Constraining the Superconducting Gap of Monolayer FeSe/SrTiO$_3$ via Statistical Analysis and Tip-Height-Dependent Tunneling Spectroscopy

Abstract

Monolayer FeSe grown on SrTiO$_3$ (001) exemplifies interface-enhanced superconductivity, exhibiting a transition temperature nearly ten times that of bulk FeSe. Yet, its tunneling spectra lack clearly identifiable superconducting coherence peaks, preventing an unambiguous determination of the gap magnitude. Here, we use ultralow-temperature scanning tunneling spectroscopy as a function of temperature, tip-sample separation, and lateral position to disentangle tunneling contributions by statistical analysis. Decay rates extracted by regression of tip-height-dependent spectroscopy reveal three energy regimes: Andreev-reflection-dominated tunneling below 6 meV, mixed Andreev and quasiparticle tunneling between 6 and 13 meV, and predominantly quasiparticle tunneling above 13 meV. Spatially resolved spectroscopy and correlation analysis further reveal that the tunneling conductance is predominantly localized near defects below 6 meV but becomes spatially extended at higher energies. Together, these results constrain the superconducting gap to lie between 6 and 13 meV. Our findings establish statistical analysis of spectroscopy as a powerful approach to constraining superconducting gap structures when complex spectral features prevent the unambiguous identification of coherence peaks.