Hunting for the topological Kondo effect: tensor network simulations of transport phenomena in Coulomb-blockaded topological superconductors.

Majorana zero-energy modes lie at the center of the efforts for creating topologically protected qubits but, so far, they eluded a clear experimental detection due to the difficulty of distinguishing them from Andreev bound states. An unambiguous signature of their presence is the appearance of the topological Kondo effect (TKE) in a Coulomb-blockaded device connected with more than two metallic leads each coupled with an individual Majorana mode. The TKE emerges as an effective low-energy description of such devices via a renormalization group approach but a quantitative microscopic characterization of the energy scales at which it appears is still missing. In our work, we propose an analysis of transport phenomena in Coulomb-blockaded topological superconductors based on tensor network simulations of their real-time dynamics after a quantum quench. We combine a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers, alongside a bosonic auxiliary degree of freedom to keep track of the charge of the device. This approach allows for the exploration of the strong coupling regime and nonperturbative transport effects linked to the presence of Majorana modes such as the quantization of the conductance in a two-terminal device. When more than two leads are present, each coupled with a single Majorana mode, we observe an anomalous current that suggests the emergence of a topological Kondo phase.