Paradoxo de Klein em sistemas mesoscópicos

Abstract

The research on mesoscopic electronic devices has attracted the curiosity of many theoretical, as well as experimental, research groups. There are two meaningful experimental examples, the two-electron electron gas and the quantum billiard single-layer graphene. The main di erence between them is the behavior of its electron's wave function. Schr odinger's equation describes the former, and Dirac's massless equation describes the latter. Particularly, the latter, due to its subnetting symmetry, exhibits interesting and peculiar transport physical phenomena not observed in others. In this thesis, we analyzed the behavior of some universal electron transport phenomena in mesoscopic systems. Such events are usually studied under the light of quantum scattering following the Hamiltonian model, to that end, we used Mahaux-Wiedenm uller formulation to the special case of a chaotic cavity coupled to two terminals - waveguides. In this context, we compared the so-called Schr odinger's, non-relativistic, and Dirac's, relativistic, Billiards with respect to transport physical properties, such as conductance and shot-noise power and its respective variances, in addition to the quantum interference terms. The Mahaux-Weidenm uller Hamiltonian Model relates the quantum scattering of electronic propagation channels through a chaotic cavity or quantum dot with a large number of resonances with a scattering matrix S, which associates the incident waves to the output waves amplitudes from the interaction cavity. We were able to link the transport properties to the scattering matrix through the Landauer-B uttiker formalism. The model generates scattering matrices following the random matrix theory. Besides the billiards comparison, we were able to associate Dirac's chaotic billiard with Klein's paradox, because of the subnetting symmetry, also called chiral symmetry, found in structures like the graphene's. Many of the previous results concerning the transport properties of these billiards are known only for ideal contact, that is, the coupling of the guides and the interaction cavity is ideal - without a potential barrier. Our study, however, is complete, with both ideal and non-ideal contacts. We show universal results that revealed abnormal behaviors in the conductance, in the ring noise power and in the respective distributions of eigenvalues. Particularly, we demonstrate Klein's paradox in the suppression/ampli cation transitions of the observables' transport in chaotic Dirac billiards.