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arXiv:1604.06055 · Physical Review Letters

Topological Varma Superfluid in Optical Lattices

Marco Fedele Di Liberto, Andreas Hemmerich, C. Morais Smith

Published Oct 11, 2016• 57 citations
arXivHTMLPDF

Abstract

Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While noninteracting fermionic topological insulators are well established by now and have been classified according to a tenfold scheme, the possible realization of topological states for bosons has not been explored much yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a nonzero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.

DOI
10.1103/physrevlett.117.163001

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Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While noninteracting fermionic topological insulators are well established by now and have been classified according to a tenfold scheme, the possible realization of topological states for bosons has not been explored much yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a nonzero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.
There has been a growing interest in realizing topologically nontrivial states of matter in band insulators, where a quantum Hall effect can appear as an intrinsic property of the band structure. While ongoing progress is under way with a number of directions, the possibility of realizing novel interaction-generated topological phases, without the requirement of a nontrivial invariant encoded in single-particle wave function or band structure, can significantly extend the class of topological materials and is thus of great importance. Here, we show an interaction-driven topological phase emerging in an extended Bose-Hubbard model on a kagome lattice, where the noninteracting band structure is topological trivial with zero Berry curvature in the Brillouin zone. By means of an unbiased state-of-the-art density-matrix renormalization group technique, we identify that the ground state in a broad parameter region is equivalent to a bosonic fractional quantum Hall Laughlin state, based on the characterization of universal properties including ground-state degeneracy, edge excitations, and anyonic quasiparticle statistics. Our work paves a way to finding an interaction-induced topological phase at the phase boundary of conventionally ordered solid phases.
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from sss-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard sss-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.
We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase---an interaction-driven topological insulator---using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest- and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.
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.
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for quantum many-body states of matter that previously had not been accessible. Here we introduce a symmetry-based method of utilizing the geometry of optical lattice to systematically control topologically non-trivial orbital hybridization. Such an orbital mixing leads to an unexpected and yet robust topological semimetal at single-particle level for a gas of fermionic atoms. When considering s-wave attractive interaction between atoms as for instance tuned by Feshbach resonance, topological superfluid state with high Chern number is unveiled in the presence of on-site rotation. This state supports chiral edge excitations, manifesting its topological nature. An experimental realization scheme is designed, which introduces a systematic way of achieving a new universality class (such as Chern number of 2) of orbital-hybridized topological phases beyond geometrically standard optical lattices.
An interesting route to the realization of topological Chern bands in ultracold atomic gases is through the use of optical flux lattices. These models differ from the tight-binding real-space lattice models of Chern insulators that are conventionally studied in solid-state contexts. Instead, they involve the coherent coupling of internal atomic (spin) states, and can be viewed as tight-binding models in reciprocal space. By changing the form of the coupling and the number NNN of internal spin states, they give rise to Chern bands with controllable Chern number and with nearly flat energy dispersion. We investigate in detail how interactions between bosons occupying these bands can lead to the emergence of fractional quantum Hall states, such as the Laughlin and Moore-Read states. In order to test the experimental realization of these phases, we study their stability with respect to band dispersion and band mixing. We also probe interesting topological phases that emerge in these systems when the Chern number is greater than 1.