Open chaotic Dirac billiards: Weak (anti)localization, conductance fluctuations, and decoherence

In this paper, we investigate the transport properties of open chaotic Dirac billiards and their intrinsic (chiral universal) symmetry classes. The prominent examples of these systems are some categories of topological insulators and graphene structures. We extend the diagrammatic method of integration over the unitary group and obtain analytical results for the semiclassical limit and for the high quantum limit in the universal regime. We show the emergence of quantum fingerprints characteristic of the chiral symmetries, which are amplified in the presence of a single open channel in each electronic terminals. We compare the chaotic Dirac billiards with the Schrodinger billiards in a myriad of regimes, exhibiting the differences between the chiral universal classes and the Wigner-Dyson classes. Two numerical methods were used to confirm our analytical findings, yielding also the distribution of conductances. We also investigate analytically the effect of dephasing using the characteristic time scales of the chaotic billiards and we show the appearance of peculiar numbers of chaos.