Dresden 2017 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 76: Poster Session: Transport 2

TT 76.13: Poster

Donnerstag, 23. März 2017, 15:00–19:00, P2-OG1

Computing topological invariants in two-dimensional periodically driven systems — •Bastian Höckendorf, Andreas Alvermann, and Holger Fehske — Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald, Greifswald, Germany

Periodically driven systems feature topological phenomena that have no analog for systems in equilibrium. Various topological invariants have been proposed to classify these phenomena but they are in general not easily computable. We show that these invariants can be connected to degeneracies of the time- and momentum-dependent spectrum of the time-evolution operator. By assigning a Chern number - a quantity that is numerically easily accessible - to each degeneracy and expressing the invariants as functions of these Chern numbers we can calculate the different invariants using one unifying concept. We demonstrate this approach for driven Harper, Kane-Mele and graphene models which are representatives of two-dimensional periodically driven systems with chiral symmetry, time-reversal symmetry and particle-hole symmetry, respectively. The given symmetries lock a subset of the degeneracies to symmetry points in the time-momentum space which gives each system special topological properties. We evaluate the corresponding invariants with our approach and compare them to the chiral edge states of the Floquet spectrum via the bulk-edge correspondence.