Fig. 4: Bulk quantum Hall effect in Eu-doped BaMnSb₂.

a Magnetic field dependences of ρ_xx and ρ_xy of the Hall bar sample E#1, measured with field perpendicular to the Sb-plane up to 64 T (see Supplementary Note 5 and Fig. 11). The arrows indicate the oscillation peak splitting in ρ_xx. b Magnetic field dependence of R_zz at various temperatures (T = 0.7, 4.1, 10, 20, 40, 80, and 150 K), measured on another Eu-doped sample (E#2) with a similar composition. The red arrows indicate the splitting in an oscillation valley. c Normalized inverse Hall resistivity (\({\rho }_{{xy}}^{0}/{\rho }_{{xy}}\)) and in-plane resistivity (ρ_xx) versus \({B}_{F}/B\) for sample E#1. d The Hall conductivity σ_yx per Sb layer normalized by 2e²/h, and longitudinal conductivity σ_xx as a function of \({B}_{F}/B\) at 4.5 K. e Temperature dependence of R_zz at 58.5 T for sample E#2. f The LLs calculated from the effective model around \({{\boldsymbol{K}}}_{\pm }\). LLs for \({{\boldsymbol{K}}}_{+}\) and \({{\boldsymbol{K}}}_{-}\) are presented as the blue and red lines, respectively. The black line is \({E}_{F}\). Bottom panel in f: The DOS at \({E}_{F}\) with Gaussian disorder broadening \({\Gamma }_{0}=2\) meV (blue) and \({\Gamma }_{0}=3\) meV (red)²³. The numbers above the black arrows label the LL filling at DOS minima.