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arXiv:1609.05470 · Physical review. B./Physical review. B

Realizing type-II Weyl points in an optical lattice

Kunal Krishnaraj Shastri, Zhaoju Yang, Baile Zhang

Published Jan 18, 2017• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.95.014306

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ 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.
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 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.
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.
Topological Lifshitz phase transition characterizes an abrupt change of the topology of the Fermi surface through a continuous deformation of parameters. Recently, Lifshitz transition has been predicted to separate two types of Weyl points: type-I and type-II (or called structured Weyl points), which has attracted considerable attention in various fields. Although recent experimental investigation has seen a rapid progress on type-II Weyl points, it still remains a significant challenge to observe their characteristic Lifshitz transition. Here, we propose a scheme to realize both type-I and type-II Weyl points in three-dimensional ultracold atomic gases by introducing an experimentally feasible configuration based on current spin-orbit coupling technology. In the resultant Hamiltonian, we find three degenerate points: two Weyl points carrying a Chern number $\ensuremath{-}1$ and a fourfold degenerate point carrying a Chern number 2. Remarkably, by continuous tuning of a convenient experimental knob, all these degenerate points can transition from type-I to type-II, thereby providing an ideal platform to study different types of Weyl points and directly probe their Lifshitz phase transition.
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.
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.