516 research outputs found
On the Cooling of Electrons in a Silicon Inversion Layer
The cooling of two-dimensional electrons in silicon-metal-oxide semiconductor
field effect transistors is studied experimentally. Cooling to the lattice is
found to be more effective than expected from the bulk electron-phonon coupling
in silicon. Unexpectedly, the extracted heat transfer rate to phonons at low
temperatures depends cubically on electron temperature, suggesting that
piezoelectric coupling (absent in bulk silicon) dominates over deformation
potential. According to our findings, at 100 mK, electrons farther than 0.1 mm
from the contacts are mostly cooled by phonons. Using long devices and low
excitation voltage we measure electron resistivity down to 100 mK and find that
some of the "metallic" curves, reported earlier, turn insulating below about
300 mK. This finding renders the definition of the claimed 2D metal-insulator
transition questionable. Previous low temperature measurements in silicon
devices are analyzed and thumb rules for evaluating their electron temperatures
are provided.Comment: 5 pages, 4 figures. Discussion corrected and a few references adde
Electron-phonon interaction via Pekar mechanism in nanostructures
We consider an electron-acoustic phonon coupling mechanism associated with
the dependence of crystal dielectric permittivity on the strain (the so-called
Pekar mechanism) in nanostructures characterized by strong confining electric
fields. The efficiency of Pekar coupling is a function of both the absolute
value and the spatial distribution of the electric field. It is demonstrated
that this mechanism exhibits a phonon wavevector dependence similar to that of
piezoelectricity and must be taken into account for electron transport
calculations in an extended field distribution. In particular, we analyze the
role of Pekar coupling in energy relaxation in silicon inversion layers.
Comparison with the recent experimental results is provided to illustrate its
potential significance
Even-odd correlations in capacitance fluctuations of quantum dots
We investigate effects of short range interactions on the addition spectra of
quantum dots using a disordered Hubbard model. A correlation function \cS(q) is
defined on the inverse compressibility versus filling data, and computed
numerically for small lattices. Two regimes of interaction strength are
identified: the even/odd fluctuations regime typical of Fermi liquid ground
states, and a regime of structureless \cS(q) at strong interactions. We
propose to understand the latter regime in terms of magnetically correlated
localized spins.Comment: 3 pages, Revtex, Without figure
Absence of bimodal peak spacing distribution in the Coulomb blockade regime
Using exact diagonalization numerical methods, as well as analytical
arguments, we show that for the typical electron densities in chaotic and
disordered dots the peak spacing distribution is not bimodal, but rather
Gaussian. This is in agreement with the experimental observations. We attribute
this behavior to the tendency of an even number of electrons to gain on-site
interaction energy by removing the spin degeneracy. Thus, the dot is predicted
to show a non trivial electron number dependent spin polarization. Experimental
test of this hypothesis based on the spin polarization measurements are
proposed.Comment: 13 pages, 3 figures, accepted for publication in PRL - a few small
change
Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation
In this paper we classify Weingarten surfaces integrable in the sense of
soliton theory. The criterion is that the associated Gauss equation possesses
an sl(2)-valued zero curvature representation with a nonremovable parameter.
Under certain restrictions on the jet order, the answer is given by a third
order ordinary differential equation to govern the functional dependence of the
principal curvatures. Employing the scaling and translation (offsetting)
symmetry, we give a general solution of the governing equation in terms of
elliptic integrals. We show that the instances when the elliptic integrals
degenerate to elementary functions were known to nineteenth century geometers.
Finally, we characterize the associated normal congruences
Density Modulations and Addition Spectra of Interacting Electrons in Disordered Quantum Dots
We analyse the ground state of spinless fermions on a lattice in a weakly
disordered potential, interacting via a nearest neighbour interaction, by
applying the self-consistent Hartree-Fock approximation. We find that charge
density modulations emerge progressively when r_s >1, even away from
half-filling, with only short-range density correlations. Classical geometry
dependent "magic numbers" can show up in the addition spectrum which are
remarkably robust against quantum fluctuations and disorder averaging.Comment: 4 pages, 3 eps figure
Hall Coefficient in an Interacting Electron Gas
The Hall conductivity in a weak homogeneous magnetic field, , is calculated. We have shown that to leading order in
the Hall coefficient is not renormalized by the
electron-electron interaction. Our result explains the experimentally observed
stability of the Hall coefficient in a dilute electron gas not too close to the
metal-insulator transition. We avoid the currently used procedure that
introduces an artificial spatial modulation of the magnetic field. The problem
of the Hall effect is reformulated in a way such that the magnetic flux
associated with the scattering process becomes the central element of the
calculation.Comment: 23 pages, 15 figure
Thermodynamic magnetization of a strongly correlated two-dimensional electron system
We measure thermodynamic magnetization of a low-disordered, strongly
correlated two-dimensional electron system in silicon. Pauli spin
susceptibility is observed to grow critically at low electron densities -
behavior that is characteristic of the existence of a phase transition. A new,
parameter-free method is used to directly determine the spectrum
characteristics (Lande g-factor and the cyclotron mass) when the Fermi level
lies outside the spectral gaps and the inter-level interactions between
quasiparticles are avoided. It turns out that, unlike in the Stoner scenario,
the critical growth of the spin susceptibility originates from the dramatic
enhancement of the effective mass, while the enhancement of the g-factor is
weak and practically independent of the electron density.Comment: As publishe
On the computation of zone and double zone diagrams
Classical objects in computational geometry are defined by explicit
relations. Several years ago the pioneering works of T. Asano, J. Matousek and
T. Tokuyama introduced "implicit computational geometry", in which the
geometric objects are defined by implicit relations involving sets. An
important member in this family is called "a zone diagram". The implicit nature
of zone diagrams implies, as already observed in the original works, that their
computation is a challenging task. In a continuous setting this task has been
addressed (briefly) only by these authors in the Euclidean plane with point
sites. We discuss the possibility to compute zone diagrams in a wide class of
spaces and also shed new light on their computation in the original setting.
The class of spaces, which is introduced here, includes, in particular,
Euclidean spheres and finite dimensional strictly convex normed spaces. Sites
of a general form are allowed and it is shown that a generalization of the
iterative method suggested by Asano, Matousek and Tokuyama converges to a
double zone diagram, another implicit geometric object whose existence is known
in general. Occasionally a zone diagram can be obtained from this procedure.
The actual (approximate) computation of the iterations is based on a simple
algorithm which enables the approximate computation of Voronoi diagrams in a
general setting. Our analysis also yields a few byproducts of independent
interest, such as certain topological properties of Voronoi cells (e.g., that
in the considered setting their boundaries cannot be "fat").Comment: Very slight improvements (mainly correction of a few typos); add DOI;
Ref [51] points to a freely available computer application which implements
the algorithms; to appear in Discrete & Computational Geometry (available
online
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