Seminar on the Theory of Complex Systems  Winter Term 2014-15

There is a growing realisation that nonequilibrium[1] is a promising avenue for exploring novel phenomena. This talk will focus on two topics. One is the “Floquet topological insulator”[2], which is induced by modulating a honeycomb system such as graphene with a circularly polarised light. A topological gap then opens in the Dirac cone in the nonequilibrium Floquet spectrum, and a dc Hall effect (anomalous quantum Hall effect) emerges, as recently demonstrated in a cold-atom system[3]. Hence this gives a third example for QHE (besides the original QHE and the Kane-Mele model). If we consider electron correlation, we have a phase diagram in which the topological phases are speared by Mott insulator phases.[4] Our second topic concerns superconductors illuminated by laser. A strong THz light field is experimentally shown[5] to induce oscillations of the su-perconducting order parameter with twice the frequency of the laser. Interestingly, a large third-harmonic generation is experimentally detected, which is theoretically captured[6] as a collective precession of Anderson’s pseudospins resonating with the Higgs (amplitude) mode of the superconductor. So a message here is nonequilibrium is so versatile as to create novel topological phases and to collectively excite superconductors.

1. [1] H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka and P. Werner, Rev. Mod. Phys. 86, 779 (2014).
2. [2] T. Oka and H. Aoki: PRB 79, 081406(R) (2009).
3. [3] G. Jotzu et al, arXiv:1406.7874.
4. [4] T. Mikami, K. Yasuda, N. Tsuji, T. Oka and H. Aoki, in prep.
5. [5] R. Matsunaga, N. Tsuji, H. Fujita, A. Sugioka, K. Makise, Y. Uzawa, H. Terai, Z. Wang, H. Aoki and R. Shimano, Science 345, 1145 (2014).
6. [6] N. Tsuji and H. Aoki, arXiv:1404.2711

The family of integrins are the major family of adhesion receptors. The 24 different subtypes have partially overlapping binding specificities to extracellular ligands. How these integrin act cooperatively to organize cellular functions is largely unknown. Here, we use biophysical techniques to show that the two fibronect-binding receptors integrin avb3 and integrin a5b1 cooperatively organize the cytoskeleton for optimized stability and traction force generation.

Topological materials have in recent years become a subject of intense research due to fundamental considerations as well as potential use for technical applications in device fabrication and quantum information. One of the hallmarks of topological materials is the existence of protected exotic zero-energy surface states, which arise as a consequence of a nontrivial topology of the bulk wave functions. In this talk, starting from the ten-fold classification of topological insulators and superconductors, I will survey recent developments, with a particular emphasis on the topological classifications of fully gapped and gapless materials in terms of crystal symmetries. As concrete examples, I discuss superconductors without inversion symmetry, which are promising candidate materials for topological superconductivity. Due to strong spin-orbit coupling the topological surface states of these superconductors exhibit an intricate spin texture. I will discuss experimental signatures of these topological surface states in charge and thermal transport measurements, as well as in Fourier-transform scanning tunneling spectra.