Time-dependent electric transport in nodal loop semimetals

Close to the Fermi energy, nodal loop semimetals have a torus-shaped, strongly anisotropic Fermi surface, which affects their transport properties. Here we investigate the non-equilibrium dynamics of nodal loop semimetals by going beyond linear response and determine the time evolution of the current after switching on a homogeneous electric field. The current grows monotonically with time for electric fields perpendicular to the nodal loop plane however it exhibits nonmonotonical behavior for field orientations aligned within the plane. After an initial nonuniversal growth ∼ E t , the current first reaches a plateau ∼ E . Then, for perpendicular directions, it increases while for in-plane directions it decreases with time to another plateau, still ∼ E . These features arise from interband processes. For long times or strong electric fields, the current grows as ∼ E3/2t or ∼E3t2 for perpendicular or parallel electric fields, respectively. This nonlinear response represents an intraband effect where the large number of excited quasiparticles respond to the electric field. Our analytical results are benchmarked by the numerical evaluation of the current from continuum and tight-binding models of nodal loop semimetals