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    Localization and universality of three-dimensional pseudospin-s fermions

    Arpan Gupta and Gargee Sharma

    Phys. Rev. B 114, 034209 – Published 23 July, 2026

    DOI: https://doi.org/10.1103/4mj4-bc99

    Abstract

    Quantum interference of electrons in disordered conductors is a sensitive probe of the internal structure of quasiparticles, revealing universal signatures of symmetry through weak localization (WL) and weak antilocalization (WAL). While these phenomena are well understood for conventional Schrödinger and Dirac-Weyl fermions, their fate in the broader class of multifold chiral fermions remains largely unexplored. We develop a unified framework for semiclassical transport and quantum interference in three-dimensional disordered fermions with an arbitrary pseudospin s. Starting with a general short-range matrix disorder M, we derive compact expressions for elastic lifetimes and ladder vertex corrections for arbitrary pseudospin with multiband effects. We then show that, in the scalar-disorder limit, while the Drude conductivity is strongly pseudospin and helicity dependent, the leading quantum-interference correction exhibits a striking universality: its magnitude remains identical to that of conventional diffusive metals and Weyl fermions, while its sign is determined solely by the parity of 2s, placing half-integer pseudospins in the symplectic class (WAL) and integer pseudospins in the orthogonal class (WL). We also analyze the role of interband and intervalley scattering for s=3/2. By solving the resulting coupled Bethe-Salpeter equations, we demonstrate that channel mixing suppresses WAL and drives a crossover toward localization. Our results establish a general theory of localization across the full pseudospin hierarchy, revealing the interplay between internal geometry, symmetry class, and transport universality.

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