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arXiv:1801.08255

Dynamical Weyl Points and 4D Nodal Rings in Cold Atomic Gases

Yan-Bin Yang, Luming Duan, Yong Xu

Published Jan 25, 2018• 13 citations
arXivHTMLPDF

Abstract

Controllability of ultracold atomic gases has reached an unprecedented level, allowing for experimental realization of the long-sought-after Thouless pump, which can be interpreted as a dynamical quantum Hall effect. On the other hand, Weyl semimetals and Weyl nodal line semimetals with touching points and rings in band structures have sparked tremendous interest in various fields in the past few years. Here, we show that dynamical Weyl points and dynamical 4D Weyl nodal rings, which are protected by the first Chern number on a parameter surface formed by quasi-momentum and time, emerge in a two-dimensional and three-dimensional system, respectively. We find that the topological pump occurs in these systems but the amount of pumped particles is not quantized and can be continuously tuned by controlling experimental parameters over a wide range. We also propose an experimental scheme to realize the dynamical Weyl points and 4D Weyl nodal rings and to observe their corresponding topological pump in cold atomic gases.

DOI
10.1103/physrevb.98.165128

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Controllability of ultracold atomic gases has reached an unprecedented level, allowing for experimental realization of the long-sought-after Thouless pump, which can be interpreted as a dynamical quantum Hall effect. On the other hand, Weyl semimetals and Weyl nodal line semimetals with touching points and rings in band structures have sparked tremendous interest in various fields in the past few years. Here, we show that dynamical Weyl points and dynamical 4D Weyl nodal rings, which are protected by the first Chern number on a parameter surface formed by quasi-momentum and time, emerge in a two-dimensional and three-dimensional system, respectively. We find that the topological pump occurs in these systems but the amount of pumped particles is not quantized and can be continuously tuned by controlling experimental parameters over a wide range. We also propose an experimental scheme to realize the dynamical Weyl points and 4D Weyl nodal rings and to observe their corresponding topological pump in cold atomic gases.
Over thirty years ago, Thouless introduced the quantized particle transport that can occur in a one-dimensional quantum system under a cyclic adiabatic variation of periodic potentials without a bias voltage. This phenomenon is attributed to the formation of a dynamical Chern insulator on a parameter surface formed by quasimomentum and time. Recently, three-dimensional topological gapless phenomena have sparked tremendous attention in various fields. Here, we demonstrate that dynamical Weyl points and dynamical 4D Weyl nodal rings protected by the first Chern number emerge in a two-dimensional and three-dimensional system, respectively. We find that the topological quantum pump occurs in these systems but the amount of pumped particles is not quantized and can be tuned continuously by controlling experimental parameters. Finally, we propose an experimental scheme to realize the dynamical Weyl points and 4D Weyl nodal rings and their corresponding topological pump in cold atomic gases.
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.
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 propose a scheme to simulate and explore Weyl semimetal physics with ultracold fermionic atoms in a two-dimensional square optical lattice subjected to experimentally realizable spin-orbit coupling and an artificial dimension from an external parameter space, which may increase experimental feasibility compared with the cases in three-dimensional optical lattices. It is shown that this system with a tight-binding model is able to describe essentially three-dimensional Weyl semimetals with tunable Weyl points. The relevant topological properties are also addressed by means of the Chern number and the gapless edge states. Furthermore, we illustrate that the mimicked Weyl points can be experimentally detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation, and the characteristic topological invariant can be measured with the particle pumping approach.
We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of $\ifmmode\pm\else\textpm\fi{}2$ behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the C4h{C}_{4h}C4h​ point-group symmetry. By applying a realizable C4{C}_{4}C4​ breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the C4{C}_{4}C4​ breaking term, which contains a topological and a normal insulating phase and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with time-of-flight imaging; (iii) the band topology of the C4{C}_{4}C4​-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high-symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.