Hosted by: Alexei Tsvelik

The topology of the band structure, which is determined by the lattice symmetries, has a strong influence on the transport properties. We consider an anisotropic honeycomb lattice and study the effect of a continuously deformed band structure on the conductivity and optical properties. We find a strong suppression of the conductivity in one direction and increment by several orders in another which leand to a considerable change of optical properties. We further study a gap generation in a two-dimensional Dirac fermion system which are coupled to in-plane phonons. At sufficiently strong electron-phonon interaction a gap appears in the spectrum of fermions. The structure of elementary excitations above the gap in the corresponding phase reveals the presence of scale invariant parity breaking terms which resemble Chern-Simons excitations. The Kubo formula remyields quantized Hall plateaux. References: EPL 119, 27001 (2017); PRB 97, 235411 (2018); PRB 93, 125112 (2016); Ann. Phys. 400, 262 (2018); arxiv:1908.00442.