Análise diagramática dos grupos universais: teoria do ruído e o sinal da quiralidade

Abstract

We investigated the electronic transport in chaotic quantum dots of graphene, also known as Dirac Billiards (DB). Notably, such nanoscopic devices intrinsically carry chiral/sublattice symmetry giving rise to exotic and non-trivial relativistic properties in quantum transport, such as Klein tunneling and non-massive electronic Dirac modes. Several studies, however, demonstrate difficulties in directly observing the chiral universal symmetry signal. Thus, motivated by the question “What is the evidence of universal chiral symmetry in quantum transport through nanostructures?”, we explored the main observables of transport in DB, conductance and the shot noise power, in the universality regime, which means that they are independent of specific nanostructure manufacturing processes and their microscopic details. Using an extension of the diagrammatic method of integration over the unitary group, which generated 11.024 diagrams, we obtained exact analytical results valid even in the semi-classical and extreme quantum limits. In particular, analyzing the formula obtained for conductance, we realized that the main quantum interference term for the universal chiral class is identical to the corresponding term for the Wigner-Dyson classes, typical semiconductors. Due to the absence of any indicator of chirality in conductance, we conjecture that this observable is insensitive to the existence of intrinsic sublattice because it does not have backscattering terms. On the other hand, an analysis of the corpuscular character of the electron embedded in the shot noise power led us to find a robust and peculiar signal for an arbitrary number of scattering channels. The signal that was found, generated by the main quantum interference correction term, is the “fingerprint” of chirality which, through our analytical expressions, can be measured for any number of open channels. In addition, the analytical results were tested and confirmed through a numerical simulation based on the Mahaux- Weidenmüller formalism. Our work demonstrate that both the corpuscular and the undulatory character contribute concomitantly through coherent backscattering to generate the chirality signal in mesoscopic physics of open systems out of equilibrium.