1,537 research outputs found
Current-Carrying Ground States in Mesoscopic and Macroscopic Systems
We extend a theorem of Bloch, which concerns the net orbital current carried
by an interacting electron system in equilibrium, to include mesoscopic
effects. We obtain a rigorous upper bound to the allowed ground-state current
in a ring or disc, for an interacting electron system in the presence of static
but otherwise arbitrary electric and magnetic fields. We also investigate the
effects of spin-orbit and current-current interactions on the upper bound.
Current-current interactions, caused by the magnetic field produced at a point
r by a moving electron at r, are found to reduce the upper bound by an amount
that is determined by the self-inductance of the system. A solvable model of an
electron system that includes current-current interactions is shown to realize
our upper bound, and the upper bound is compared with measurements of the
persistent current in a single ring.Comment: 7 pager, Revtex, 1 figure available from [email protected]
Quantum interference and electron-electron interactions at strong spin-orbit coupling in disordered systems
Transport and thermodynamic properties of disordered conductors are
considerably modified when the angle through which the electron spin precesses
due to spin-orbit interaction (SOI) during the mean free time becomes
significant. Cooperon and Diffusion equations are solved for the entire range
of strength of SOI. The implications of SOI for the electron-electron
interaction and interference effects in various experimental settings are
discussed.Comment: 4 pages, REVTEX, 1 eps.figure Submitted to Phys. Rev. Let
Indirect coupling between spins in semiconductor quantum dots
The optically induced indirect exchange interaction between spins in two
quantum dots is investigated theoretically. We present a microscopic
formulation of the interaction between the localized spin and the itinerant
carriers including the effects of correlation, using a set of canonical
transformations. Correlation effects are found to be of comparable magnitude as
the direct exchange. We give quantitative results for realistic quantum dot
geometries and find the largest couplings for one dimensional systems.Comment: 4 pages, 3 figure
Spin separation in cyclotron motion
Charged carriers with different spin states are spatially separated in a
two-dimensional hole gas. Due to strong spin-orbit interaction holes at the
Fermi energy have different momenta for two possible spin states travelling in
the same direction and, correspondingly, different cyclotron orbits in a weak
magnetic field. Two point contacts, acting as a monochromatic source of
ballistic holes and a narrow detector in the magnetic focusing geometry are
demonstrated to work as a tunable spin filter.Comment: 4 pages, 2 figure
Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid
In previous work we have proposed that the non-Fermi-liquid spectral
properties in a variety of low-dimensional and strongly correlated electron
systems are caused by the infrared catastrophe, and we used an exact functional
integral representation for the interacting Green's function to map the
tunneling problem onto the x-ray edge problem, plus corrections. The
corrections are caused by the recoil of the tunneling particle, and, in systems
where the method is applicable, are not expected to change the qualitative form
of the tunneling density of states (DOS). Qualitatively correct results were
obtained for the DOS of the 1D electron gas and 2D Hall fluid when the
corrections to the x-ray edge limit were neglected and when the corresponding
Nozieres-De Dominicis integral equations were solved by resummation of a
divergent perturbation series. Here we reexamine the x-ray edge limit for these
two models by solving these integral equations exactly, finding the expected
modifications of the DOS exponent in the 1D case but finding no changes in the
DOS of the 2D Hall fluid with short-range interaction. We also provide, for the
first time, an exact solution of the Nozieres-De Dominicis equation for the 2D
electron gas in the lowest Landau level.Comment: 6 pages, Revte
Continuous Wavelets on Compact Manifolds
Let be a smooth compact oriented Riemannian manifold, and let
be the Laplace-Beltrami operator on . Say 0 \neq f
\in \mathcal{S}(\RR^+), and that . For , let
denote the kernel of . We show that is
well-localized near the diagonal, in the sense that it satisfies estimates akin
to those satisfied by the kernel of the convolution operator on
\RR^n. We define continuous -wavelets on , in such a
manner that satisfies this definition, because of its localization
near the diagonal. Continuous -wavelets on are analogous to
continuous wavelets on \RR^n in \mathcal{S}(\RR^n). In particular, we are
able to characterize the Hlder continuous functions on by
the size of their continuous wavelet transforms, for
Hlder exponents strictly between 0 and 1. If is the torus
\TT^2 or the sphere , and (the ``Mexican hat''
situation), we obtain two explicit approximate formulas for , one to be
used when is large, and one to be used when is small
Zero-Field Satellites of a Zero-Bias Anomaly
Spin-orbit (SO) splitting, , of the electron Fermi surface
in two-dimensional systems manifests itself in the interaction-induced
corrections to the tunneling density of states, . Namely, in
the case of a smooth disorder, it gives rise to the satellites of a zero-bias
anomaly at energies . Zeeman splitting, , in a weak parallel magnetic field causes a narrow {\em plateau} of
a width at the top of each sharp satellite peak.
As exceeds , the SO satellites cross over to the
conventional narrow maxima at with SO-induced
plateaus at the tops.Comment: 7 pages including 2 figure
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