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The authors solve the quantum scattering problem across an electrostatic barrier in $\mathcal{PT}$-symmetric topological nodal-line semimetals to evaluate their linear and nonlinear longitudinal and Hall conductances via the Landauer-Büttiker formalism. Mapping these transport properties is vital for exploiting momentum-space degeneracies in low-dissipation quantum and neuromorphic device architectures. They reveal that Klein tunneling persists at normal incidence via Berry-curvature-induced momentum locking, with $\mathcal{PT}$-breaking mass terms inducing robust transverse Hall currents and dramatically amplifying nonlinear transport signatures.
Klein tunneling survives across extended 3D nodal rings via Berry-curvature momentum locking, unlocking massive nonlinear Hall responses that could anchor dissipation-less topological switching.
Topological nodal-line semimetals are three-dimensional quantum materials characterized by band crossings that form closed loops in momentum space. In $\mathcal{PT}$-symmetric realizations, these nodal rings are stabilized in the absence of spin-orbit coupling, giving rise to drumhead surface states and unconventional transport responses. In this work, we study charge transport across a nodal-line semimetal containing a finite electrostatic barrier, with both leads described by the same equilibrium material. By solving the corresponding scattering problem, we show that the transmission across the barrier exhibits {Klein-tunneling behavior protected at normal incidence by the nodal topology}, despite the extended nodal-line dispersion, which can be traced back to Berry-curvature-induced momentum locking. Using the Landauer-B\"uttiker formalism, we derive general expressions for the linear and nonlinear conductances, including both longitudinal and Hall components, and evaluate them at zero and finite temperature. Our analytical and numerical results elucidate the dependence of the conductance on barrier height and width, as well as on a $\mathcal{PT}$-breaking mass term. We identify distinct transport regimes in which nonlinear contributions are strongly enhanced and transverse Hall currents emerge, providing clear transport signatures of nodal-line topology and suggesting potential routes toward device applications.