Novel Phenomena in Dilute Electron Systems in Two Dimensions

We review recent experiments that provide evidence for a transition to a conducting phase in two dimensions at very low electron densities. The nature of this phase is not understood, and is currently the focus of intense theoretical and experimental attention.Comment: To appear as a Perspective in the Proceedings of the National Academy of Sciences. Reference to Chakravarty, Kivelson, Nayak, and Voelker's paper added (Phil. Mag., in press

Metal-insulator transition in two-dimensional electron systems

The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization, in two-dimensional systems of noninteracting or weakly interacting electrons, the ever-present randomness causes the resistance to rise as the temperature is decreased, leading to an insulating ground state. However, new evidence has emerged within the past decade indicating a transition from insulating to metallic phase in two-dimensional systems of strongly interacting electrons. We review earlier experiments that demonstrate the unexpected presence of a metallic phase in two dimensions, and present an overview of recent experiments with emphasis on the anomalous magnetic properties that have been observed in the vicinity of the transition.Comment: As publishe

Formation of three-particle clusters in hetero-junctions and MOSFET structures

A novel interaction mechanism in MOSFET structures and $GaAs/AlGaAs$ hetero-junctions between the zone electrons of the two-dimensional (2D) gas and the charged traps on the insulator side is considered. By applying a canonical transformation, off-diagonal terms in the Hamiltonian due to the trapped level subsystem are excluded. This yields an effective three-particle attractive interaction as well as a pairing interaction inside the 2D electronic band. A type of Bethe- Goldstone equation for three particles is studied to clarify the character of the binding and the energy of the three-particle bound states. The results are used to offer a possible explanation of the Metal-Insulator transition recently observed in MOSFET and hetero-junctions.Comment: 4 page

Differentiability of fractal curves

While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve is differentiable at all points except for a countable set. For a parameter set of codimension one, the curve is continuously differentiable. However, there are no twice differentiable self-affine curves in the plane, except for parabolic arcs

On a complex differential Riccati equation

We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical "one-dimensional" results we discuss new features of the considered equation like, e.g., an analogue of the Cauchy integral theorem

Universal Behaviour of Metal-Insulator Transitions in the p-SiGe System

Magnetoresistance measurements are presented for a strained p-SiGe quantum well sample where the density is varied through the B=0 metal-insulator transition. The close relationship between this transition, the high field Hall insulator transition and the filling factor $\nu$=3/2 insulating state is demonstrated.Comment: 6 pages, 4 figures. Submitted to EP2DS XIII conference 199