Effect of fermionic components on trion-electron scattering

To test the validity of replacing a composite fermion by an elementary fermion, we here calculate the transition rate from a state made of one free electron and one trion to a similar electron-trion pair, through the time evolution of such a pair induced by Coulomb interaction between elementary fermions. To do it in a convenient way, we describe the trion as one electron interacting with one exciton, and we use the tools we have developed in the new composite-exciton many-body theory. The trion-electron scattering contains a direct channel in which ``in'' and ``out'' trions are made with the same fermions, and an exchange channel in which the ``in'' free electron becomes one of the ``out'' trion components. As expected, momenta are conserved in these two channels. The direct scattering is found to read as the bare Coulomb potential between elementary particles multiplied by a form factor which depends on the ``in'' and ``out'' trion relative motion indices $\eta$ and $\eta'$, this factor reducing to $\delta_{\eta\eta'}$ in the zero momentum transfer limit: In this direct channel, the trion at large distance reacts as an elementary particle, its composite nature showing up for large momentum transfer. On the contrary, the fact that the trion is not elementary does affect the exchange channel for all momentum transfers. We thus conclude that a 3-component fermion behaves as an elementary fermion for direct processes in the small momentum transfer limit only

Fresnel polarisation of infra-red radiation by elemental bismuth

We revisit the classical problem of electromagnetic wave refraction from a lossless dielectric to a lossy conductor, where both media are considered to be non-magnetic, linear, isotropic and homogeneous. We derive the Fresnel coefficients of the system and the Poynting vectors at the interface, in order to compute the reflectance and transmittance of the system. We use a particular parametrisation of the referred Fresnel coefficients so as to make a connection with the ones obtained for refraction by an interface between two lossless media. This analysis allows the discussion of an actual application, namely the Fresnel polarisation of infra-red radiation by elemental bismuth, based on the concept of pseudo Brewster’s angle.We acknowledge helpful discussions with M. Vasilevskiy, P. Alpuim, J. Caridad and B. Figueiredo. The authors thank the European Structural and Investment Funds in the FEDER component, through the Operational Programme for Competitiveness and Internationalization (COMPETE 2020) [under the Project GNESIS -Graphenest's New Engineered System and its Implementation Solutions; Funding Reference: POCI-01-0247-FEDER-033566], European Regional Development Fund. This work was also supported by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UID/FIS/04650/2019