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arXiv:1611.05573 · Physical Review A

Bogoliubov excitations in the Bose-Hubbard extension of a Weyl semimetal

Ya-Jie Wu, Wen-yan Zhou, Su-Peng Kou

Published Feb 21, 2017• 9 citations
arXivHTMLPDF

Abstract

In this paper, a Bose-Hubbard extension of a Weyl semimetal is proposed that can be realized for ultracold atoms using laser-assisted tunneling and Feshbach resonance technique in three-dimensional optical lattices. The global phase diagram is obtained consisting of a superfluid phase and various Mott insulator phases by using Landau theory. The Bogoliubov excitation modes for the weakly interacting case have nontrivial properties (Weyl nodes, bosonic surface arc, etc.), analogs of those in Weyl semimetals of electronic systems, which are smoothly carried over to those of Bloch bands for the noninteracting case. The properties of the insulating phases for the strongly interacting case are explored by calculating both the quasiparticle and quasihole dispersion relation, which shows that two quasiparticle spectra touch at Weyl nodes.

DOI
10.1103/physreva.95.023620

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In this paper, a Bose-Hubbard extension of a Weyl semimetal is proposed that can be realized for ultracold atoms using laser-assisted tunneling and Feshbach resonance technique in three-dimensional optical lattices. The global phase diagram is obtained consisting of a superfluid phase and various Mott insulator phases by using Landau theory. The Bogoliubov excitation modes for the weakly interacting case have nontrivial properties (Weyl nodes, bosonic surface arc, etc.), analogs of those in Weyl semimetals of electronic systems, which are smoothly carried over to those of Bloch bands for the noninteracting case. The properties of the insulating phases for the strongly interacting case are explored by calculating both the quasiparticle and quasihole dispersion relation, which shows that two quasiparticle spectra touch at Weyl nodes.
Abstract Recent studies on ultracold atoms have reported the implementation of laser-assisted tunneling in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate a two-band Bose–Hubbard model with its single-particle energy bands showing gapless nodal lines, which can be realized for ultracold atoms in the cubic optical lattices using laser-assisted tunneling. We analyze the superfluid–Mott insulator (MI) phase transition in this model and obtain a global phase diagram by using the strong-coupling expansion method. The excitation spectra in strong and weak coupling limits inherit the topological properties of single-particle energy bands to show the structures of nodal lines. The topological invariants, the flat surface states and the critical properties are analyzed theoretically in detail. The excitation spectra in the MI and superfluid phases are measurable in ultracold atom experiments to prove our results.
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.
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.
Motivated by recent developments in the experimental study of Bose-Fermi mixtures, we investigate ground-state phase diagrams and excitation spectra for Bose-Fermi mixtures in a three-dimensional (3D) optical lattice. The Gutzwiller approximation is used to identify a new phase in which both superfluid bosons and metal fermions coexist. As a useful probe to identify the quantum phases, we also calculate the excitation spectra. In Mott insulator phase, two excitation features appear in the spectra that correspond to particle and hole excitations. In superfluid phase, there are Bogoliubov modes and amplitude modes. In coexisting phase, two gapless dispersive modes are identified, which shift due to interaction between bosons and fermions.
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.
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.