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arXiv:1611.08671 · Physical review. B./Physical review. B

Weyl points and topological nodal superfluids in a face-centered-cubic optical lattice

Li-Jun Lang, Shaoliang Zhang, K. T. Law, Qi Zhou

Published Jul 25, 2017• 19 citations
arXivHTMLPDF

Abstract

We point out that a face-centered-cubic (fcc) optical lattice, which can be realized by a simple scheme using three lasers, provides one a highly controllable platform for creating Weyl points and topological nodal superfluids in ultracold atoms. In noninteracting systems, Weyl points automatically arise in the Floquet band structure when shaking such fcc lattices, and sophisticated design of the tunneling is not required. More interestingly, in the presence of attractive interaction between two hyperfine spin states, which experience the same shaken fcc lattice, a three-dimensional topological nodal superfluid emerges, and Weyl points show up as the gapless points in the quasiparticle spectrum. One could either create a double Weyl point of charge 2, or split it into two Weyl points of charge 1, which can be moved in the momentum space by tuning the interactions. Correspondingly, the Fermi arcs at the surface may be linked with each other or separated as individual ones.

DOI
10.1103/physrevb.96.035145

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We point out that a face-centered-cubic (fcc) optical lattice, which can be realized by a simple scheme using three lasers, provides one a highly controllable platform for creating Weyl points and topological nodal superfluids in ultracold atoms. In noninteracting systems, Weyl points automatically arise in the Floquet band structure when shaking such fcc lattices, and sophisticated design of the tunneling is not required. More interestingly, in the presence of attractive interaction between two hyperfine spin states, which experience the same shaken fcc lattice, a three-dimensional topological nodal superfluid emerges, and Weyl points show up as the gapless points in the quasiparticle spectrum. One could either create a double Weyl point of charge 2, or split it into two Weyl points of charge 1, which can be moved in the momentum space by tuning the interactions. Correspondingly, the Fermi arcs at the surface may be linked with each other or separated as individual ones.
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.
The recent discovery of the Lorentz symmetry-violating ``type-II'' Weyl semimetal phase has renewed interest in the study of Weyl physics in condensed-matter systems. However, tuning the exceptional properties of this novel state has remained a challenge. Optical lattices, created using standing laser beams, provide a convenient platform to tune tunneling parameters continuously in time. In this paper, we propose a generalized two level system exhibiting type-II Weyl points that can be realized using ultracold atoms in an optical lattice. The system is engineered using a three-dimensional lattice with complex $\ensuremath{\pi}$ phase tunneling amplitudes. Various unique properties of the type-II Weyl semimetal such as open Fermi surface, anomalous chirality, and topological Fermi arcs can be probed using the proposed optical lattice scheme.
Recently three-dimensional topological quantum materials with gapless energy spectra have attracted considerable interest in many branches of physics. Besides the celebrated example, Dirac and Weyl points which possess gapless point structures in the underlying energy dispersion, the topologically protected gapless spectrum, can also occur along a ring, named Dirac and Weyl nodal rings. Ultracold atomic gases provide an ideal platform for exploring new topological materials with designed symmetries and dispersion. However, whether Dirac and Weyl rings can exist in the single-particle spectrum of cold atoms remains elusive. Here we propose a realistic model for realizing Dirac and Weyl rings in the single-particle band dispersion of a cold-atom optical lattice. Our scheme is based on a previously experimentally implemented Raman coupling setup for realizing spin-orbit coupling. Without the Zeeman field, the model preserves both pseudo-time-reversal and inversion symmetries, allowing Dirac rings. The Dirac rings split into Weyl rings with a Zeeman field that breaks the pseudo-time-reversal symmetry. We examine the superfluidity of attractive Fermi gases in this model and also find Dirac and Weyl rings in the quasiparticle spectrum.
Three-dimensional topological gapless matters with gapless degeneracies protected by a topological invariant defined over a closed manifold in momentum space have attracted considerable interest in various fields ranging from condensed matter materials to ultracold atomic gases. As a highly controllable and disorder free system, ultracold atomic gases provide a versatile platform to simulate topological gapless matters. Here, the current progress in studies of topological gapless phenomena in three-dimensional cold atom systems is summarized in the review. It is mainly focused on Weyl points, structured (type-II) Weyl points, Dirac points, nodal rings and Weyl exceptional rings in cold atoms. Since interactions in cold atoms can be controlled via Feshbach resonances, the progress in both superfluids for attractive interactions and non-interacting cold atom gases is reviewed.
We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected "Fermi arc" surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well within experimental reach with an extension of techniques recently used in ultracold gases.
Weyl points exist in a fascinating topological state of matter with linear band crossings analogous to magnetic monopoles. Tremendous efforts have been devoted to investigating fermionic topological materials with Weyl points in the single-particle band dispersion. It remains elusive for realizing interaction-induced Weyl points, especially for bosons. Motivated by recent experimental progress in ultracold atoms, we propose a scheme to create Weyl points for Bogoliubov excitations of a bosonic superfluid in a three-dimensional cubic optical lattice. The unique design of the lattice leads to interaction-induced time-reversal symmetry breaking for a ppp-orbital superfluid, which in turn induces Weyl Bogoliubov excitations. Analogous to Weyl semimetals of electronic systems, the superfluid also supports topologically protected edge modes due to the bulk-boundary correspondence.