Extended Data Figure 8: Analysis of the mechanism of phase transition from 2H to 1T′ by the Hall effect.

a, c, Gate-dependent Raman intensity ratio. The ratio (1T′/1T′ + 2H)) is extracted from Lorentz fitting of Raman spectroscopy at each gate (as in Fig. 2b). Red arrows show forward and backward gate sweeping. From a, we determine the threshold for transition from phase 2H to 1T′ to be 3.2 V (red dashed line) on the basis of fitting with the Preisach model. The corresponding carrier density at this threshold is higher than that predicted theoretically⁷, perhaps because of the presence of kinetic barriers during transition, which were not considered in the theoretical calculation. In order to compare with the predicted critical doping level, where the two phases are energetically degenerate, we determined the corresponding critical voltage in c, following a typical method⁵⁰. The red dashed lines indicate that transition from phase 2H to 1T′ occurred at a bias of 2.6 V while the reverse process began at 2.2 V. The average (2.4 V) refers to the critical voltage at which the two phases are energetically degenerate. b, d, The Hall resistance [R_xy – R_xy(0)] for the same sample at 3.2 V (b) and 2.4 V (d), as a function of the magnetic field, B. Here R_xy is the transverse resistance under the magnetic field while R_xy(0) is the transverse resistance without magnetic field. The slopes of their linear fittings (dashed lines) give the corresponding carrier densities to be 2.2 × 10¹⁴ cm⁻² and 8.5 × 10¹³ cm⁻², respectively. The latter, which excludes the kinetic barrier, matches the carrier range that is predicted⁷ to drive this phase transition (0.4–1 × 10¹⁴ cm⁻²).