Quantum transport in topological nodal-line semimetals

ABSTRACT Topological nodal-line semimetals offer an attractive research platform for exploring a variety of novel phenomena, which have attracted great research interest in the past decade. There are three unique features of the nodal-line semimetals: (i) band crossing along the closed loop that carries Berry phase, (ii) torus-shaped Fermi surface as the Fermi energy deviates from the nodal loop, and (iii) drumhead-like surface states induced by the band topology, which comprise the main scenarios for most of its electronic properties. Here, we review recent progress on the quantum transport theory of nodal-line semimetals. We show that the properties (i) and (ii) result in a fascinating interplay between the effective dimensionality of electron diffusion and the band topology, which may give rise to 3D weak localization or 2D weak anti-localization effect that can be probed by the magnetoconductivity induced by a weak magnetic field. Moreover, (i) and (ii) can also be revealed by the pattern of the Shubnikov–de Hass oscillation in a strong magnetic field. For the massive nodal-line semimetals with spin-orbit coupling, we show that the magnetic field can induce a topological Lifshitz transition of the Fermi torus from genus 1 to 0. Interestingly, the Lifshitz transition is in good coincidence with the sign reversal of the magnetoresistivity. Compared to the conventional Fermi sphere, the Fermi torus possesses multiple reflection channels, which may give rise to novel scattering processes such as anomalous Andreev reflection at the interface between the semimetal and a superconductor. Besides the bulk states, the drumhead surface states also possess interesting properties. It is shown that the spin polarization of the surface states can induce resonant spin-flipped reflection, which can be detected through both spin and charge transport measurements. We also briefly review the recent experimental progress on the transport properties of nodal-line semimetals and compare the results with the theoretical predictions. Graphical Abstract