Wigner crystal in snaked nanochannels: Outlook

We study properties of Wigner crystal in snaked nanochannels and show that they are characterized by a conducting sliding phase at low charge densities and an insulating pinned phase emerging above a certain critical charge density. We trace parallels between this model problem and the Little suggestion for electron transport in organic molecules. We also show that in the presence of periodic potential inside the snaked channel the sliding phase exists only inside a certain window of electron densities that has similarities with a pressure dependence of conductivity in organic conductors. Our studies show emergence of dynamical glassy phase in a purely periodic potential in the absence of any disorder that can explain enormously slow variations of resistivity in organic conductors. Finally we discuss the KAM concept of superfluidity induced by repulsive Coulomb interaction between electrons. We argue that the transition from the sliding KAM phase to the pinned Aubry phase corresponds to the superfluid-insulator transition.     

Zero field Wigner crystal

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.     

One-dimensional Wigner crystal?

The linear response in a charge density wave (CDW) type state is investigated in the framework of 1+1-dimensional QED. It is shown that the system is unstable or stable against static, periodic electric perturbations when the Fermi level is placed in an allowed band or a forbidden one, respectively.     

Two-dimensional Wigner crystal in magnetic fields

Orbital magnetic moment and the frequency dependent conductivities of the Wigner crystal are examined in the harmonic approximation. The effects of scattering on the collective modes are also discussed.     

Structure of the Wigner crystal

A model of the Wigner crystal with two localized electrons per cell is developed. The ground state energy of this model is evaluated. The Coulomb interaction within a cell is treated exactly for a certain range of electron concentrations. The calculation demonstrates that at very low electron concentrations the crystal contains a single localized electron per cell. As the concentration is increased the crystal comes to contain two, three or more electrons per cell. At high electron concentrations the entire crystal can be treated as a single cell.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp 47–51, June, 1988.     

Polarization catastrophe in the polaronic Wigner crystal

We consider a three dimensional Wigner crystal of electrons lying in a host ionic dielectric. Owing to their interaction with the lattice polarization, each localized electron forms a polaron. We study the collective excitations of such a polaronic Wigner crystal at zero temperature, taking into account the quantum fluctuations of the polarization within the Feynman harmonic approximation. We show that, contrary to the ordinary electron crystal, the system undergoes a polarization catastrophe when the density is increased. An optical signature of this instability is derived, whose trend agrees with the experiments carried out in Nd-based cuprates. Received 4 July 2002 Published online 17 September 2002     

Exchange frequencies in the 2D Wigner crystal

Using path integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2D Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2D (3)He. Using the resulting multispin exchange model we find the spin Hamiltonian for r(s) < or = 175 +/- 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.     

Orbital magnetic moment of two-dimensional Wigner crystal

The orbital magnetic moment is calculated for the two-dimensional Wigner crystal within the harmonic approximation. It is shown that the temperature dependence of the magnetic moment in the crystalline state is in the marked contrast with that of the liquid state.     

Commensurability-dependent transport of a Wigner crystal in a nanoconstriction

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.     

Melting of a Wigner crystal in an ionic dielectric

The melting of a Wigner Crystal of electrons placed into a host polar material is examined as a function of the density and the temperature. When the coupling to the longitudinal optical modes of the host medium is turned on, the WC is progressively transformed into a polaronic Wigner crystal. We estimate the critical density for crystal melting at zero temperature using the Lindeman criterion. We show that above a certain critical value of the Fr?hlich electron-phonon coupling, the melting towards a quantum liquid of polarons is not possible, and the insulator-to-metal transition is driven by the ionization of the polarons (polaron dissociation). The phase diagram at finite temperature is obtained by making use of the same Lindeman criterion. Results are also provided in the case of an anisotropic electron band mass, showing that the scenario of polaron dissociation can be relevant in anisotropic compounds such as the superconducting cuprates at rather moderate e-ph couplings. Received 13 August 1999     

Some dynamical properties of a two-dimensional Wigner crystal

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 χ_αβ(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.     

Taking one charge off a two-dimensional Wigner crystal

A planar array of identical charges at vanishing temperature forms a Wigner crystal with hexagonal symmetry. We take off one (reference) charge in a perpendicular direction, hold it fixed, and search for the ground state of the whole system. The planar projection of the reference charge should then evolve from a sixfold coordination (centre of a hexagon) for small distances to a threefold arrangement (centre of a triangle), at large distances d from the plane. The aim of this paper is to describe the corresponding non-trivial lattice transformation. For that purpose, two numerical methods (direct energy minimisation and Monte Carlo simulations), together with an analytical treatment, are presented. Our results indicate that the d = 0 and d → ∞ limiting cases extend for finite values of d from the respective starting points into two sequences of stable states, with intersecting energies at some value d_t; beyond this value the branches continue as metastable states.     

Synchronization,zero-resistance states and rotating Wigner crystal

We show, in a framework of a classical nonequilibrium model, that rotational angles of electrons moving in two dimensions (2D) in a perpendicular magnetic field can be synchronized by an external microwave field whose frequency is close to the Larmor frequency. The synchronization eliminates collisions between electrons and thus creates a regime with zero diffusion corresponding to the zero-resistance states observed in experiments with high mobility 2D electron gas (2DEG). For long range Coulomb interactions electrons form a rotating hexagonal Wigner crystal. Possible relevance of this effect of synchronization-induced self-assembly for planetary rings is discussed.     

Rate of equilibration of a one-dimensional Wigner crystal

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.     

Persistent current with fractional period in a multichannel Wigner crystal ring

We calculate the persistent current in a multichannel semiconductor ring with strongly correlated electrons when they form a Wigner crystal (WC). Pinning this crystal with a smooth gate potential leads to the suppression of the amplitude of the Aharonov–Bohm oscillations and to the fractionalization of the period. A fractional period Φ₀/w (w = 2,3,…,6) appears because of the strong coupling between channels in the tunneling process of the WC through the pinning barrier.