The in-plane magnetoconductance of the strongly interacting two-dimensional electron system in a silicon MOSFET (metal-oxide-semiconductor-field-effect transistor) exhibits an unmistakable kink at a well-defined electron density,
nk. The kink at
nk is near, but not at the critical density
nc determined from resistivity measurements, and the density at which
nk occurs varies with temperature. These features are inconsistent with expectations for a quantum phase transition. We suggest instead that this is a percolation transition and present a detailed model based on the formation of a mixed insulating and metallic phase within which a metal-insulator transition takes place by percolation.
The resistivities of the dilute, strongly interacting two-dimensional electron systems in the insulating phase of a silicon MOSFET are the same for unpolarized electrons in the absence of magnetic field and for electrons that are fully spin polarized by the presence of an in-plane magnetic field. In both cases the resistivity obeys Efros-Shklovskii variable range hopping $\ensuremath{\rho}(T)={\ensuremath{\rho}}_{0}\text{exp}[{({T}_{ES}/T)}^{1/2}]$, with
TES and $1/{\ensuremath{\rho}}_{0}$ mapping onto each other if one applies a shift of the critical density
nc reported earlier. With and without magnetic field, the parameters
TES and $1/{\ensuremath{\rho}}_{0}={\ensuremath{\sigma}}_{0}$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.
We report temperature and density dependences of the spin susceptibility of strongly interacting electrons in Si inversion layers. We measured (i) the itinerant electron susceptibility ${\ensuremath{\chi}}^{*}$ from the Shubnikov-de Haas oscillations in crossed magnetic fields and (ii) thermodynamic susceptibility ${\ensuremath{\chi}}_{\mathrm{T}}$ sensitive to all the electrons in the layer. Both ${\ensuremath{\chi}}^{*}$ and ${\ensuremath{\chi}}_{\mathrm{T}}$ are strongly enhanced with lowering the electron density in the metallic phase. However, there is no sign of divergency of either quantity at the density of the metal-insulator transition
nc. Moreover, the value of ${\ensuremath{\chi}}_{\mathrm{T}}$, which can be measured across the transition down to very low densities deep in the insulating phase, increases with density at
n<nc, as expected. In the absence of magnetic field, we found the temperature dependence of ${\ensuremath{\chi}}^{*}$ to be consistent with Fermi-liquid-based predictions, and to be much weaker than the power law predicted by non-Fermi-liquid models. We attribute a much stronger temperature dependence of ${\ensuremath{\chi}}_{\mathrm{T}}$ to localized spin droplets. In strong enough in-plane magnetic field, we found the temperature dependence of ${\ensuremath{\chi}}^{*}$ to be stronger than that expected for the Fermi liquid interaction corrections.
We study how the non-Fermi-liquid two-phase state reveals itself in transport properties of high-mobility Si-MOSFETs. We have found features in zero-field transport, magnetotransport, and thermodynamic spin magnetization in a 2D correlated electron system that may be directly related with the two-phase state. The features manifest above a density-dependent temperature
T∗ that represents a high-energy scale, apart from the Fermi energy. More specifically, in magnetoconductivity, we found a sharp onset of the regime $\ensuremath{\delta}\ensuremath{\sigma}(B,T)\ensuremath{\propto}{(B/T)}^{2}$ above a density-dependent temperature
Tkink(n), a high-energy behavior that ``mimics'' the low-temperature diffusive interaction regime. The zero-field resistivity temperature dependence exhibits an inflection point
Tinfl(n). In thermodynamic magnetization, the weak-field spin susceptibility per electron $\ensuremath{\partial}\ensuremath{\chi}/\ensuremath{\partial}n$ changes sign at
TdM/dn(n). All three notable temperatures,
Tkink,Tinfl, and
TdM/dn behave critically $\ensuremath{\propto}(n\ensuremath{-}{n}_{c})$, are close to each other, and are intrinsic to high-mobility samples solely; we therefore associate them with an energy scale
T∗ caused by interactions in the 2DE system.
This chapter focuses on studies of the critical behavior of conductivity in two-dimensional electron systems (2DES) with different amounts and types of disorder as well as different ranges of Coulomb interactions, in order to identify possible universality classes of the 2D metal-insulator transition (MIT). It discusses the manifestations of glassiness in both low- and high-disorder samples. The chapter examines the critical region near the 2D MIT in particular on describing conductivity measurements that have demonstrated dynamical scaling, the main signature of the MIT as a quantum phase transition. It also focuses on experiments that probe the nature of the insulating state, as well as charge dynamics across the MIT, in both high- and low-disorder 2DESs. There is substantial evidence that in many materials near the MIT both strong electronic correlations and disorder play an important role, and thus their competition is expected to lead to glassy behavior of electrons, in analogy with other frustrated systems.
We report thermodynamic magnetization measurements of two-dimensional electrons in several high-mobility Si metal-oxide-semiconductor field-effect transistors. We provide evidence for an easily polarizable electron state in a wide density range from insulating to deep into the metallic phase. The temperature and magnetic field dependence of the magnetization is consistent with the formation of large-spin droplets in the insulating phase. These droplets melt in the metallic phase with increasing density and temperature, though they survive up to large densities.