Fig. 3: Extrinsic AHE with linear scaling relation and Kondo resonance in non-magnetic transition metal dichalcogenides (TMDs) 6R-TaS₂.

a Map of AHE (\({\sigma }_{{{\rm{AHE}}}}\) vs. \({\sigma }_{{xx}}\)) for various materials in double logarithmic coordinates, spanning over the side-jump (\({\sigma }_{{{\rm{AHE}}}}\propto {\sigma }_{{xx}}^{1.6}\)), intrinsic (\({\sigma }_{{{\rm{AHE}}}}\propto\) constant), and skew-scattering (\({\sigma }_{{{\rm{AHE}}}}\propto {\sigma }_{{xx}}\)) regimes. The solid lines are the linear fitting of \({\sigma }_{{{\rm{AHE}}}}\) vs. \({\sigma }_{{xx}}\) for 6R-TaS₂ device #1, #2 and #3. The dashed line is the linear fitting of \({\sigma }_{{{\rm{AHE}}}}\) vs. \({\sigma }_{{xx}}\) for MnGe¹⁹. b The linear dependence of \({\sigma }_{{{\rm{AHE}}}}\) vs. \({\sigma }_{{xx}}\) for 6R-TaS₂ samples with a linear scale. c T-dependent dI/dV spectrum of the 1H layer at zero magnetic field (V_s = −5 mV, I = 400 pA). d Zero-field scanning tunneling spectroscopy (STS) of the superconducting gap at T = 0.3 K and atomically resolved topography of the 1H layer (inset). The red dot shows the location where the STS spectra were measured. e Kondo resonance in the 1 T layer from 0.3 K (superconducting state) to up to 12 K (normal state) (V_s = −50 mV, I = 400 pA). f Kondo resonance of the 1 T layer at T = 0.3 K. Inset shows scanning tunneling microscopy (STM) topography of the 1 T layer with the \(\sqrt{13}\times \sqrt{13}\) charge-density-wave (CDW) pattern. The red dot shows the location where the STS spectra were measured.