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Register a new userTopological Marker Currents in Chern Insulators
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Added by
Marcello Davide Caio
Publication date
2018
fields
Physics
and research's language is
English
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Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behavior of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents, with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment.
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Topological states of matter were first introduced for non-interacting fermions on an infinite uniform lattice. Since then, substantial effort has been made to generalize these concepts to more complex settings. Recently, local markers have been developed that can describe the topological state of systems without translational symmetry and well-defined gap. However, no local marker for interacting matter has been proposed yet that is capable of directly addressing an interacting system. Here we suggest such a many-body local marker based on the single-particle Greens function. Using this marker we identify topological transitions in finite lattices of a Chern insulator with Anderson disorder and Hubbard interactions. Importantly, our proposal can be straightforwardly generalised to non-equilibrium systems.
We detect the topological properties of Chern insulators with strong Coulomb interactions by use of cluster perturbation theory and variational cluster approach. The common scheme in previous studies only involves the calculation of the interacting bulk Chern number within the natural unit cell by means of the so-called topological Hamiltonian. With close investigations on a prototype model, the half-filled Haldane Hubbard model, which is subject to both periodic and open boundary conditions, we uncover the unexpected failure of this scheme due to the explicit breaking of the translation symmetry. Instead, we assert that the faithful interacting bulk Chern number in the framework of quantum cluster approaches can be computed in the enlarged unit cell, which is free of the fault caused by the explicit translation symmetry breaking and consistent with the interacting bulk-edge correspondence.
We explore the non-equilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and non-topological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally-observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample.
The recent discovery of topological Kondo insulators has triggered renewed interest in the well-known Kondo insulator samarium hexaboride, which is hypothesized to belong to this family. In this Letter, we study the spin texture of the topologically protected surface states in such a topological Kondo insulator. In particular, we derive close relationships between (i) the form of the hybridization matrix at certain high-symmetry points, (ii) the mirror Chern numbers of the system, and (iii) the observable spin texture of the topological surface states. In this way, a robust classification of topological Kondo insulators and their surface-state spin texture is achieved. We underpin our findings with numerical calculations of several simplified and realistic models for systems like samarium hexaboride.
We formulate a Chern-Simons composite fermion theory for Fractional Chern Insulators (FCIs), whereby bare fermions are mapped into composite fermions coupled to a lattice Chern-Simons gauge theory. We apply this construction to a Chern insulator model on the kagome lattice and identify a rich structure of gapped topological phases characterized by fractionalized excitations including states with unequal filling and Hall conductance. Gapped states with the same Hall conductance at different filling fractions are characterized as realizing distinct symmetry fractionalization classes.
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