Sign reversal of magnetoresistivity in massive nodal-line semimetals due to the Lifshitz transition of the Fermi surface

Topological nodal-line semimetals offer an interesting research platform to explore exotic phenomena associated with its torus-shaped Fermi surface. Here, we study magnetotransport in the massive nodal-line semimetal with spin-orbit coupling and finite Berry curvature distribution which exists in many candidates. The magnetic field leads to a deformation of the Fermi torus through its coupling to the orbital magnetic moment, which turns out to be the main scenario of the magnetoresistivity (MR) induced by the Berry curvature effect. We show that a small deformation of the Fermi surface yields a positive MR $\propto B^2$, different from the negative MR by pure Berry curvature effect in other topological systems. As the magnetic field increases to a critical value, a topological Lifshitz transition of the Fermi surface can be induced, and the MR inverts its sign at the same time. The temperature dependence of the MR is investigated, which shows a totally different behavior before and after the Lifshitz transition. Our work uncovers a unique scenario of the MR induced solely by the deformation of the Fermi surface and establishes a relation between the Fermi surface topology and the sign of the MR.

Figure 1

(a) Schematic diagram of the torus-shaped Fermi surface in nodal-line semimetal, with the major radius $k_0$, minor radius $\kappa$, toroidal angle $\theta$, and poloidal angle $\phi$. (b) Finite distribution of Berry curvature in the poloidal cross section. (c)–(e) Fermi surface deformation induced by the magnetic field, with (c) a slight deformation, (d) critical point of topological Lifshitz transition, and (e) Fermi surface with genus one.

Figure 2

MR as a function of magnetic field $B$ for different gap $\mathrm{\Delta }$ in the regime of slight Fermi surface deformation. The relevant parameters are ${\epsilon }_F=41\mathrm{meV}, T=5\mathrm{K}, k_0=10{\mathrm{nm}}^{-1}, \tau ={10}^{-14}\mathrm{s}$, and $v_0={10}^5$ m/s

Figure 3

(a) MR as a function of $B$ for different gap $\mathrm{\Delta }$ with and without sign reversal. (b) Correspondence between the sign reversal point and the critical field $B^{*}$ (open circles) for the Lifshitz phase transition. The right panel of (b) illustrates the Lifshitz transition induced by the magnetic field, which can be compared with the MR results. Other parameters are the same as those in Fig. 2.

Figure 4

Temperature dependence of MR for different Fermi energies ${\epsilon }_F$ (a) without and (b) with Lifshitz transition illustrated by the inset. The parameters are $\mathrm{\Delta }=20\mathrm{meV}, B=3\mathrm{T}$ and the others are the same as those in Fig. 2.