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arXiv:1811.00563 · Physical review. B./Physical review. B

Dropping an impurity into a Chern insulator: A polaron view on topological matter

Arturo Camacho-Guardian, Nathan Goldman, Pietro Massignan, Georg M. Bruun

Published Feb 5, 2019• 40 citations
arXivHTMLPDF

Abstract

We investigate the properties of an impurity particle interacting with a Fermi gas in a Chern-insulating state. The interaction leads to the formation of an exotic polaron, which consists of a coherent superposition of the topologically trivial impurity and the surrounding topological cloud. We characterize this intriguing topologically composite object by calculating its transverse (Hall) conductivity, using diagrammatic as well as variational methods. The ``polaronic Hall conductivity,'' i.e., the transverse drag exerted by the dressing cloud on the impurity, is shown to exhibit a sharp jump from zero to a finite value whenever the surrounding cloud enters a topologically nontrivial state. In this way, the polaron partially inherits the topological properties of the Chern insulator through genuine interaction effects. This is also analyzed at the microscopic level of wave functions, by identifying a ``composite Berry curvature'' for the polaron, which closely mimics the Berry curvature of the Chern insulator's band structure. Finally, we discuss how this interplay between topology and many-body correlations can be studied in cold-atom experiments, using available technologies.

DOI
10.1103/physrevb.99.081105

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We investigate the properties of an impurity particle interacting with a Fermi gas in a Chern-insulating state. The interaction leads to the formation of an exotic polaron, which consists of a coherent superposition of the topologically trivial impurity and the surrounding topological cloud. We characterize this intriguing topologically composite object by calculating its transverse (Hall) conductivity, using diagrammatic as well as variational methods. The polaronic Hall conductivity,'' i.e., the transverse drag exerted by the dressing cloud on the impurity, is shown to exhibit a sharp jump from zero to a finite value whenever the surrounding cloud enters a topologically nontrivial state. In this way, the polaron partially inherits the topological properties of the Chern insulator through genuine interaction effects. This is also analyzed at the microscopic level of wave functions, by identifying a composite Berry curvature'' for the polaron, which closely mimics the Berry curvature of the Chern insulator's band structure. Finally, we discuss how this interplay between topology and many-body correlations can be studied in cold-atom experiments, using available technologies.
We study the Hall response of topologically trivial mobile impurities (Fermi polarons) interacting weakly with majority fermions forming a Chern-insulator background. This setting involves a rich interplay between the genuine many-body character of the polaron problem and the topological nature of the surrounding cloud. When the majority fermions are accelerated by an external field, a transverse impurity current can be induced. To quantify this polaronic Hall effect, we compute the drag transconductivity, employing controlled diagrammatic perturbation theory in the impurity-fermion interaction. We show that the impurity Hall drag is not simply proportional to the Chern number characterizing the topological transport of the insulator on its own---it also depends continuously on particle-hole breaking terms, to which the Chern number is insensitive. However, when the insulator is tuned across a topological phase transition, a sharp jump of the impurity Hall drag results, for which we derive an analytical expression. We describe how to experimentally detect the polaronic Hall drag and its characteristic jump, setting the emphasis on the circular dichroism displayed by the impurity's absorption rate.
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Emergent Weyl Nodes and Berry Curvature in Bose Polarons via ppp-Wave Feshbach Coupling
We show that an impurity quasiparticle immersed in a Bose-Einstein condensate, known as a Bose polaron, exhibits topological properties characterized by a nonzero Berry curvature, which is induced by Weyl nodes that emerge via interspecies ppp-wave Feshbach resonance. Such nodes occur even in the absence of spin degrees of freedom and spin-orbit coupling. For charged impurities, the corresponding ppp-wave polarons are shown to be accompanied by chiral anomaly. The above predictions can be tested in a cold atomic environment by observing the Hall transport of the atomic or ionic impurity cloud.
We study the coherent nonequilibrium dynamics of interacting two-dimensional systems after a quench from a trivial to a topological Chern insulator phase. While the many-body wave function is constrained to remain topologically trivial under local unitary evolution, we find that the Hall response of the system can dynamically approach a thermal value of the postquench Hamiltonian, even though the efficiency of this thermalization process is shown to strongly depend on the microscopic form of the interactions. Quite remarkably, the effective temperature of the steady-state Hall response can be arbitrarily tuned with the quench parameters. Our findings suggest a way of inducing and observing low-temperature topological phenomena in interacting ultracold atomic gases, where the considered quench scenario can be realized in current experimental setups.
Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.
An impurity atom immersed in an ultracold atomic Fermi gas can form a quasiparticle, so-called Fermi polaron, due to impurity-fermion interaction. We consider a three-dimensional homogeneous dipolar Fermi gas as a medium, where the interatomic dipole-dipole interaction (DDI) makes the Fermi surface deformed into a spheroidal shape, and, using a Chevy-type variational method, investigate the ground-state properties of the Fermi polaron: the effective mass, the momentum distribution of a particle-hole excitation, the drag parameter, and the medium-density modification around the impurity. These quantities are shown to exhibit spatial anisotropies in such a way as to reflect the momentum anisotropy of the background dipolar Fermi gas. We also give numerical results for the polaron properties at the unitarity limit of the impurity-fermion interaction in the case in which the impurity and fermion masses are equal. It has been found that the transverse effective mass and the transverse momentum drag parameter of the polaron both tend to decrease by $\ensuremath{\sim}10%$ when the DDI strength is raised from 0 up to around its critical value, while the longitudinal ones exhibit a very weak dependence on the DDI.