Spin-orbit coupled fermions offer a fascinating playground for realizing interesting topological quantum phases and the associated quantum critical phenomena. In two dimensions and in the presence of an attractive s-wave pairing interaction and a Zeeman field, spin-orbit coupled fermions can condense into a fully gapped non-Abelian topological superfluid phase separated from a conventional s-wave superfluid phase by a topological quantum phase transition. The critical point for this transition is marked by the proliferation of gapless nodal quasiparticles which can be tracked by studying the momentumresolved excitation spectrum from the center of the Brillouin zone. In three dimensions the same system goes through a series of topological quantum transitions with increasing Zeeman field and the low energy excitations in some of these phases realize the long-sought low-temperature analog of Weyl fermions of particle physics. In this talk I will describe in some detail the interesting topological phases and the associated quantum criticality that can be realized using spin-orbit coupled fermions in cold atom systems.
Spin-orbit coupled fermions offer a fascinating playground for realizing interesting topological quantum phases and the associated quantum critical phenomena. In two dimensions and in the presence of an attractive s-wave pairing interaction and a Zeeman field, spin-orbit coupled fermions can condense into a fully gapped non-Abelian topological superfluid phase separated from a conventional s-wave superfluid phase by a topological quantum phase transition. The critical point for this transition is marked by the proliferation of gapless nodal quasiparticles which can be tracked by studying the momentumresolved excitation spectrum from the center of the Brillouin zone. In three dimensions the same system goes through a series of topological quantum transitions with increasing Zeeman field and the low energy excitations in some of these phases realize the long-sought low-temperature analog of Weyl fermions of particle physics. In this talk I will describe in some detail the interesting topological phases and the associated quantum criticality that can be realized using spin-orbit coupled fermions in cold atom systems.
We develop a theory for interacting fermions in the presence of spin-orbit coupling and Zeeman fields, and show that many new superfluids phases, which are topological in nature, emerge. Depending on values of spin-orbit coupling, Zeeman fields, and interactions, initially gapped s-wave superfluids acquire p-wave, d-wave, f-wave and higher angular momentum components, which produce zeros in the excitation spectrum, rendering the superfluid gapless. Several multi-critical points, which separate topological superfluid phases from normal or non-uniform, are accessible depending on spin-orbit coupling, Zeeman fields or interactions, setting the stage for the study of tunable topological superfluids.
Abstract The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
We investigate the BCS-BEC crossover in three-dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a nontopological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum-resolved photoemission spectroscopy.
Topological Fermi superfluids have played the central role in various fields of physics. However, all previous studies focus on the cases where Cooper pairs have zero center-of-mass momenta (i.e., normal superfluids). The topology of Fulde–Ferrell (FF) superfluids with nonzero momentum pairings have never been explored until recent findings that FF superfluids in a spin–orbit (SO) coupled Fermi gas can accommodate Majorana fermions in real space in low dimensions and Weyl fermions in momentum space in three dimension. In this review, we first discuss the mechanism of pairings in SO coupled Fermi gases in optical lattices subject to Zeeman fields, showing that SO coupling as well as Zeeman fields enhance FF states while suppress Larkin–Ovchinnikov states. We then present the low temperature phase diagram including both FF superfluids and topological FF superfluids phases in both two dimension and three dimension. In one dimension, Majorana fermions as well as phase dependent order parameter are visualized. In three dimension, we show the properties of Weyl fermions in momentum space such as anisotropic linear dispersion, Fermi arch, and gaplessness away from k⊥ = 0. Finally, we discuss some possible methods to probe FF superfluids and topological FF superfluids in cold atom systems.
Abstract The equal Rashba-Dresselhaus (ERD) spin-orbit coupling, as the first type to be implemented in cold atom experiments, provides a unique platform for exploring topological quantum phases. This work investigates the ground state of a two-dimensional Fermi gas featuring both ERD coupling and a Zeeman field, mapping out its topological phase diagram throughout the BCS-BEC crossover. We classify the homogeneous superfluid phases into topologically trivial gapped or nontrivial gapless phase based on the nodal structure of the quasiparticle excitation spectrum. We reveal the evolution of topological superfluid states under various conditions by systematically characterizing the phase distribution across key parameters including the spin-orbit coupling strength, two-body binding energy, Zeeman field, and chemical potential. Our findings indicate that spin-orbit coupling enhances triplet pairing and stabilizes the gapless superfluid phase. Moreover, small binding energy, and strong Zeeman field are found to promote the emergence of the gapless phase, particularly the US-II phase identified in this work. These results elucidate the phase transition mechanisms in low-dimensional quantum systems.
The two-dimensional spin-imbalanced Fermi gas subject to s-wave pairing and spin-orbit coupling is considered a promising platform for realizing a topological chiral-p-wave superfluid. In the BCS limit of s-wave pairing, i.e., when Cooper pairs are only weakly bound, the system enters the topological phase via a second-order transition driven by increasing the Zeeman spin-splitting energy. Stronger attractive two-particle interactions cause the system to undergo the BCS-BEC crossover, in the course of which the topological transition becomes first order. As a result, topological and nontopological superfluids coexist in spatially separated domains in an extended region of phase space spanned by the strength of s-wave interactions and the Zeeman energy. Here we investigate this phase-coexistence region theoretically using a zero-temperature mean-field approach. Exact numerical results are presented to illustrate basic physical characteristics of the coexisting phases and to validate an approximate analytical description derived for weak spin-orbit coupling. Besides extending our current understanding of spin-imbalanced superfluid Fermi systems, the present approach also provides a platform for future studies of unconventional Majorana excitations that, according to topology, should be present at the internal interface between coexisting topological and nontopological superfluid parts of the system.