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

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" is shown to be non-zero whenever the surrounding cloud is prepared in a non-trivial Chern insulating state, which we attribute to the transverse drag exerted by the dressing cloud on the impurity. In this way, the polaron partially inherits the topological properties of the Chern insulator through genuine interaction effects. This is also analysed 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.

6 +4 pages, 4+4 figures

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• Tracing non-Abelian anyons via impurity particles
• Anyonic molecules in atomic fractional quantum Hall liquids: a quantitative probe of fractional charge and anyonic statistics
• Dynamical formation of polarons in a Bose-Einstein condensate: A variational approach
• Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator
• Topological transport of mobile impurities
• Fractional angular momentum and anyon statistics of impurities in Laughlin liquids
• Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices
• Collective excitations of a Bose-Einstein condensate of hard-core bosons and their mediated interactions: from two-body bound states to mediated superfluidity
• Polaron in a $p+ip$ Fermi topological superfluid
• Chiral polaron formation on the edge of topological quantum matter
• Polaron spectra and edge singularities for correlated flat bands
• Mobile impurity probing a two-dimensional superfluid phase transition
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Electronic properties of the Dirac and Weyl systems with first- and higher-order dispersion in non-Fermi-liquid picture
• Electronic properties and polaronic dynamics of semi-Dirac system within ladder approximation
• Lattice Bose polarons at strong coupling and quantum criticality
• Attractive polaron in a Dirac system within the ladder approximation
• Attractive polaron formed in doped nonchiral/chiral parabolic system within ladder approximation
• Emergent topological phases and coexistence of gapless and spectral-localized Floquet quantum spin Hall states via electron-phonon interaction
• Composite polaron formed on surface of two-dimensional lattice system in weak coupling regime
• The Bose-Hubbard polaron from weak to strong coupling
• Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions
• Sensing the binding and unbinding of anyons at impurities
• Bound states in two-dimensional Fermi systems with quadratic band touching