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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
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 =3/2 insulating state is
demonstrated.Comment: 6 pages, 4 figures. Submitted to EP2DS XIII conference 199
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