  New materials such as nodal-line semimetals offer a unique setting for novel
transport phenomena. Here, we calculate the quantum correction to conductivity
in a disordered nodal-line semimetal. The torus-shaped Fermi surface and
encircled $\pi$ Berry flux carried by the nodal loop result in a fascinating
interplay between the effective dimensionality of electron diffusion and band
topology, which depends on the scattering range of the impurity potential
relative to the size of the nodal loop. For a short-range impurity potential,
backscattering is dominated by the interference paths that do not encircle the
nodal loop, yielding a 3D weak localization effect. In contrast, for a
long-range impurity potential, the electrons effectively diffuse in various 2D
planes and the backscattering is dominated by the interference paths that
encircle the nodal loop. The latter, leads to weak antilocalization with a 2D
scaling law. Our results are consistent with symmetry consideration, where the
two regimes correspond to the orthogonal and symplectic classes, respectively.
Furthermore, we present weak-field magnetoconductivity calculations at low
temperatures for realistic experimental parameters, and predict that clear
scaling signatures $\propto\sqrt{B}$ and $\propto -\ln B$, respectively. The
crossover between the 3D weak localization and 2D weak antilocalization can be
probed by tuning the Fermi energy, giving a unique transport signature of the
nodal-line semimetal.

Mesoscale and Nanoscale Physics;Disordered Systems and Neural Networks;Materials Science