Optical Signatures and Quantum Geometry in Proximity-Induced Topological Superconductors

Abstract: Proximity-induced superconductivity at topological insulator-superconductor (TI-SC) interfaces offers a promising route to topological superconductivity with Majorana boundary modes. However, probing the interfacial superconductivity at buried interfaces is challenging with conventional surface methods. Here, we present a theoretical study of the longitudinal optical response of a TI-SC heterostructure, focusing on the complex interface sheet conductance as a direct and layer-selective probe of the interfacial superconducting gap. Within a minimal TI--SC model, we demonstrate that proximity-induced superconductivity at the buried interface generates a two-dimensional topological superconducting phase supporting Majorana edge modes. Using a Bogoliubov-de Gennes slab model and the Kubo formalism, we compute the optical conductance and introduce a thickness-extrapolation protocol that isolates the interface contribution only. The resulting interface conductance exhibits a robust, thickness-independent coherence peak at an energy set by the proximity-induced gap, distinguishable from both the parent superconductor's pair-breaking feature and the ungapped Dirac cone on the top surface. We further demonstrate that the low-frequency spectral weight of this interface resonance obeys a quantum-metric sum rule, quantitatively linking the optical response to the quantum geometry of the proximitized interfacial state. Our results propose terahertz/infrared spectroscopy of the interfacial sheet conductance as a non-invasive diagnostic of Majorana-hosting TI--SC interfaces.