Topological Kondo Effect / Charge fluctuations, topology and entanglement

In this talk, I present two different works on topological superconductors. In the first part, we will focus on electronic transport mediated by Majorana bound states. We study a floating superconducting island carrying several such impurities, a potential building block for a quantum computer. The Majorana fermions affect the statistics of the charge carriers, which leads to very resilient fractionalized transport. Additionnaly, when an additional charge degree of freedom is present in the island, the model maps to the Multi-Channel Kondo model, but at large interaction. In a second time, we will discuss entanglement. Entanglement markers have been fundamental to the study of topological or gapless systems in general, but are challenging to measure. Bipartite charge fluctuations have been proposed as a weak measurement of entanglement. We extend results on standard Luttinger Liquids to generic families of one-dimensional non-interacting topological systems. A volume law arises, and is linked to the Quantum Fisher information, with non-analyticities at the phase transitions. Critical points are characterized by universal coefficients. Higher dimensional generalizations are discussed and directly probe the topological nature of semi-metals.