| Summary: | Coupling Majorana fermions to metallic conduction electrons will lead to the so-called topological Kondo effect, which is an embodiment of the exotic non-local properties that Majorana fermions possess. Using its minimal setup, this thesis studies the influence of this effect on the scattering properties of conduction electrons by analysing the component of the electron tunnelling density of states (tDOS) which oscillates at twice the Fermi wavenumber kF. We find that at zero bias this 2kF-tDOS displays a non-monotonic behaviour as the temperature is lowered. Starting from the exponential suppression at temperatures much larger than the characteristic Kondo temperature, the 2kF-tDOS may show a Kondo logarithmic peak before it crosses over to a T"3 decay, depending on the ratio of the junction-to-tunnelling distance at which the tDOS is being measured and the characteristic Kondo length. This then provides a way to estimate the extent of the Kondo screening cloud. At energies much below the Kondo temperature, the 2kF-tDOS is described by a universal scaling function indicative of strong correlations. The non-Fermi-liquid scattering occurs in this energy regime, which can be identified by the vanishing of single-particle-to-single-particle scattering at topological Kondo fixed point that in turn manifests in the complete suppression of the 2kF-tDOS at zero temperature and bias. Furthermore, we also have provided a practical method to use the 2kF-tDOS to extract information about the single-particle scattering matrix for more general quantum impurity systems.
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