Localization and universality of three-dimensional pseudospin-$s$ fermions

TL;DR

This paper develops a unified semiclassical framework for three-dimensional disordered pseudospin-$s$ fermions, revealing universal quantum interference signatures and the influence of pseudospin parity on localization phenomena.

Contribution

It introduces a comprehensive theory for quantum interference and localization in 3D pseudospin-$s$ fermions, highlighting universality and symmetry class distinctions based on pseudospin parity.

Findings

Quantum interference correction magnitude is universal across pseudospin-$s$ fermions.

Sign of quantum correction depends solely on the parity of 2s, classifying systems into symplectic or orthogonal classes.

Interband and intervalley scattering can suppress WAL and induce localization.

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 the conventional Schr\"odinger 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 from a general short-range matrix disorder $\mathcal{M}$, we derive compact expressions for elastic lifetimes and ladder vertex corrections for arbitrary pseudospin with multiband effects, and then show that in the scalar-disorder limit while the Drude conductivity is strongly pseudospin and helicity dependent, in contrast, 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 an interplay between internal geometry, symmetry class, and transport universality.