Topology at Scale: Bridging Topological Phases, Critical Phenomena, and Real-Space Embedding

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• Antimo Marrazzo (SISSA)
• Thursday 27 November 2025, 14:00-15:30
• Seminar Room 3, RDC.

If you have a question about this talk, please contact Bo Peng.

Although the theory of topological insulators and superconductors is traditionally formulated in reciprocal space for ideal crystals, many robust, topological phases emerge over more mesoscopic length scales and in non-periodic media where standard definitions and computational tools are of no avail. In this talk, I will discuss two complementary examples of topology at scale: disordered topological insulators and proximity-driven topological superconductors.

Topological insulators are characterized by an insulating bulk and conductive boundary modes protected by the nontrivial topology of the bulk electronic structure. While topological invariants are generally regarded as global quantities, I will argue that space-resolved topological markers can act as bona fide local order parameters, bridging topological phases and the theory of critical phenomena by revealing the role of fluctuations and correlations in the local topology under disorder and vacancies [1-4]. Through large-scale numerical simulations, we find that short-scale fluctuations of topological markers vanish upon coarse-graining, except at the topological phase transition, where their correlation length peaks and large-scale topological fluctuations remain [4]. Such a topological correlation function is characterized by critical exponents that appear universal across disorder types, yet they can resolve different topological phase transitions [4].

When a superconductor is placed in contact with a normal (i.e., non-superconducting) material, Cooper pairs can penetrate the latter and induce superconductivity via the proximity effect. Notably, s-wave superconductors can induce p-wave topological superconductivity in materials that are intrinsic topological insulators or that display Rashba spin textures. I will present our ongoing efforts [5] towards ab initio theory and simulations of the superconducting proximity effect based on real-space embedding and Wannier functions [6], paving the way for large-scale atomistic simulations of proximity-induced topological superconductivity.

[1] R. Favata and A. Marrazzo, Single-point spin Chern number in a supercell framework, Electron. Struct. 5 014005 (2023)

[2] N. Baù and A. Marrazzo, Local Chern marker for periodic systems, Phys. Rev. B 109 014206 (2024)

[3] N. Baù and A. Marrazzo, Theory of local Z2 topological markers for finite and periodic two-dimensional systems, Phys. Rev. B 110 054203 (2024)

[4] R. Favata, N. Baù, A. Marrazzo, Fluctuations and Correlations of Local Topological Order Parameters in Disordered Two-dimensional Topological Insulators, Phys. Rev. Lett. 135, 026603 (2025)

[5] N. Baù, M. Dowlatabadi, T. Chiarotti, M. Capone, A. Marrazzo, in preparation

[6] A. Marrazzo, S. Beck, R. R. Margine, N. Marzari, A. A. Mostofi, J. Qiao, I. Souza, S. S. Tsirkin, J. R. Yates, G. Pizzi, Wannier-function software ecosystem for materials simulations, Rev. Mod. Phys. 96 045008 (2024)

This talk is part of the Theory of Condensed Matter series.

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