Fate of the extended states in a vanishing magnetic field: The role of spins in strongly interacting two-dimensional electron systems

In noninteracting two-dimensional (2D) electron systems, the extended states “float up” in energy in the vanishing perpendicular magnetic field $B_{\perp },$ giving rise to an insulator. However, in strongly interacting 2D systems, the extended states remain at a finite energy as $B_{\perp }\to 0,$ thus allowing conduction. Here we show that polarizing the electrons’ spins in strongly interacting systems causes the extended states to once more “float up” in energy, as they do for noninteracting electrons. The difference between extended states that float up (an insulator) or remain at a constant energy (a metal) is thus unambiguously tied to the existence of the spins.