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1.
Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χαβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field. 相似文献
2.
We study the competition between the Wigner crystal and the Laughlin liquid states in an ultracold quasi-two-dimensional rapidly rotating polarized fermionic dipolar gas, and find that the Wigner crystal has a lower energy below a critical filling factor. We examine the quantum crystal to liquid transition for different confinements in the third direction. Our analysis of the phonon spectra of the Wigner crystal taking into account the phonon-phonon interactions also shows the stability of the Wigner crystal for sufficiently low filling factors (nu < 1/7). 相似文献
3.
F. Selva D. Weinmann 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,18(1):137-148
A Wigner crystal structure of the electronic ground state is induced by strong Coulomb interactions at low temperature in
clean or disordered two-dimensional (2d) samples. For fermions on a mesoscopic disordered 2d lattice, being closed to a torus,
we study the persistent current in the regime of strong interaction at zero temperature. We perform a perturbation expansion
starting from the Wigner crystal limit which yields power laws for the dependence of the persistent current on the interaction
strength. The sign of the persistent current in the strong interaction limit is independent of the disorder realization and
strength. It depends only on the electro-statically determined configuration of the particles in the Wigner crystal.
Received 14 March 2000 相似文献
4.
A general approach for investigating vibrational excitations of electron lattices is applied to a two-dimensional honeycomb Wigner crystal. In harmonic approximation we find imaginary transverse acoustic frequencies extending along the main symmetry directions in the Brillouin zone, implying a dynamical instability. 相似文献
5.
《Physics letters. A》2005,344(5):383-386
After a brief summary of the mechanism of quantal Wigner electron crystallization, we emphasize experimental situations in three, two, and one dimensions in which fingerprints of Wigner solid-like correlations are in evidence. Special stress is placed on the way applied magnetic fields can aid Wigner localization, as first pointed out in relation to n-type InSb by Durkan et al. (1968). Semiconductor heterojunctions with a two-dimensional electron fluid in the presence of a transverse magnetic field are given some prominence in relation to melting of the Wigner solid and its connection with magnetic properties. It is also proposed that a Wigner “hole” solid may be induced by a magnetic field of 60 T in a specific high cuprate and that the fulleride phase diagram may also contain Wigner solids. 相似文献
6.
A. Casado A. Fernández-Rueda T. Marshall J. Martínez R. Risco-Delgado E. Santos 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,11(3):465-472
The theory of parametric down conversion within the framework of the Wigner representation has been treated recently in a
series of papers using the standard model Hamiltonian. Here we take a more fundamental point of view studying the mechanism,
inside the crystal, for the production of the signal and idler beams. We begin from the evolution equations for the quantum
field operators, pass to the Wigner function and solve the resulting (Maxwell) equations with the use of the Green's function
method. We derive the time dependence of the coincidence detection probability as a function of the parameters of the nonlinear
crystal (in particular the length) the radius of the pumping beam, and the bandwidth of the filters in front of the detectors.
Received 24 January 2000 and Received in final form 24 March 2000 相似文献
7.
Summary The dispersion relations and the shear modulus of the 2D Wigner crystal (WC) in the presence of a strong magnetic field are
evaluated using a density functional method which includes the effect of electronic correlations. Comparison is made with
previous theoretical results on the magnetophonons and the shear modulus. The effect of correlation on the stability of the
crystal is discussed.
In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching. 相似文献
8.
S.Ya. Rakhmanov 《Solid State Communications》1979,30(12):779-782
The possibility of existance of a super-crystalline (Wigner) phase in a semimetal or impurity semiconductor film placed in a high magnetic field, is discussed and a comparison is made with a crystal in a three-dimensional specimen.
Such a phase exists in a succession of magnetic field or particle density intervals. The vibrational spectrum depends on magnetic field, while the bind energy is only density-dependent. The mean-square displacement x2 of the particles in the lattice sites are also independent on the magnetic field over a wide temperature range. 相似文献
9.
《中国物理快报》2017,(3)
We investigate the spin-orbit coupling effect in a two-dimensional(2D)Wigner crystal.It is shown that sufficiently strong spin-orbit coupling and an appropriate sign of g-factor could transform the Wigner crystal to a topological phonon system.We demonstrate the existence of chiral phonon edge modes in finite size samples,as well as the robustness of the modes in the topological phase.We explore the possibility of realizing the topological phonon system in 2D Wigner crystals confined in semiconductor quantum wells/heterostructure.It is found that the spin-orbit coupling is too weak for driving a topological phase transition in these systems.It is argued that one may look for topological phonon systems in correlated Wigner crystals with emergent effective spin-orbit coupling. 相似文献
10.
11.
The two-dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a parameter range where theory and many experiments had previously suggested the Wigner crystal phase, thus calling into question our current understanding. This Letter shows how very small quantitative corrections (<1%) in the energy due to the weak interaction between composite fermions can cause a fundamental change in the nature of the ground state, thus providing insight into the puzzling experimental results. 相似文献
12.
We consider a system of one-dimensional spinless particles interacting via long-range repulsion. In the limit of strong interactions the system is a Wigner crystal, with excitations analogous to phonons in solids. In a harmonic crystal the phonons do not interact, and the system never reaches thermal equilibrium. We account for the anharmonism of the Wigner crystal and find the rate at which it approaches equilibrium. The full equilibration of the system requires umklapp scattering of phonons, resulting in exponential suppression of the equilibration rate at low temperatures. 相似文献
13.
A candidate for the insulating phase of the 2D electron gas, seen
in high mobility 2D MOSFETS and heterojunctions, is a Wigner
crystal pinned by the incipient disorder. With this in view, we
study the effect of collective pinning on the physical properties
of the crystal formed in zero external magnetic field. We use an
elastic theory to describe to long wavelength modes of the
crystal. The disorder is treated using the standard Gaussian
variational method. We calculate various physical properties of
the system with particular emphasis on their density dependence.
We revisit the problem of compressibility in this system and
present results for the compressibility obtained via effective capacitance measurements in
experiments using bilayers. We present results for
the dynamical conductivity, surface acoustic wave anomalies and
the power radiated by the crystal through phonon emission at
finite temperatures. 相似文献
14.
Summary Electron crystallization due to sufficiently strong Coulomb repulsions leads to a model of electrons oscillating about lattice
sites in harmonic potentials. We have studied the orbital diamagnetism of such a localized Wigner oscillator in an applied
magnetic field of arbitrary strength. The two contributions from orbital angular momentum and from Langevin-Pauli behaviour
are separately calculated using Feynman's theorem. Possible relevance to the melting curve of the Wigner crystals in a magnetic
field is pointed out.
Riassunto La localizzazione di elettroni per effetto di repulsioni coulombiane sufficientemente forti porta ad un modello di elettroni che oscillano attorno a siti reticolari in potenziali armonici. Si studia il diamagnetismo orbitale di un siffatto oscillatore localizzato di Wigner in campo magnetico d'intensità arbitraria. Il contributo dovuto al momento angolare orbitale e quello di Langevin-Pauli sono calcolati separatamente mediante il teorema di Feynman. Si discute la possibile connessione dei risultati con il problema della curva di fusione del cristallo di Wigner in campo magnetico.相似文献
15.
作为密度矩阵一种形式的Wigner函数是量子相空间里的分布。用它描述相对论费密子时,它的通常表达形式为4×4矩阵函数。本文得到相对论带电费密子的2×2矩阵形式的Wigner函数以及它所满足的Liouville方程。这一方程与量子电动力学里带电费密子满足的Dirac方程完全等价。在描述中能核碰撞的Walecka模型里,当只有矢量介子(或标量介于取平均场近似)时,核子满足一定形式的Dirac方程。本文的方程也与之等价。还证明了(2×2)Wigner函数与相对论费密子的波函数在描述量子体系上起着同样的作用。量子体系的可观察量的全部知识都可以通过这里的Wigner函数得到。
关键词: 相似文献
16.
S. Yeremenko A. Baltu?ka M.S. Pshenichnikov D.A. Wiersma 《Applied physics. B, Lasers and optics》2000,70(7):S109-S117
We propose a new criterion for the assessment of ultrashort pulse reconstruction quality. Our idea is based on the use of a two-dimensional Wigner representation of the electric field. This allows introducing a single measure to represent the quality of both phase and amplitude retrieval. The new criterion is employed to examine two contemporary pulse characterization techniques: FROG (Frequency Resolved Optical Gating) and SPIDER (Spectral Interferometry for Direct Electric-field Reconstruction). For SPIDER, the influence of reference pulse stretching on the quality of phase extraction is investigated. Next, we ascertain the limitations in the use of a Fabri-Perrot etalon in the SPIDER apparatus for producing delayed pulse replicas. For the FROG technique we examine the impact of the doubling crystal orientation on the quality of the amplitude-phase retrieval of sub-5-fs pulses. The introduced criterion is also applied to study the respective sensitivity of FROG and SPIDERto the limited phase-matching bandwidth of the non-linear medium and detector noise. 相似文献
17.
18.
S.A. Mikhailov K. Ziegler 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(1):117-120
A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice.
It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational
symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized
quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points.
We also argue that internal rotational symmetry of individual dots can be broken in arrays of quantum dots, due to degenerate
ground states and inter-dot Coulomb coupling.
Received 12 September 2001 / Received in final form 24 April 2002 Published online 9 July 2002 相似文献
19.
20.
We present the first transport measurements of a classical Wigner crystal through a constriction formed by a split-gate electrode. The Wigner crystal is formed on the surface of superfluid helium confined in a microchannel. At low temperatures, the current is periodically suppressed with increasing split-gate voltage, resulting in peaklike transport features. We also present the results of molecular dynamics simulations that reproduce this phenomenon. We demonstrate that, at the split-gate voltages for which the current is suppressed, the electron lattice is arranged such that the stability of particle positions against thermal fluctuations is enhanced. In these configurations, the suppression of transport due to interelectron Coulomb forces becomes important. 相似文献