Change in resistivity between T=0.35 K and T=5 K (ρ(0.35K)-ρ(5K)) as function of front gate and back gate voltages (which can be mapped into density and valley splitting). Blue color indicate metallic behavior while red color indicate insulating behavior. Below the dashed line (A) the system is valley polarised showing insulating behaviour.

Spin is crucial in determining the nature of the two-dimensional electron system (2DES). Lifting spin degeneracy by applying an in-plane magnetic field first dramatically increases the resistivity and second, tends to drive a metallic system into an insulating one (MIT). Experiments had suggested that this is the case regardless of valley degeneracy, being observed in valley-degenerate systems such as Si-MOSFETs as well as non-valley-degenerate p-type GaAs. The detailed phenomenology is, however, more complex and has yet to be fully understood. It might be expected that the role played by the valley degree of freedom is, in essence, equivalent to that of the spin degree of freedom. This, to some extent, has been demonstrated in recent experiments in AlAs quantum wells in which a valley splitting is induced and tuned by applying symmetry breaking strain. These experiments showed that for certain fixed electron densities, spin and valley both need to be polarized before insulating behavior is observed in contrast to previous experiments in silicon where lifting only the spin degeneracy is sufficient to induce a transition to insulating behavior. This indicates that other parameters must also be at play. Electron density and disorder are both already known to be vital and call for these to be examined in conjunction with spin and valley degrees of freedom. Here, we have addressed the temperature dependence of the resistivity in silicon-on-insulator quantum-well structures in which the valley splitting can be swept electrically, in addition to, and independently from the electron density. We have found that increasing valley polarization increases resistivity, and strong metallic temperature dependence is suppressed, although incompletely, depending on density (see the figure). Furthermore, upon crossing the valley partially polarized–fully-polarized boundary, our data reveal an insulating contribution to the resistivity arising from the upper-valley-subband edge. We hypothesized that this may be due to scattering induced by localized magnetic moments in the localized tail of the upper valley subband via a Kondo mechanism. In turn, our results suggest that in parallel magnetic field experiments of valley-degenerate systems, localized valley moments may scatter electrons in the lower spin subband via an analogous mechanism which may provide an avenue for understanding some of the unexplained phenomenology.