Postdoc Alfonso Maiellaro

Entanglement Order Parameters and Transport in Topological Superconductors

Topological superconductivity (TSC) is an exotic phase of matter characterized by a fully gapped superconducting bulk that hosts Majorana bound states protected by non-Abelian statistics and symmetries. Traditionally, TSC has been explored in semiconducting nanowires proximized by conventional superconductors. Recently, evidence for TSC has also been observed at LaAlO3/SrTiO3 (LAO/STO) interfaces. In the first part of this talk, we introduce an entanglement-based non-local order parameter for topological superconductors. Through various toy-lattice models, we demonstrate that this parameter is ideal for characterizing topological superconductors in both one-dimensional and quasi-one-dimensional systems. Specifically, for the Kitaev chain, this order parameter is quantized to ln(2)/2 in the topological phase and vanishes in the trivial phase. It accurately scales at quantum phase transitions, remains stable under interactions, and is robust against disorder and local perturbations. In the second part, we explore the transport properties of an oxide-based Josephson junction formed by constraining the 2DEG at the LAO/STO (001) interface into a quasi-1D system. We find that the strong enhancement of the critical current with an applied magnetic field can be linked to the emergence of Majorana bound states with an orbital-flavored internal structure, a feature absent in single-band models. These results provide strong evidence that the anomalous Josephson patterns observed experimentally are indicative of topological properties.