Optical Signatures and Quantum Geometry in Proximity-Induced Topological Superconductors

Topological-insulator-superconductor (TI-SC) heterostructures provide a promising platform for proximity-induced topological superconductivity, but diagnosing superconductivity at a buried interface remains challenging for conventional surface-sensitive probes. Here, we develop a quantitative theory of the longitudinal optical response of a TI-SC heterostructure and show that the complex sheet conductance provides an interface-selective route to isolating and diagnosing the buried proximitized interface state. Starting from a minimal model, we derive a low-energy description of the heterointerface in which the induced gap emerges directly from the TI-SC coupling. Combined with a slab-based thickness-extrapolation procedure, this framework yields a practical protocol for separating the buried interfacial sheet conductance from bulk and exposed-surface optical contributions. The extracted interface response exhibits a robust, thickness-independent coherence peak at an energy set by the proximity-induced gap, clearly distinguishable from both the pair-breaking scale of the parent superconductor and the Dirac cone on the exposed TI surface. At low energies, the heterointerface is described by an effective time-reversal-invariant topological-superconducting theory, while the associated low-frequency optical spectral weight admits a quantum-geometric interpretation through the optical sum rule. Our results establish terahertz/infrared spectroscopy of thickness-extracted sheet conductance as a noninvasive route to identifying and quantifying proximity-induced superconductivity at buried TI-SC interfaces.