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.
Topological phases in ladder models
2018. 03. 12. 14:15
Building F, Entrance III, Department of Theoretical Physics, Library
Balázs Hetényi (BME/Bilkent)