Spin-valley phase diagram of the two-dimensional metal-insulator transition

The metallic behaviour of the resistivity observed at low temperatures in low-disorder, dilute, two-dimensional (2D) carrier systems is of considerable interest as it defies the scaling theory of localization in two dimensions. Although the origin of the metallic behaviour remains unknown and controversial, there is widespread evidence that the spin degree of the freedom plays a crucial role. Here, we directly probe the role of another discrete electronic degree of freedom, namely the valley polarization. Using symmetry-breaking strain together with an in-plane magnetic field to tune the valley and spin polarizations of an AlAs 2D electron system at fixed density, we map out a spin-valley phase diagram for its metal-insulator transition. The insulating phase occurs in the quadrant where the system is sufficiently spin and valley polarized. This observation establishes the equivalent roles of spin and valley degrees of freedom in the 2D metal-insulator transition.