Zeeman-activated Berry curvature magnetotransport from the bulk of non-magnetic metals with inversion symmetry

TL;DR

The paper identifies a universal weak-field mechanism for negative longitudinal magnetoresistance (NLMR) in centrosymmetric, non-magnetic metals with strong spin–orbit coupling. By symmetry analysis and a four-band model, it shows that an infinitesimal Zeeman coupling activates a $d$-wave Berry curvature whose strength is governed by band non-parabolicity, independent of the field magnitude and $g$-factor, and that this BC couples to orbital motion to produce an intrinsic NLMR. Using semiclassical transport with Berry curvature corrections, the authors derive a leading BC-induced conductivity correction $\Delta \sigma_{yy}(B_y) \propto B_y^2$ that scales with the density-of-states modification and is independent of disorder, yielding $\Delta \rho/\rho \approx -\Delta \sigma/\sigma$. The effect is shown to be generic across all centrosymmetric point groups and applicable to both topological and conventional bands, with potential relevance to materials like Bi$_2$Se$_3$ and Bi$_{1-x}$Sb$_x$. This work broadens the understanding of magnetotransport in nonmagnetic materials by linking Zeeman activation of BC to intrinsic, topology-insensitive NLMR, and suggests new avenues to explore quantum geometry-driven transport in a wide class of materials.

Abstract

The Berry curvature (BC), a quantity encoding the geometry of electronic wavefunctions, governs various electronic transport effects in quantum materials. In magnetic systems, the BC is reponsible for the intrinsic part of the anomalous Hall conductivity. Local concentrations of BC in non-centrosymmetric materials can lead instead to the quantum nonlinear Hall effect. Here, we argue that the bulk of non-magnetic metals with inversion symmetry, systems where the BC is forced to vanish at any momentum, can be endowed with substantial concentrations of BC even with an infinitesimally small Zeeman coupling. This Zeeman-activated BC, independent of the magnetic field strength and instead related to the degree of non-parabolicity of the electronic bands, couples to the electronic orbital motion to generate a negative longitudinal magnetoresistance that scales with the relaxation time as the Drude resistivity. We show that the Zeeman-actived BC and the related intrinsic negative magnetoresistivity are generic: they appear in all centrosymmetric point groups and can occur both in topological and conventional conductors.

Figures (3)

• Figure 1: Density plots of the $d$-wave Berry curvature $\Omega_x^{+}({\bf k})$ induced by the generalized Zeeman coupling in the $k_x,k_y$ and $k_y,k_z$ planes. In both cases we have chosen $b=a=1$.
• Figure 2: Top pannel: Sketch of a device for longitudinal magnetoresistance measurement with the direction of the driving electric field and the applied in-plane magnetic field. The right panel shows an ensuing negative longitudinal magnetoresistance quadratic in the magnetic field. Bottom pannel: Behavior of the negative magnetoresistance $\Delta \rho(B_y)/\rho(0)$ obtained using the generalized Zeeman coupling Eq. \ref{['eq:zeemangeneralized']} as a function of the Fermi wavevector $k_F$ measured in units of the inverse of the characteristic material dependent length scale $l_0=\sqrt{a/b}$. The magnetoconductivity is rescaled by the factor $(l_0/l_B)^4$ with $l_B=\sqrt{\hbar / (e B_y)}$ the Landau magnetic length.
• Figure 3: Berry curvature for the four-band model. The upper panel shows a density plot of $\Omega^{+}_{\bm k, x}$ for the conduction band for different projection planes. The middle panel shows $\Omega^{+}_{\bm k, y}$ and the bottom panel shows $\Omega^{+}_{\bm k, z}$.