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Les événements de janvier 2018


  • Séminaire des doctorants

    • Jeudi 11 janvier 11:00-12:00 - Pierre Delplace - ENS Lyon

      Anomalous topological Floquet states

      Résumé : Since the discovery of the quantum spin Hall effect, the search for novel topological insulating states has been stimulating tremendous efforts, impacting many areas of physics beyond semi-conductors physics. In particular it was proposed, and then observed in photonic lattices, that specific periodic drives can lead to unusual dynamical topological states, referred to as topological Floquet states. Whereas such driving protocols were first proposed to simply dynamically trigger a topological phase transition, it was later realized that novel topological states, with no equilibrium (or static) counterpart, can be induced : the so-called anomalous topological Floquet states. More specifically, the usual topological index used to account for the existence of boundary states, namely the first Chern number, vanishes, and an other "dynamical" invariant must be used.
      In this seminar, I will discuss the roles of two different symmetries in this context. First I will show how a Z2-valued dynamical invariant can be defined when the evolution operator is constrained by time-reversal symmetry, thus generalizing the pioneering work by Kane and Mele to periodically driven systems. Then I will discuss the recently introduced "phase rotation symmetry" that was proposed to achieve anomalous states.

      Lieu : salle 208a, aîle sud LPS, bât 510


  • Séminaire des doctorants

    • Jeudi 25 janvier 10:30-11:30 - Jean-Noël Fuchs - LPTMC Jussieu & LPS Orsay

      Berry phase and quantum metric for Bloch electrons

      Résumé : In this talk, I will try to answer the following question : what is the effective Hamiltonian describing a Bloch electron restricted to a single band, but in in the presence of other bands and of external electromagnetic fields ? I will first review Peierls’ answer involving the Peierls’ substitution and leading to well-known semiclassical equations of motion (cf. Ashcroft-Mermin). Then I will argue that, although this answer leads to many successes, it is too naive as it only involves the band energy spectrum but completely forgets the corresponding eigenvectors. Eventually, I will turn to the modern understanding – which goes back to Thouless, Berry and Haldane – of the existence of a geometric structure hidden within band theory (namely a Berry phase and a quantum metric). This will allow us to derive a modified effective single-band Hamiltonian. The corresponding semiclassical equations of motion (cf. Qian Niu and collaborators) include extra terms such as the Karplus-Luttinger anomalous velocity and the orbital magnetic moment. If time permits, I will end by showing how the quantum Hall effect appears in hindsight as electric transport in a peculiar band insulator in zero external magnetic field.

      Lieu : salle caffet theo, 1er étage, aîle sud LPS, bât 510


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