Metal-insulator transition in a 2D electron gas: Equivalence of two approaches for determining the critical point

The critical electron density for the metal-insulator transition in a two-dimensional electron gas can be determined by two distinct methods: (i) a sign change of the temperature derivative of the resistance, and (ii) vanishing activation energy and vanishing nonlinearity of current-voltage characteristics as extrapolated from the insulating side. We find that, in zero magnetic field (but not in the presence of a parallel magnetic field), both methods give equivalent results, adding support to the existence of a true zero-field metal-insulator transition.