A model of Wigner liquid

A two-dimensional low-density system of charge carriers with strong Coulomb interaction, which can lead to the appearance of a short-wavelength soft mode (precursor of crystallization) is examined. This system provides elementary excitations of two types: Fermi excitations and Bose excitations with a gap in the spectrum. The latter excitations are similar to rotons in superfluid helium. A model involving the Fermi liquid and the soft mode is proposed, and interaction of different excitations with each other is described phenomenologically as in the Landau theory of Fermi liquid. By solving the derived equations, it was found that, as the temperature increases, the effective mass of Fermi excitations decreases and the gap in the Bose excitation spectrum increases.     

Noise at the crossover from Wigner liquid to Wigner glass

Using a simple classical model for interacting electrons in two dimensions with random disorder, we show that a crossover from a Wigner liquid to a Wigner glass occurs as a function of charge density. The noise power increases strongly at the crossover and the characteristics of the 1/f(alpha) noise change. When the temperature is increased, the noise power decreases. We compare these results with recent noise measurements in systems with two-dimensional metal-insulator transitions.     

On the superconductivity of a Wigner liquid

The disorder effect on the interaction of quasiparticles between each other is discussed. The occurrence of a soft mode is taken as the basic assumption. The interaction through the soft mode results in attraction between Fermi quasiparticles (this is apart from the repulsion that has remained from the initial Coulomb interaction between particles). This attraction (in the vicinity of the Fermi surface) is strengthened with increasing concentration of the scattering centers. Therefore, even if the pure system exhibits no superconductivity, superconductivity could appear in the impurity system.     

Effective mass of quasiparticles in a Wigner liquid

The exchange interaction and effective mass of fermionic excitation in a low-density (r ^S ? 1) system of two-dimensional electrons are estimated from simple considerations. For the ratio of effective (renormalized due to interaction) to band mass, the dependence ${{m^* } \mathord{\left/ {\vphantom {{m^* } m}} \right. \kern-0em} m} = ({A \mathord{\left/ {\vphantom {A {\sqrt {r_S } }}} \right. \kern-0em} {\sqrt {r_S } }})\exp (\alpha \sqrt {r_S } )$ is obtained, where A and α are constants on the order of unity. The effective g factor is independent of r ^S and is larger than its bare value in the two-valley case (silicon). Comparison with experimental data shows a qualitative agreement with silicon.     

Wigner liquid conductivity in a parallel magnetic field

It is assumed that comparatively low-mobility objects (clusters of a small number of electrons) can appear in a two-dimensional strongly correlated electronic system (Wigner liquid) against the background of mobile Fermi-type carriers. These formations can get “pinned” to inhomogeneities and play the role of additional scatterers. Clusters of two and three electrons are discussed (for a short-range order in the arrangement of electrons, as in a triangular lattice). The number of these clusters depends on both temperature and the parallel magnetic field. This results in the temperature and field dependences of the resistance and magnetization of the system. According to a simple model, resistance increases and the metal-dielectric transition occurs as the parallel magnetic field grows stronger. The model predicts a nonlinear magnetic field dependence of magnetization.     

Classical Wigner crystallization,liquid structure factor peak height and freezing of liquid alkalis

It is pointed out that, in studying crystallization, one should focus on the first reciprocal lattice vector which has its analogue in the first peak of the liquid structure factor. A freezing criterion of a classical one-component plasma emerging from the structure factor at the first peak, which transcends the Lindemann's Law, is then applied to the nearly-free-electron liquids Na and K and compared with experiments.     

Two-dimensional electron system in high magnetic fields: Wigner crystal versus composite-fermion liquid

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.     

Conductivity rules in the Fermi and charge-spin separated liquid

Ioffe–Larkin rule applies for the pure charge-spin separation regardless of its dimensionality. Here, an extension to this rule as a result of the coexistence of spinon, holon and electron as a single entity in the 2-dimensional (2D) system is derived, which is also in accordance with the original rule.     

Conductivity of two-dimensional crystals over liquid helium for different holding fields

The results are presented of the experimental study of electron crystals over liquid helium with surface electron density of 3.2×10⁸ and 6.4×10⁸ cm⁻² (melting temperatures 0.4 and 0.58 K) at temperature 83 mK and for holding electric fields 300–1200 V/cm. The measurements are performed in the frequency range 1–14 MHz where the coupled phonon–ripplon resonances are observed in the experimental cell. The real and imaginary parts of the complex conductivity of the crystal have been obtained as a result of analysis of an electron layer response on exciting ac voltage with frequency corresponding to the mode (0,1) of the coupled phonon–ripplon oscillations. An analysis of the results allows us to suppose that structural defects of the electron crystal play an essential role in dissipation processes.     

Moving Wigner glasses and smectics: dynamics of disordered Wigner crystals

We examine the dynamics of driven classical Wigner solids interacting with quenched disorder from charged impurities. For strong disorder, the initial motion is plastic, in the form of crossing winding channels. For increasing drive, there is a reordering into a moving Wigner smectic with the electrons moving in separate 1D channels. These different dynamic phases can be related to the conduction noise and I(V) curves. For strong disorder, we show criticality in the voltage onset just above depinning. We obtain the dynamic phase diagram for driven Wigner solids and demonstrate a finite threshold of force for transverse sliding, recently observed experimentally.     

General Wigner Transforms Studied by Virtue of Weyl Ordering of the Wigner Operator

By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for derivingmiscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can alsobe easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transformsand the squeezing transforms in quantum optics is investigated.     

General Wigner Transforms Studied by Virtue of Weyl Ordering of the Wigner Operator

By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated.     

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.     

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.     

The Wigner distribution function

In this letter, the relationship between the characteristic function for two arbitrary noncommuting observables and a generalized Wigner distribution function is established. This distribution function is shown to have no simple interpretation in the sense of probability theory but, in lieu of its special properties, can be used directly for calculating the expectation values of observables.