We show the insulating region of the metal-insulator transition phenomena in disordered two-dimensional electron systems contains new information about the quantum critical dynamics at low T because the insulating region and the quantum critical region are two aspects of the localized phase.
We reconcile the possible presence of a quantum critical point in metal insulator transition phenomena in two-dimensional electron systems with observed electronic properties in the low resistivity region which are those of a weakly disordered Fermi liquid. The central issue of whether the ground state of an interacting 2D electron system in the presence of weak potential scattering from disorder is a metal or an insulator remains unresolved. Additional new effects which may become important at extremely low electron densities are briefly mentioned.
We present a theory of the metal-insulator transition in a disordered two-dimensional electron gas. A quantum critical point, separating the metallic phase, which is stabilized by electronic interactions, from the insulating phase, where disorder prevails over the electronic interactions, has been identified. The existence of the quantum critical point leads to a divergence in the density of states of the underlying collective modes at the transition, causing the thermodynamic properties to behave critically as the transition is approached. We show that the interplay of electron-electron interactions and disorder can explain the observed transport properties and the anomalous enhancement of the spin susceptibility near the metal-insulator transition.
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 discuss the metal–insulator transition phenomenon in two dimensions in terms of a quantum critical point that controls a range of the low temperature insulator region as well as the usual quantum critical sector. We show that this extended range of criticality permits a determination of both the dynamical critical exponent z and the correlation length critical exponent ν from published data from a single experiment in the insulator critical region. The resulting value of the product zν is consistent with the temperature dependence of the resistance in the quantum critical sector. This provides strong quantitative evidence for the presence of a quantum critical point.
We show that the quantum critical point associated with the metal-insulator transition phenomenon in two dimensions controls an extended critical region encompassing not only the usual quantum critical sector but also a range of the low-temperature insulator region. The extended range of criticality permits a unified analysis of data from the insulating region and quantum critical sector, allowing us to determine both the dynamical critical exponent z and the correlation length critical exponent $\ensuremath{\nu}$ from published data from a single experiment in the insulator critical region. We show that the critical exponents determined from the insulator sector consistently describe the temperature dependence of the resistance data from the same experiment in the quantum critical sector. This provides evidence for the presence of a quantum critical point in these systems.