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SUMMARY:Topology at Scale:  Bridging Topological Phases\, Critical Phenome
 na\, and Real-Space Embedding - Antimo Marrazzo (SISSA)
DTSTART:20251127T140000Z
DTEND:20251127T153000Z
UID:TALK236002@talks.cam.ac.uk
CONTACT:Bo Peng
DESCRIPTION:Although the theory of topological insulators and superconduct
 ors is traditionally formulated in reciprocal space for ideal crystals\, m
 any robust\, topological phases emerge over more mesoscopic length scales 
 and in non-periodic media where standard definitions and computational too
 ls are of no avail. In this talk\, I will discuss two complementary exampl
 es of topology at scale: disordered topological insulators and proximity-d
 riven topological superconductors. \n\nTopological insulators are characte
 rized by an insulating bulk and conductive boundary modes protected by the
  nontrivial topology of the bulk electronic structure. While topological i
 nvariants are generally regarded as global quantities\, I will argue that 
 space-resolved topological markers can act as bona fide local order parame
 ters\, 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 simulat
 ions\, 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 r
 emain [4]. Such a topological correlation function is characterized by cri
 tical exponents that appear universal across disorder types\, yet they can
  resolve different topological phase transitions [4]. \n\nWhen a supercond
 uctor is placed in contact with a normal (i.e.\, non-superconducting) mate
 rial\, Cooper pairs can penetrate the latter and induce superconductivity 
 via the proximity effect. Notably\, s-wave superconductors can induce p-wa
 ve topological superconductivity in materials that are intrinsic topologic
 al insulators or that display Rashba spin textures. I will present our ong
 oing efforts [5] towards ab initio theory and simulations of the supercond
 ucting proximity effect based on real-space embedding and Wannier function
 s [6]\, paving the way for large-scale atomistic simulations of proximity-
 induced topological superconductivity.\n\n\n[1] R. Favata and A. Marrazzo\
 , _Single-point spin Chern number in a supercell framework_\, Electron. St
 ruct. 5 014005 (2023) \n\n[2] N. Baù and A. Marrazzo\, _Local Chern marke
 r for periodic systems_\, Phys. Rev. B 109 014206 (2024)\n\n[3] N. Baù an
 d A. Marrazzo\, _Theory of local Z2 topological markers for finite and per
 iodic two-dimensional systems_\, Phys. Rev. B 110  054203 (2024)\n\n[4] R.
  Favata\, N. Baù\, A. Marrazzo\, _Fluctuations and Correlations of Local 
 Topological Order Parameters in Disordered Two-dimensional Topological Ins
 ulators_\, Phys. Rev. Lett. 135\, 026603 (2025)\n\n[5] N. Baù\, M. Dowlat
 abadi\, T. Chiarotti\, M. Capone\, A. Marrazzo\, _in preparation_\n\n[6] A
 . Marrazzo\, S. Beck\, R. R. Margine\, N. Marzari\, A. A. Mostofi\, J. Qia
 o\, I. Souza\, S. S. Tsirkin\, J. R. Yates\, G. Pizzi\, _Wannier-function 
 software ecosystem for materials simulations_\, Rev. Mod. Phys. 96 045008 
 (2024)\n
LOCATION:Seminar Room 3\, RDC
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