Localization in two-dimensional fermions with arbitrary pseudospin

In condensed matter, limited symmetry constraints allow free fermionic excitations to exist beyond the conventional Weyl and Dirac electrons of high-energy physics. These excitations carry a higher pseudospin, naturally generalizing the Weyl fermion. How do electrons beyond the conventional Dirac and Weyl fermions localize under disorder? In this Letter, we solve the problem of localization of two-dimensional free fermionic excitations carrying an arbitrary pseudospin-$s$. We derive exact analytical expressions for fermionic wavefunctions and exploit their curious mathematical connection to Pascal's triangle to evaluate relevant quantities such as scattering time, renormalized velocity, Cooperon, and magnetoconductivity. We discover that the gapless Cooperon mode solely depends on the pseudospin even when the Fermi surface is composed of multiple pockets, leading to weak localization (antilocalization) behavior for integer (half-integer) $s$, irrespective of the band index. Remarkably, the localization corrections increase with $s$, but the relative localization corrections are found to decrease with $s$, i.e., faster-moving relativistic electrons are less susceptible to disorder effects. Coupled with our elementary analysis on electron-electron interactions, this sheds insights on Anderson and many-body localization in these materials.