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arXiv:1607.05109 · Physical Review A

Exotic topological states with Raman-induced spin-orbit coupling

Y. Deng, Tao Shi, Hui Hu, Li You, S. Yi

Published Feb 13, 2017• 5 citations
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Abstract

We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin flip in ultracold pseudospin-$1/2$ atomic Fermi gases trapped in optical lattices. In the absence of interspecies interactions, the system supports type-I and II Weyl semimetals in three-dimensional and gapped Chern insulators and gapless topological semimetal states in two-dimensional lattices. By turning on the $s$-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, which supports the chiral edge states at opposite boundaries with the same chirality, is predicted.

DOI
10.1103/physreva.95.023611

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We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin flip in ultracold pseudospin-1/21/21/2 atomic Fermi gases trapped in optical lattices. In the absence of interspecies interactions, the system supports type-I and II Weyl semimetals in three-dimensional and gapped Chern insulators and gapless topological semimetal states in two-dimensional lattices. By turning on the sss-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, which supports the chiral edge states at opposite boundaries with the same chirality, is predicted.
We theoretically predict a topological matter---topological inhomogeneous Fulde-Ferrell superfluid---in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near sss-wave Feshbach resonances. The realization of such a spin-orbit-coupled Fermi system has already been demonstrated recently by using a two-photon Raman process and the extra one-dimensional confinement is easy to achieve using a tight two-dimensional optical lattice. The topological Fulde-Ferrell superfluid phase is characterized by a nonzero center-of-mass momentum and a nontrivial Berry phase. By tuning the Rabi frequency and the detuning of Raman laser beams, we show that such an exotic topological phase occupies a significant part of parameter space and therefore it could be easily observed experimentally, by using, for example, momentum-resolved and spatially resolved radio-frequency spectroscopy.
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.
Topological superfluids usually refer to a superfluid state which is gapped in the bulk but metallic at the boundary. Here we report that a gapless, topologically nontrivial superfluid with an inhomogeneous Fulde-Ferrell pairing order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas, in the presence of both in-plane and out-of-plane Zeeman fields. The Fulde-Ferrell pairing-induced by the spin-orbit coupling and in-plane Zeeman field-is responsible for this gapless feature. This exotic superfluid has a significant Berezinskii-Kosterlitz-Thouless transition temperature and has robust Majorana edge modes against disorder owing to its topological nature.
We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit-coupled atomic Fermi gases under a Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well known that the system is either a Bardeen-Cooper-Schrieffer superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zero-energy Majorana modes. However, in the weakly interacting regime the topological superfluid prefers to stay at the trap edge, in contrast to a FFLO superfluid, which occurs near the trap center. As a result, it is unlikely to experimentally observe an inhomogeneous FFLO superfluid with topo-logical order without specifically tailoring the geometry or other parameters of the Fermi cloud.
We theoretically predict an exotic topological superfluid state with a spatially modulated pairing gap in one-dimensional spin-orbit-coupled Fermi gases. This inhomogeneous topological superfluidity is induced by applying simultaneously a perpendicular Zeeman magnetic field and an equally weighted Rashba and Dresselhaus spin-orbit coupling in one-dimensional optical lattices. Based on the self-consistent Bogoliubov-de Gennes theory, we confirm that this novel topological phase is a unique condensation of Cooper pairs, which manifests the interplay between the inhomogeneity of a superfluid and its nontrivial topological structure. The properties of the emergent Majorana bound states are investigated in detail by examining the associated Z2 topological number, the eigenenergy and density of states spectra, as well as the wave functions of the localized Majorana end modes. The experimental feasibility of observing this new topological state of matter is also discussed.
The recent experimental realization of spin-orbit (SO) coupling for ultracold bosons and fermions opens an exciting avenue for engineering quantum matter that may be challenging to realize in solid-state materials such as SO-coupled pseudospin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been experimentally realized, the generation of two-dimensional (2D) SO coupling and its topological properties are largely unexplored. Here we propose an experimental scheme for realizing a 2D Rashba-type SO coupling in a square lattice for pseudospin-1 Fermi gases. Because of the extended spin degree of freedom, many interesting topological phases could exist without relying on lattice point group symmetries that are crucial in solid-state materials. These exotic phases include triply degenerate points, quadratic band touching, a large Chern number (C=5C=5C=5) superfluid with five Majorana modes, triple-Weyl fermions, and so on. Our scheme can be generalized to larger spins and provides a distinctive route for engineering topological quantum matter by utilizing large spin degrees of freedom, instead of specific lattice symmetries.