Extended Data Fig. 12: Experimental indications of a further novel phase close to the Lifshitz transition of the half metal, termed phase V.

We find this additional phase near the density in which the doubly degenerate inner electron pocket is present, consistent with the result r_s > 34 (dashed red) for the electron pocket in Fig 1e of the main manuscript. Potentially this phase resembles phase II and/or III but for the doubly degenerate case. a, Conductance as a function of charge carrier density for different temperatures at E = −0.6 V/nm and B = 0.6 T. The insulating correlated phases are highlighted in blue. The maximum/minimum charge carrier density at which phase V is stable is marked by a black square/circle. b, Zoom-in of a around phase V. c, Resistance as a function of temperature T for phase V at E = −0.6 V/nm, B = 0.6 T, and n = −3.4 x 10¹¹ cm⁻². d, Conductance as a function of charge carrier density and magnetic field at E = −0.6 V/nm. The maximum/minimum charge carrier density at which phase V is stable at B = 0.6 T is marked by a black square/circle. e, Conductance as a function of charge carrier density and electric field at B = 0.6 T. The maximum/minimum charge carrier density at which phase V is stable at E = −0.6 V/nm is marked by a black square/circle.