Nontrivial Berry phase in magnetic BaMnSb2 semimetal

Abstract

The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either time-reversal or inversion symmetry breaking to lift degeneracy at Dirac points. Here we demonstrate experimentally that canted antiferromagnetic BaMnSb₂ is a 3D Weyl semimetal with a 2D electronic structure. The Shubnikov-de Hass oscillations of the magnetoresistance give nearly zero effective mass with high mobility and the nontrivial Berry phase. The ordered magnetic arrangement (ferromagnetic ordering in the ab plane and antiferromagnetic ordering along the c axis below 286 K) breaks the time-reversal symmetry, thus offering us an ideal platform to study magnetic Weyl fermions in a centrosymmetric material.

Keywords: 3D semimetal; nontrivial Berry phase; topological material.

Fig. 1.

(A) Schematic crystal structure of BaMnSb₂. (B) Image of a single crystal. (C) Temperature dependence of magnetic susceptibilities along the ab plane (χ_ab) and c direction (χ_c). Inset shows magnetic susceptibilities near the transition temperature T_N. (D) Temperature dependence of electrical resistivities along the ab plane (ρ_ab) and c direction (ρ_c). Inset shows the temperature dependence of ρ_c/ρ_ab. The data are replotted in logarithmic scales for (E) ρ_ab(T) and (F) ρ_c(T).

Fig. 2.

(A) Brillouin zone of BaMnSb₂ (half). (B) Band structure within ±1 eV from the Fermi energy for k_z = 0 (Bottom), Z/2 (Middle), and Z (Top). (C) Spin configuration of Mn.

Fig. 3.

(A) Demonstration of the field dependence of ρ_ab at 7 and 60 K. The dashed line represents the smooth background at 7 K. (B) Field dependence of oscillatory component ∆ρ_ab at indicated temperatures. (C) ∆ρ_ab plotted as a function of H⁻¹. (D) Landau level fan diagram obtained from Δρ_ab. (E) Fast Fourier transformation of oscillatory ∆ρ_ab at indicated temperatures. (F) Temperature dependence of FFT amplitude for ∆ρ_ab. Inset shows normalized oscillation amplitude versus T/H for ∆ρ_ab, ∆ρ_xy, and ∆ρ_c at the second LL.

Fig. 4.

(A) Field dependence of Hall resistivity ρ_xy at indicated temperatures. (B) Oscillatory Hall component ∆ρ_xy plotted as a function of H⁻¹. (C) Field dependence of oscillatory Hall (Δσ_xy) conductivities. (D) Landau level fan diagram constructed from Δσ_xy(H) at 2 K. (E) Oscillatory Δρ_ab(H) and Δρ_xy(H) plotted as $\text{ln}\left(\frac{\mathrm{\Delta }\rho }{{\rho }_0}\frac{\text{sinh}\left(\Omega /H\right)}{\Omega /H}\right)$ versus $H^{-1}$ ($\Omega =2{\pi }^2{k}_B{m}^{\ast }T/e\hslash$). (F) Temperature dependence of carrier concentration.

Fig. 5.

(A) Demonstration of the field dependence of ρ_c at 1.85 and 60 K. (B) Field dependence of oscillatory component ∆ρ_c at indicated temperatures.

Fig. S1.

X-ray diffraction pattern of BaMnSb₂ powder by crushing single crystals.