Title: "Topological bands and topological phase transitions in magnonic systems"

Abstract: "In electronic systems, various interesting phenomena such as spin Hall effect and topological insulators originate from Berry curvature of Bloch wavefunctions. We theoretically study analogous phenomena for magnons (spin waves). We propose that the dipolar interaction gives rise to nonzero Berry curvature [1-3]. In a thin-film ferromagnet in a long-wavelength regime, we can calculate the Berry curvature for each magnonic band, and only when the magnetic field is out-of-plane, the Berry curvature is nonzero. When the exchange coupling is included, the magnonic bands are modified, and there appear a number of band anticrossing points. Around such an anticrossing point, the Berry curvature is enhanced. This Berry curvature gives rise to thermal Hall effect of magnons [1,2], and it also gives rise to a shift of wavepackets in reflection or refraction [3]. Furthermore, in analogy to the quantum Hall effect for electrons, we can design topological magnon band structure. By introducing artificial spatial periodicity into the magnet, for example by fabricating nanostructures with two different magnets in a periodic structure or by making a periodic array of nanomagnets, we theoretically propose emergence of topological edge modes, analogous to those in electronic quantum Hall effect. The edge modes are chiral, and propagate along the edge of the magnet in one way. We call this a topological magnonic crystal [4,5].

[5] R. Shindou, J. Ohe, R. Matsumoto, S. Murakami, and E. Saitoh, Phys. Rev. B 87, 174402 (2013)."

The recent developments in topological physics were motivated by two major earlier developments, that of the Haldane and Kane-Mele models.  Both were two-dimensional systems, hexagonal lattices.  In the former, time-reversal and inversion symmetries were simultaneously broken, in such a way that an effective mass changes sign at different Dirac points.  This model exhibits quantized Hall conductance.  The latter coupled two Haldane models, one for each spin-channel, and was the first model to exhibit quantized spin Hall conductance.  In this talk, I will report our efforts to realize the analogs of the above in one-dimension. In simple 1D systems are too restricted, however, ladder models can be constructed to give analogs of the Haldane and Kane-Mele models.  Our Haldane 1D analog model exhibits topological behavior, and it also occurs as a result of the simultaneous breaking of inversion and time-reversal symmetries.  The possible gap closure points are symmetric around the origin, but their positions are also tunable.  The topological index in this case is the mirror winding number.  If time permits, I will also discuss the coupling of two modified Creutz ladder models into a model which can be viewed as the 1D analog of the Kane-Mele model.

A variety of quantum systems exhibit Weyl points in th eir spectra, where two bands cross in a point of three dimensional parameter spacewith a conical dispersion in the vicinity of the point. In this talk, the soft constraint regime is considered theoretically, where the parameters are dynamical quantum variables. It is shown that in general the soft constraint in semi-classical limit results in Weyl discs, where two states are (almost) degenerate in a finite two-dimensional region of the thee dimensional space. Concrete calculations are provided for two setups: Weyl points in four-terminal superconducting structures and a Weyl exciton that is a bound state of a Weyl electron and a massive hole.

Work with Janis Erdmanis and Yuli V. Nazarov.