Fig. 3: Tunable Chern states by dual-gating.

Color maps of σ_xx and ρ_yx as a function of dual-gate voltages for Mn(Bi_0.74Sb0_0.26)₂Te₄ at flake thicknesses of (a, b) 21-SLs, (c, d) 18-SLs, and (e, f) 14-SLs, respectively, measured at temperature of 2 K and magnetic field of 9 T. The white dashed lines in the color maps trace the boundaries of the quantization plateaus with the respective quantum states indexed in the ρ_yx maps. Line profiles of σ_xx and σ_xy versus backgate voltage curves swept across the charge neutrality as indicated by the black arrows in the color maps for the (g) 21-SLs, (h) 18-SLs, and (i) 14-SLs Mn(Bi_0.74Sb0_0.26)₂Te₄. The σ_xy plateaus and the corresponding σ_xx minima (indicated by the black arrows) are indexed to the Chern numbers in (g)–(i). Vertical dashed lines in (g)–(i) mark the backgate voltages corresponding to the \({\uprho}_{{{{{\mathrm{xx}}}}}}^{{{{{\mathrm{CNP}}}}}}\) determined at zero magnetic field. The surface band structures in (g)–(i) are sketched to illustrate the LL spectra observed for the respective thicknesses at 9 T. The red shades in (g)–(i) denote the Chern states forming near the CNP.