 2017• 0 citations
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From a semimetal to a chiral Fulde-Ferrell superfluid

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The recent realization of two-dimensional (2D) synthetic spin-orbit (SO) coupling opens a broad avenue to explore novel topological states for ultracold atoms. Here, we propose a scheme to realize chiral Fulde-Ferrell superfluid for ultracold fermions, and show a generic theory that the topology of chiral superfluid phases can be uniquely determined from the normal states. The main findings are twofold. First, a semimetal is driven by a type of 2D SO coupling, and can be tuned into massive Dirac fermion phase with or without inversion symmetry. Without inversion symmetry, the superfluid phase of nonzero pairing momentum is favored under an attractive interaction. Furthermore, we show a fundamental theorem that the Chern number of a 2D chiral superfluid can be obtained from the 1D invariants of Fermi surfaces, with which the chiral Fulde-Ferrell superfluid with a broad topological region is predicted. This generic theorem is also useful for condensed-matter physics and material science in the search for new topological superconductors.

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Majorana fermions in quasi-1D and higher dimensional ultracold optical lattices

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The recent realization of two-dimensional (2D) synthetic spin-orbit (SO) coupling opens a broad avenue to explore novel topological states for ultracold atoms. Here, we propose a scheme to realize chiral Fulde-Ferrell superfluid for ultracold fermions, and show a generic theory that the topology of chiral superfluid phases can be uniquely determined from the normal states. The main findings are twofold. First, a semimetal is driven by a type of 2D SO coupling, and can be tuned into massive Dirac fermion phase with or without inversion symmetry. Without inversion symmetry, the superfluid phase of nonzero pairing momentum is favored under an attractive interaction. Furthermore, we show a fundamental theorem that the Chern number of a 2D chiral superfluid can be obtained from the 1D invariants of Fermi surfaces, with which the chiral Fulde-Ferrell superfluid with a broad topological region is predicted. This generic theorem is also useful for condensed-matter physics and material science in the search for new topological superconductors.
We show that Majorana fermions (MFs) exist in twoand three-dimensional (2D,3D) fermionic optical lattices with strictly 1D spin-orbit coupling (SOC) which has already been realized in experiments. For a quasi-1D topological BCS superfluid, there are multiple MFs at each end which are topologically protected by a chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero energy flat band. An additional experimentally tunable in-plane Zeeman field drives the system to a topological Fulde-Ferrell (FF) superfluid phase. We find that even though the multiple MFs are robust against the in-plane Zeeman field if the order parameters at the different chains are enforced to be identical, they are destroyed in the self-consistently obtained FF phase where the order parameters are inhomogeneous on the boundaries. Our results are useful to guide the experimentalists on searching for MFs in the context of ultracold fermionic atoms.