We investigate the dynamics of the Weyl quasiparticles emerged in an optical lattice where the topological Weyl semimetal and trivial band insulator phases can be adjusted with the on-site energy. The evolution of the density distribution is demonstrated to have an anomalous velocity in the Weyl semimetal but a steady Zitterbewegung effect in the band insulator. Our analysis demonstrates that the chirality of the system can be directly determined from the positions of the atomic center of mass. Furthermore, the amplitude and the period of the relativistic Zitterbewegung oscillations are shown to be observable with the time-of-flight experiments.
We investigate the dynamics of the Weyl quasiparticles emerged in an optical lattice where the topological Weyl semimetal and trivial band insulator phases can be adjusted with the on-site energy. The evolution of the density distribution is demonstrated to have an anomalous velocity in the Weyl semimetal but a steady Zitterbewegung effect in the band insulator. Our analysis demonstrates that the chirality of the system can be directly determined from the positions of the atomic center of mass. Furthermore, the amplitude and the period of the relativistic Zitterbewegung oscillations are shown to be observable with the time-of-flight experiments.
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 point-group symmetry. By applying a realizable 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 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-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.
Weyl semimetals are three-dimensional, topologically protected, gapless phases which show exotic phenomena such as Fermi arc surface states or negative magnetoresistance. It is an open question whether interparticle interactions can turn the topological semimetal into a topologically nontrivial Mott-insulating phase. We investigate an experimentally motivated model for Weyl physics of cold atoms in optical lattices, with the main focus on interaction effects and topological properties, by means of dynamical mean-field theory. We characterize topological phases by numerically evaluating the Chern number via the Ishikawa-Matsuyama formula for interacting phases. Within our studies, we find that the Chern numbers become trivial when interactions lead to insulating behavior. For a deeper understanding of the Weyl-semimetal-to-Mott-insulator topological phase transition, we evaluate the topological properties of quasiparticle bands as well as so-called blind bands. Finally, we consider a system with an open boundary along one spatial direction in order to study correlation effects of surface states. In a narrow regime close to the topological phase transition, we find a correlation-induced state in which the surface becomes metallic while the bulk is semimetallic.
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.
Although Weyl semimetals have been extensively studied for exploring rich topological physics, the direct observation of the celebrated chiral magnetic effect (CME) associated with the so-called dipolar chiral anomaly has long intrigued and challenged physicists, still remaining elusive in nature.Here we propose a feasible scheme for experimental implementation of ultracold atoms that may enable us to probe the CME with a pure topological current in an artificial Weyl semimetal.The paired Weyl points with the dipolar chiral anomaly emerge in the presence of the well-designed spin-orbital coupling and laser-assisted tunneling.Both of the two artificial fields are readily realizable and highly tunable via current optical techniques using ultracold atoms trapped in threedimensional optical lattices, providing a reliable way for manipulating Weyl points in the momentum-energy space.By applying a weak artificial magnetic field, the system processes an auxiliary current originated from the topology of a paired Weyl points, namely, the pure CME current.This topological current can be extracted from measuring the center-of-mass motion of ultracold atoms, which may pave the way to directly and unambiguously observe the CME in experiments.
Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.
Abstract We propose a realistic scheme to directly probe the Chern number of topological Weyl semimetals in optical lattices. The Weyl semimetal states can be realized with ultracold fermionic atoms trapped in three-dimensional optical lattices, and are topologically characterized by k z -dependent Chern number, where k z is the out-of-plane quasimomentum. We demonstrate with numerical simulations that this characteristic topological invariant can be extracted from the shift of the hybrid Wannier center in the optical lattice, based on the particle pumping approach. Through in situ measurement of atomic density, the topological properties of the Weyl semimetal states are then directly revealed.