Fermion Number Fractionalization in Dirac Materials
In this presentation, we will discuss the main developments and current state of the research project. In general lines, we propose to investigate a spectral function (asymmetry, in particular) of several models with topological backgrounds, especially in the context that concerns the so-called Dirac materials. We will start by discussing about the ‘fermion number’ quantity and its values in some field theories. Afterwards, some notions on the spectral geometry of Laplace-type operators will be inserted, also relating them to the Dirac-type ones, which are fundamental to understand the formalism to be derived and adopted in order to calculate the fermion number; the key idea of our study lies in the application of techniques provided by the heat kernel trace. After that, we will present some results obtained by applying the said method in certain theoretical models of interest, containing Dirac fermions. At long last, some partial results under evaluation will be briefly introduced, setting up the prospects of our work, together with a small assertion with respect to the experimental importance.