Even/Odd-parity STS spectra induced by quantum well mirror symmetry breaking in iron-based superconductors

Abstract

Determining whether superconducting scanning tunneling spectroscopy (STS) is uniquely dictated by crystal structure constitutes a fundamental challenge in condensed matter physics. Here, we systematically investigate bulk FeSe single crystals, monolayer FeSe, and $\mathrm{KCa_2Fe_4As_4F_2}$. We resolve one-, two-, and three-order checkerboard quantum-well structures that perfectly match the experimentally observed one, two, and three pairs of superconducting coherence peaks. In bulk FeSe, quantum wells promote real-space Cooper pairing and form degenerate antiferromagnetic checkerboard sublattices, yielding bosonic even-parity STS responses. In monolayer FeSe, mirror symmetry breaking suppresses Cooper pairing and induces nondegenerate ferromagnetic sublattice dichotomy, producing fermionic odd-parity STS spectra. We establish a universal gap scaling law $\Delta(T, \xi) = \eta(T)/\xi^2$, where $\eta(T)$ is a temperature-dependent prefactor and $\xi$ denotes quantum-well depth that governs the number and magnitude of superconducting gaps. For $\mathrm{KCa_2Fe_4As_4F_2}$, our predicted gap pairs of $\pm6.2$ meV, $\pm5.6$ meV, and $\pm4.2$ meV are in excellent agreement with experimental results of $\pm6.2$ meV, $\pm5.4$ meV, and $\pm4.4$ meV. This quantum-well mechanism unifies mirror symmetry breaking, checkerboard sublattice ordering, Cooper pairing, fermion-boson duality, and half-Bogoliubov states for STS interpretation, offering new insights toward a unified high-$T_\text{c}$ superconductivity theory.