High-temperature superconductivity and topological quantum matter remain among the central challenges in condensed matter physics. Their coexistence offers a promising route toward realizing Majorana zero modes and fault-tolerant quantum technologies. While studies of topological materials and electron-phonon coupling have largely relied on single particle descriptions, the role of strong electronic correlations remains unresolved. In particular, it is unclear (i) how correlations modify electron-phonon coupling [1] and lattice dynamics in determining superconducting transition temperatures and (ii) how electron-electron interactions drive topological systems beyond the single-particle limit.

In this talk, I will discuss our efforts to address these questions using parameter tuning-free embedded dynamical mean-field theory (eDMFT) [2]. By combining epitaxial thin-film growth, angle-resolved photoemission spectroscopy (ARPES), and scanning tunneling microscopy/spectroscopy (STM/S). Focusing on FeX (X = Se, S, Te) thin films on SrTiO₃ (001), we demonstrate a strong dependence of the superconducting transition temperature () on the FeX₄ tetrahedral bond angle, highlighting the crucial role of lattice geometry in correlated superconductivity [3]. We further present evidence for topological superconductivity and identify a distinct phase that competes with strong electronic correlations[4]. Remarkably, both the measured superconducting gap and the eDMFT-derived electron-phonon coupling exhibit a dome-shaped dependence on the tetrahedral angle [5]. I will then show how these insights can be extended toward a predictive, materials-by-design framework for topological superconductivity. Applying a multiscale framework to FeTe₀.₅Se₀.₅ and FeSe/GaAs heterostructures, we predict multiple topological superconducting phases and identify experimentally viable materials platforms in which topology, superconductivity, and strong correlations can be engineered in concert [5,6]. Together, these results demonstrate how electronic correlations, lattice geometry, and interface engineering can be harnessed to control superconductivity and topology, providing a pathway toward the rational design of correlated topological quantum materials and future Majorana-based quantum technologies.

References:
[1] S. Mandal et al. PRB 89, 220502(R) (2014); S. Gerber et al. Science 357, 71 (2017).
[2] A. Sihi, S. Mandal, & K. Haule, Phys. Rev. B (Lett.) 113, L201116 (2026); (Editor's suggestion)
[3] S. Mandal et al. PRL. 119, 067004 (2017); Q. Zou, et al. Nano Letters 25, (47) 16572 (2025)
[4] H. Lin, et al. Nature Communications 17, 1188 (2026)
[5] Q. Zou, et al. Phys. Rev. B 114, 225123 (2026) (Editor's suggestion)
[6] Jacobs et al. arXiv:2609.10381 (2026).