Spectral function as a probe to detect winding and Chern number of topological phases of matter.

Kiran B Estake, Dibyendu Roy

Topological insulators are the insulating phases of matter which cannot be deformed into each other adiabatically without having to go through a quantum phase transition. In this short talk I will discuss the definition of topological insulators in 1D with the Su-Shrieffer-Heeger (SSH) model as an example and define winding number for it. It is found that the spectral function contains the topology information (either winding number for 1D or Chern number for 2D topological insulators). I will define the spectral function and discuss it as a probe to detect topological winding number. I will illustrate it for a generalized version of the SSH model and the Kitaev chain. If time permits, I will also discuss the spectral function as a probe to detect Chern number in 2D insulators.