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The problem of finding equilibrium configurations of one-component charged particles, induced by externalelectrostaticfieldsinplanarsystems,isasubjectofactivestudiesinfundamentalaswellinexperimental investigations. In this paper the results of numerical analysis of the equilibrium configurations of charged particles (electrons), confined in a circular region by an infinite external potential at its boundary are presented. Equilibrium configurations with minimal energy are searched by means of special calculation scheme. This computational scheme consists of the following steps. First, the configuration of the system with the energy as close as possible to the expected energy value in the ground equilibrium state is found using a model of stable configurations. Next, classical Newtonian molecular dynamics is used using viscous friction to bring the system into equilibrium with a minimum energy. With a sufficient number of runs, we obtain a stable configuration with an energy value as close as possible to the global minimum energy value for the ground stable state for a given number of particles. Our results demonstrate a significant efficiency of using the method of classical molecular dynamics (MD) when using the interpolation formulas in comparison with algorithms based on Monte Carlo methods and global optimization. This approach makes it possible to significantly increase the speed at which an equilibrium configuration is reached for an arbitrarily chosen number of particles compared to the Metropolis annealing simulation algorithm and other algorithms based on global optimization methods

Quasi-two-dimensional systems play an important role in the manufacture of various devices for the needs of nanoelectronics. Obviously, the functional efficiency of such systems depends on their structure, which can change during phase transitions under the influence of external conditions (e.g., temperature). Until now, the main attention has been focused on the search for signals of phase transitions in continuous two-dimensional systems. One of the central issues is the analysis of conditions for the nucleation of the hexatic phase in such systems, which is accompanied by the appearance of defects in the Wigner crystalline phase at a certain temperature. However, both practical and fundamental questions arise about the critical number of electrons at which the symmetry of the crystal lattice in the system under consideration will begin to break and, consequently, the nucleation of defects will start. The dependences of the orientational order parameter and the correlation function, which characterize topological phase transitions, as functions of the number of particles at zero temperature have been studied. The calculation results allow us to establish the precursors of the phase transition from the hexagonal phase to the hexatic one for N = 92, 136, and 187 considered as an example. [ABSTRACT FROM AUTHOR]

Abstract We study the ground-state properties of quasi-one-dimensional paramagnetic electron fluid using variational quantum Monte Carlo method. The electrons are transversally confined using the harmonically regularized Coulomb potential with long range order. In this work we have investigated the crossover from liquid to crystalline phase in the finite width paramagnetic quantum wire. The calculated pair correlation function shows the oscillations of period $$2r_\text {s} a_0$$ 2 r s a 0 , where $$a_0$$ a 0 is the Bohr’s radius and $$r_\text {s}$$ r s is Wigner Seitz radius or electron-density parameter which corresponds to a $$k=4k_\text {F}$$ k = 4 k F peak with $$k_\text {F}$$ k F being Fermi wave vector in the static structure factor at finite electron density. It is a signature of the onset of Wigner crystallization. It is found that the cross-over from liquid to a quasi-Wigner phase is due to enhancement of the electron correlation effects as $$r_\text {s}$$ r s increases or as the wire width b decreases.

We study multi-valley electron gases in the low density (rs ≫ 1) limit. Here the ground-state is always a Wigner crystal (WC), with additional pseudo-spin order where the pseudo-spins are related to valley occupancies. Depending on the symmetries of the host semiconductor and the values of the parameters such as the anisotropy of the effective mass tensors, we find a striped or chiral pseudo-spin antiferromagnet, or a time-reversal symmetry breaking orbital loop-current ordered pseudo-spin ferromagnet. Our theory applies to the recently-discovered WC states in AlAs and in mono and bilayer transition metal dichalcogenides. We identify a set of interesting electronic liquid crystalline phases that could arise by continuous quantum melting of such WCs. [ABSTRACT FROM AUTHOR]

Many quantum phenomena responsible for key applications in material science and quantum chemistry arise in the strongly correlated regime. This is at the same time, a costly regime for computer simulations. In the limit of strong correlation analytic solutions exist, but as we move away from this limit numerical simulation are needed, and accurate quantum solutions do not scale well with the number of interacting particles. In this work we propose to use few-particle harmonic traps in combination with twisted light as a quantum emulator to investigate the transition into a strongly-correlated regime. Using both analytic derivations and numerical simulations we generalize previous findings on 2 Coulomb interacting fermions trapped in a one-dimensional harmonic trap to the case of 3 fermions. The 4 signatures of strong correlation we have identified in the one-dimensional harmonic trap are: (i) the ground state density is highly localized around N equilibrium positions, where N is the number of particles, (ii) the symmetric and antisymmetric ground state wavefunctions become degenerate, (iii) the von Neumann entropy grows, (iv) the energy spectrum is fully characterized by N normal modes or less. Our findings describe the low-energy behavior of electrons in quantum wires and ions in Paul traps. Similar features have also been reported for cold atoms in optical lattices.

The problem of finding equilibrium configurations of similarly charged particles (ions) induced by external electrostatic fields in planar systems is of great interest for fundamental and applied research. In this paper, the results of numerical analysis of equilibrium configurations of negatively charged particles (electrons) confined in a circular region by an infinite external potential at its boundary are presented. A hybrid numerical algorithm is developed to seek stable configurations with minimal energies. The algorithm is based on interpolation formulas derived using the analysis of equilibrium configurations obtained by means of the variational principle of the minimum energy for an arbitrary finite number of particles in a circular model. The solution of nonlinear equations of the given model make it possible to predict structure formation in the form of rings (shells) filled with electrons, the number of which decreases when passing from the external ring to the internal one. The number of rings depends on the total number of charged particles. The obtained interpolation formulas of the distribution of the total number of electrons over the rings are used as initial configurations for the molecular-dynamics method. Our results demonstrate the significant efficiency of the application of the classical molecular dynamics (MD) method when using interpolation formulas in comparison with algorithms based on Monte Carlo methods and global optimization. For an arbitrarily chosen number of particles in the considered system, the proposed method makes it possible to enhance the speed at which the stable configuration with the minimum energy is reached by several orders in comparison with the classical-molecular-dynamics method. [ABSTRACT FROM AUTHOR]

Self-organizing neural networks are used to analyze uncorrelated white noises of different distribution types (normal, triangular, and uniform). The artificially generated noises are analyzed by clustering the measured time signal sequence samples without its preprocessing. Using this approach, we analyze, for the first time, the current noise produced by a sliding "Wigner-crystal"-like structure in the insulating phase of a 2D electron system in silicon. The possibilities of using the method for analyzing and comparing experimental data obtained by observing various effects in solid-state physics and numerical data simulated using theoretical models are discussed. [ABSTRACT FROM AUTHOR]

Metastable states appear in many areas of physics as a result of symmetry-breaking phase transitions. An important challenge is to understand the microscopic mechanisms which lead to the formation of the energy barrier separating a metastable state from the ground state. In this paper, we describe an experimental example of the hidden metastable domain state in 1T-TaS2, created by photoexcitation or carrier injection. The system is an example of a charge density wave superlattice in the Wigner crystal limit displaying discommensurations and domain formation when additional charge is injected either through contacts or by photoexcitation. The domain walls and their crossings in particular display interesting, topologically entangled structures, which have a crucial role in the metastability of the system. We model the properties of experimentally observed thermally activated dynamics of topologically protected defects—dislocations—whose annihilation dynamics can be observed experimentally by scanning tunnelling microscopy as emergent phenomena described by a doped Wigner crystal. The different dynamics of trivial and non-trivial topological defects are quite striking. Trivial defects appear to annihilate quite rapidly at low temperatures on the timescale of the experiments, while non-trivial defects annihilate rarely, if at all. [ABSTRACT FROM AUTHOR]

The energy of a two-dimensional electron crystal in the low-density limit is studied. The first correction to the electrostatic energy of a crystal is shown to be 1.62733 r s − 3 / 2 Ry. The answer is obtained using the method of numerical integration. [ABSTRACT FROM AUTHOR]

We examine a charge lattice coupled to a one-dimensional asymmetric potential in the presence of an applied magnetic field, which induces gyrotropic effects in the charge motion. This system could be realized for Wigner crystals in nanostructured samples, dusty plasmas, or other classical charge-ordered states where gyrotropic motion and damping can arise. For zero magnetic field, an applied external ac drive can produce a ratchet effect in which the particles move along the easy flow direction of the substrate asymmetry. The zero field ratchet effect can only occur when the ac drive is aligned with the substrate asymmetry direction; however, when a magnetic field is added, the gyrotropic forces generate a Hall effect that leads to a variety of new behaviors, including a transverse ratchet motion that occurs when the ac drive is perpendicular to the substrate asymmetry direction. We show that this system exhibits commensuration effects as well as reversals in the ratchet effect and the Hall angle of the motion. The magnetic field also produces a nonmonotonic ratchet efficiency when the particles become localized at high fields.

We consider simulations of Wigner crystals in solid state systems interacting with random quenched disorder in the presence of thermal fluctuations. When quenched disorder is absent, there is a well defined melting temperature determined by the proliferation of topological defects, while for zero temperature, there is a critical quenched disorder strength above which topological defects proliferate. When both thermal and quenched disorder are present, these effects compete, and the thermal fluctuations can reduce the effectiveness of the quenched disorder, leading to a reentrant ordered phase in agreement with the predictions of Nelson (1983 Phys. Rev. B 27 2902–14). There are two competing theories for the low temperature behavior, and our simulations show that both capture aspects of the actual response. The critical disorder strength separating ordered from disordered states remains finite as the temperature goes to zero, as predicted by Cha and Fertig (1995 Phys. Rev. Lett. 74 4867–70), instead of dropping to zero as predicted by Nelson. At the same time, the critical disorder strength decreases with decreasing temperature, as predicted by Nelson, instead of remaining constant, as predicted by Cha and Fertig. The onset of the reentrant phase can be deduced based on changes in the transport response, where the reentrant ordering appears as an increase in the mobility or the occurrence of a depinning transition. We also find that when the system is in the ordered state and thermally melts, there is an increase in the effective damping or pinning. This produces a drop in the electron mobility that is similar to the peak effect phenomenon found in superconducting vortices, where thermal effects soften the lattice or break down its elasticity, allowing the particles to better adjust their positions to take full advantage of the quenched disorder.

Inspired by recent studies of the two-dimensional Wigner crystals for electrons, we study the time evolution of a gas of particles interacting with a Dirac pair potential. We find that the gas crystalizes into a square lattice for low free-particle quantum numbers.

Metastable states appear in many areas of physics as a result of symmetry-breaking phase transitions. An important challenge is to understand the microscopic mechanisms which lead to the formation of the energy barrier separating a metastable state from the ground state. In this paper, we describe an experimental example of the hidden metastable domain state in 1T-TaS2, created by photoexcitation or carrier injection. The system is an example of a charge density wave superlattice in the Wigner crystal limit displaying discommensurations and domain formation when additional charge is injected either through contacts or by photoexcitation. The domain walls and their crossings in particular display interesting, topologically entangled structures, which have a crucial role in the metastability of the system. We model the properties of experimentally observed thermally activated dynamics of topologically protected defects—dislocations—whose annihilation dynamics can be observed experimentally by scanning tunnelling microscopy as emergent phenomena described by a doped Wigner crystal. The different dynamics of trivial and non-trivial topological defects are quite striking. Trivial defects appear to annihilate quite rapidly at low temperatures on the timescale of the experiments, while non-trivial defects annihilate rarely, if at all.

Multielectron bubbles (MEBs) are cavities in liquid helium that contain electrons and possibly vapour. They provide a versatile platform for exploring properties of interacting electrons in two dimensions in a regime of densities that has not been previously available. Since the electrons are pushed against the deformable curved inner surface of the bubble, MEBs also provide an environment to study the roles of curvatures. In this review, we describe the current understanding of MEBs, with a focus on their stability issues, and highlight recent experimental studies of this interesting system. [ABSTRACT FROM AUTHOR]

The molecular dynamics method is used to study the melting of two-dimensional clusters that can form in electronic systems above the surface of superfluid helium with the help of triangular, square, hexagonal and round holding electrodes. Clusters with a fixed surface density of 108 cm−2, but different numbers of particles (from 3 to 406), are considered. It is shown that in defect-free clusters, the transition to a disordered state occurs abruptly and the melting point, Тmelt, is easy to determine. The dependence of Тmelt on the cluster size is observed for clusters with N < 400 particles. In square clusters with N < 50, the ordering of particles is imposed by the boundary conditions, whereas for N > 100, a triangular lattice with defects near the boundary is observed. In round clusters, electrons begin to move easily in the angular direction at rather low temperatures, but the "radial melting" temperature is consistent with the melting point of small square clusters. In the presence of defects, the transition to a disordered state begins from the defect region and gradually spreads to the entire cluster. There is no clear definition of the melting point in this scenario. [ABSTRACT FROM AUTHOR]

The molecular dynamics method is used to study the structure of two-dimensional clusters that can be created in electronic systems above the surface of superfluid helium, using triangular, square, hexagonal and round holding electrode geometries. Clusters with a fixed surface density of 108 cm−2, but different numbers of particles (from 3 to 406) are considered. The spatial configurations of particles in clusters are calculated corresponding to a temperature of 10−2 K. The shape of the cluster significantly affects the arrangement of the electrons inside. If the symmetry of the cluster is consistent with the triangular symmetry of the electronic crystal, then for some numbers of particles, clusters with ideal defect-free packing are possible; otherwise, the clusters contain defects. An additional external field applied to the cluster significantly changes the configuration of its particles. [ABSTRACT FROM AUTHOR]

The Cohn-Kumar conjecture states that the triangular lattice in dimension 2, the E8 lattice in dimension 8, and the Leech lattice in dimension 24 are universally minimizing in the sense that they minimize the total pair interaction energy of infinite point configurations for all completely monotone functions of the squared distance. This conjecture was recently proved by Cohn-Kumar-Miller-Radchenko-Viazovska in dimensions 8 and 24. We explain in this note how the conjecture implies the minimality of the same lattices for the Coulomb and Riesz renormalized energies as well as jellium and periodic jellium energies, hence settling the question of their minimization in dimensions 8 and 24. [ABSTRACT FROM AUTHOR]

We investigate non-perturbative corrections to the large N expansion of the homogeneous electron gas. These are associated with instanton solutions to the effective action of the plasmon field. We show that, although the large field behavior of that action dominates the quadratic bare Coulomb term, there are no solutions at large field, and consequently none at large density. We argue that solutions would exist at low density if the large N theory had a Wigner crystal (WC) phase. However, we argue that this is not the case. Together with the implied convergence of the large N expansion, this implies that the homogeneous electron gas with N component spins and a Coulomb interaction scaling like 1 ∕ N can only have a WC phase below a curve in the plane of N and density, which asymptotes to zero density at infinite N. We argue that for systems with a semi-classical expansion for order parameter dynamics, and a first order quantum transition between fluid and crystal phases, there are instantons associated with the decays of meta-stable fluid and crystal phases in the appropriate regions of the phase diagram. We argue that the crystal will decay into one or more colloidal or bubble phases (Kivelson and Spivak, 2006) rather than directly into the fluid. It is possible that the bubble phases remain stable all the way to the density where the crystal solution disappears. The bubbles of fluid will expand as the density is raised and gradually convert the system into a fluid filled with chunks of crystal. The transition to a translationally invariant phase is likely to be second order. Unfortunately, the HEG does not have a crystal phase at large N , where these semi-classical ideas could be examined in detail. We suggest that the evidence for negative dielectric function at intermediate densities for N = 2 is an indicator of this second order transition. While the infinite N limit does not have a negative dielectric function at any density, it is possible that the closed large N equation for the plasmon two point function, derived in Banks (2018) might capture at least the qualitative features of the second order transition. [ABSTRACT FROM AUTHOR]

A two-dimensional Wigner crystal formed by electrons located above a rectangular electrode with uniformly distributed positive charge has been studied by molecular dynamics methods. The authors have analyzed not only possible electron configurations over a narrow electrode region at a fixed electron density, depending on the width of the electrode, but also patterns of transitions from one configuration to another. In addition, this paper considers an electron configuration consisting of several chains. Using the Fourier transform for time dependencies of average electron coordinates during modeling, the authors have determined plasma oscillation spectra. Frequencies observed during modeling have been compared with theoretical frequencies for one and two chains. [ABSTRACT FROM AUTHOR]

Transport results from measuring ultra-clean two-dimensional systems, containing tunable carrier densities from 7 × 10 8 cm − 2 to ∼ 1 × 10 10 cm − 2 , reveal a strongly correlated liquid up to r s ≈ 40 where a Wigner crystallization is anticipated. A critical behavior is identified in the proximity of the metal-to-insulator transition. The nonlinear DC responses for r s > 40 captures hard pinning modes that likely undergo a first order transition into an intermediate phase in the course of melting. [ABSTRACT FROM AUTHOR]

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime.

This study sets out to describe the interaction of charged confined particles with a gravitational field. The system consisted of charged particles interacting electrostatically between themselves and with a confining box whose walls have a linear charge distribution. We studied numerically several configurations including the introduction of a tilt, that takes into account the Earth's gravitational field. In our analysis, we included the α parameter for describing the position of the center of mass and its evolution according to the influence of the box size. We also studied in detail the competition between the gravitational field and electrostatic forces over the system. Such a competition determines the shape and size of the distributed charges. When the electrostatic force is dominant, the charges are distributed almost symmetrically. Whereas, when the gravitational field is preponderant, the distribution of particles tends to have a hive-like shape and then as the tilt angle increases the distribution is flattened. This effect is exacerbated when the particles have bigger masses and the inclination is higher. From a physical analysis, we obtained an expression to determine the center of mass of the distributed particles, depending on the box's size and other physical parameters. Finally, based on the data analysis, we obtained fitting equations for the gravitational (logarithmic) and electrostatic (exponential) energies as a function of the enveloping area. • A detailed analysis of charged particles confined in a box with linear distributed charged walls is carried out. • The effects of gravitational field were taken into account by means of the box tilt and particle mass. • Based on physical factors such as gravitational field, electrostatic force and box size, an equation for the distributions' center of mass was established. • The study of the competition between the gravitational and electrostatic energies enabled the determination of the sizes and shapes of the enveloping areas. • From data analysis, exponential and logarithmic fitting equations for the gravitational and electrostatic energies were obtained respectively. [ABSTRACT FROM AUTHOR]

Transport results from measuring ultra-clean two-dimensional systems, containing tunable carrier densities from 7 × 10 8 cm − 2 to ∼ 1 × 10 10 cm − 2 , reveal a strongly correlated liquid up to r s ≈ 40 where a Wigner crystallization is anticipated. A critical behavior is identified in the proximity of the metal-to-insulator transition. The nonlinear DC responses for r s > 40 captures hard pinning modes that likely undergo a first order transition into an intermediate phase in the course of melting.

We study the Wigner crystallization on partially filled topological flat bands of kagome, honeycomb and checkerboard lattices. We identify the Wigner crystals (WCs) by analyzing the Cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength, measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The Wigner crystallization observed by us is a robust and general phenomenon, existing in all three lattice models for a broad range of filling factors and interaction parameters. The shape of the resulting WCs is determined by the boundary conditions of the chosen plaquette. It is to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles.

We discuss melting of a Wigner crystal formed on a free surface of superfluid $$^4$$ He, in quasi-one-dimensional (Q1D) channels of width between 5 and 15 $$\upmu $$ m. We reexamine our previous transport data (Ikegami et al. in Phys Rev B 82:201104(R), ), in particular, by estimating the number of electrons across the channel in a more accurate way with the aid of numerical calculations of distributions of the electrons in the channels. The results of reexamination indicate more convincingly that the melting of the Wigner crystal in the Q1D geometry is understood by the finite size effect on the Kosterlitz-Thouless-Halperin-Nelson-Young melting process. We also present technical details of the transport measurements of the electrons in a Q1D geometry, including a fabrication method of devices used for the transport measurements, numerical simulations of response of the devices, and a procedure for analyzing transport data. [ABSTRACT FROM AUTHOR]

Femtosecond techniques addressing phase transitions induced by optical pumps have allowed recently to put an ambitious goal to attend hidden states which are inaccessible and even unknown under equilibrium conditions. Recently, the group from Slovenia led by D. Mihailovic achieved a bistable switching to a hidden electronic state in 1T-TaS. The state is stable until an erase procedure reverts it to the thermodynamic ground state. A notoriously intricate nature of this material requires to consider simultaneous evolution of electrons and holes as mobile charge carriers, and crystallized electrons modifiable by intrinsic defects (voids and interstitials); all that on the CDW background. Our model considers mutual transformations among the three reservoirs of electrons, together with the heat production, which are dictated by imbalances of three partial chemical potentials. The phenomenological approach sheds a light on a very complicated and not yet resolved physics of this material which includes interplaying effects like CDW, Wigner crystal, commensurability, polarons, and Mott state. [ABSTRACT FROM AUTHOR]

We study transport properties of a Wigner crystal driven by an external force on the surface of superfluid 4, in the "quantum wire" regime, i.e. in the quasi-one-dimensional (quasi-1D) case when a typical width of the channel is comparable to the inter-electron separation. Utilizing molecular dynamics simulations, we investigate the electronic transport through the channels with different constrictions: (i) geometrical constrictions with varying shape and size, and (ii) a saddle-point potential with varying gate voltage. The average particle velocity has been calculated as a function of the driving force or gate voltage. We have revealed a significant difference in the dynamical behavior for long and short constrictions. In particular, we found that the oscillations of the average particle velocity in channels with short constrictions exhibit a clear correlation with the transitions between the states with different numbers of rows of particles in the constriction, while for channels with longer constrictions these oscillations are suppressed. The obtained results are in agreement with the recent experimental observations, and thus bring new important insights into the dynamics of electrons floating on the surface of superfluid 4 in channels with constrictions. Special Issue Comments: This article presents results on the dynamics of electrons moving on the surface of liquid helium in narrow channels with constrictions, with a focus on the "quantum wire", i.e. single file, regime. This article is connected to the Special Issue articles about advanced statistical properties in single file dynamics39 and the experiments on liquid helium.40 [ABSTRACT FROM AUTHOR]

-Abstract: We investigate an ensemble of excitons in a coupled quantum well excited via an applied laser field. Using an effective disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function P(M) to create M excitons as well as their correlation function. It shows clear evidence of the existence of two phases corresponding to a liquid and a crystal phase. We demonstrate that not only the correlation function but also the distribution P(M) is very well suited to monitor this transition. [ABSTRACT FROM AUTHOR]

The mobility of 2D electrons on pure He and on 0.5 % solution of He in He was investigated for different electron densities in the temperature range 0.12 to 1.3 K. The electrons in the same electron density show the same transition temperature from liquid state to Wigner crystal state in both pure He and in the solution. In the high temperature range where the gas-scattering is dominant, the electrons show a smaller mobility in the solution than in the pure He due to the electron collision with He gas atoms which have a higher vapor pressure. In the middle temperature range where the ripplon-scattering is dominant, the mobility in the solution is smaller than in He. This is explained by a smaller surface tension caused by He atoms collected at the surface. In the low temperature range where electrons are in the Wigner crystal state, the mobility gradually increases with decreasing temperature in the solution, while it stays almost constant in the pure He. The mobility increase is more pronounced in the low electron density. The results are qualitatively in agreement with the existing theory which includes the bulk He quasiparticle reflection from surface dimples and the effect of the surface layer of He atoms. [ABSTRACT FROM AUTHOR]

Abstract: The pair correlation function of a strongly interacting one-dimensional quantum dot is evaluated analytically within the framework of the spin coherent Luttinger liquid model. The influence of electron interactions and temperature on the competition between finite-size effects and electronic correlations is analyzed, also in the regime of large numbers of particles. The development of Wigner molecule correlations is observed as interactions get stronger. The visibility of such signatures is enhanced for temperatures comparable with the spin excitation energy of the system due to a suppression of the uncorrelated Friedel contribution to the pair correlation function. [Copyright &y& Elsevier]

We present transport measurements of electrons on the surface of liquid helium confined to a microscopic channel, the effective width of which can be controlled electrostatically. Above 1K the electron system is liquid-like and the conductance varies smoothly with the channel width. At lower temperatures the system forms a classical quasi-onedimensional Wigner crystal (WC). Close to the WC melting temperature, the current oscillates as the channel width is varied, due to reentrant melting as recently reported [H. Ikegami, H. Akimoto, D. G. Rees, and K. Kono: Phys. Rev. Lett. 109 (2012) 236802]. In the WC regime we observe Bragg-Cherenkov ripplon scattering, a signature of strong spatial electron order, for both the widely open channel and the single electron chain. [ABSTRACT FROM AUTHOR]

Abstract: We study the effective interaction between two parallel charged plates, modelling macromolecules, or colloids, in the strongly coupled Coulomb regime. Neutralizing mobile ions are point-like and confined in the inter-plate slab. A cumulant technique provides exact expansions, beyond the leading strong-coupling order, that are in remarkable agreement with simulation data for both the ionic profile and the inter-plate pressure. The present approach amounts to a summation over relevant excitations around the Wigner Crystal ground state formed at infinite coupling; It thereby differs from previous virial-like strong-coupling theories and generalizes a recent work by the authors to asymmetric plates. [Copyright &y& Elsevier]

The ground-state behavior of electron-electron quantum bilayer systems within the neutralizing background and zero magnetic field is studied by including unequal density of layers. The quantum self-consistent mean-field approximation of Singwi, Tosi, Land and Sjölander (qSTLS) is used to study the intra- and inter layer properties, such as the static pair-correlation functions, the static structure factors, the static density susceptibility and the static local-field correction factors over a wide range of layer density parameter r and layer spacing d. We find that the inclusion of unequal density brings a phase transition from charge density wave (CDW) to coupled Wigner crystal (WC) ground state at the close proximity of the layers. We also find that inclusion of unequal density markedly reduce critical r for the onset of Wigner crystallization. The results are compared with recent findings of the equal density effects in electron-electron quantum bilayer systems. [ABSTRACT FROM AUTHOR]

Abstract: The bifurcation of the electron system in a quantum wire has been observed in the form of the suppression and disappearance of the quantised conductance plateau at . We now present low-temperature transport measurements of a top-gated split-gate quantum wire that serve to further characterise this double-row régime of transport. A small distortion of the confinement caused by asymmetrical biasing of the split gates gives rise to a radical change in the conductance characteristics of the wire, beginning with the introduction of a plateau at which rises to around with greater differential bias between the split gates. DC source–drain bias measurements in this régime show a split zero-bias peak at low conductances merging into a single peak around , which then persists up to the plateau at . [Copyright &y& Elsevier]

Abstract: We investigate an effective one-dimensional conducting channel considering both the contact umklapp and the Coulomb electron–electron interaction. We show that, at low electronic density, the proximity to the Wigner crystal reproduces the anomaly in conductance at . The crucial ingredient of our theory is the fact that the gate voltage acts as a bias controlling the intensity of the umklapp term. At large gate voltages, the umklapp vanishes and we obtain a conducting quantum wire with a perfect conductance. At low gate voltages, the Wigner crystal is pinned by the umklapp term, giving rise to an insulating behavior with vanishing conductance. This crossover pattern has a transition point which can be identified with the anomalous conductance around . This picture is obtained within the framework of a renormalization group calculation. The conductance static regime is achieved by taking first the limit of finite length and then the limit of zero frequency. [Copyright &y& Elsevier]

Applying high magnetic fields parallel to the surface of a high-mobility 2D electron gas, we have recently observed a transition from the fractional quantum Hall liquid to an insulating phase, for filling factors as high as ν = 0.8 [B. A. Piot et al., Nature Phys. doi:10.1038/nphys1094]. This transition can be seen as a continuous distortion of the 2D Wigner crystal into a 'quasi-3D' insulating state. Here, we provide additional arguments confirming that carrier localization cannot be accounted for by disorder effects alone, and instead is most likely due to the stabilization of an electron solid by the strong parallel magnetic field in a 'quasi-3D' geometry. [ABSTRACT FROM AUTHOR]

Wigner solids in two-dimensional electron systems in high magnetic field B exhibit a striking, microwave or rf resonance, that is understood as a pinning mode. The temperature, Tm, above which the resonance is absent, is interpreted as the melting temperature of the solid. Studies of Tm for many B and many sample densities n show that Tm is a function of the Landau level filling ν alone for a given sample. This indicates that quantum mechanics figures importantly in the melting. Tm also appears to be increased by larger sample disorder. [ABSTRACT FROM AUTHOR]

Oil-water mixtures are ubiquitous in nature and are particularly important in biology and industry. Usually additives are used to prevent the liquid droplets from coalescing. Here, we show that stabilization can also be obtained from electrostatics, because of the well known remarkable properties of water. Preferential ion uptake leads to a tunable droplet charge and surprisingly stable, additive-free, water-in-oil emulsions that can crystallize. For particle-stabilized ("Pickering") emulsions we find that even extremely hydrophobic, nonwetting particles can be strongly bound to (like-charged) oil-water interfaces because of image charge effects. These basic insights are important for emulsion production, encapsulation, and (self-)assembly, as we demonstrate by fabricating a diversity of structures in bulk, on surfaces, and in confined geometries. [ABSTRACT FROM AUTHOR]

Abstract: Magnetoresistance (MR) of GaAs two-dimensional hole systems (2DHSs) is investigated in the strongly insulating regime. By rotating the samples, the total magnetic field and the perpendicular component to the 2DHS are controlled independently. In the low- region, a large positive -dependence of the longitudinal resistivity is observed when is small, while it is replaced by a negative one when is large. For higher , dips are observed in the vs curve and the values of at the dip depend on . The results are discussed both in the framework of single-particle localization and in the framework of Wigner crystallization. [Copyright &y& Elsevier]

Abstract: We report on low-temperature thermopower measurements of interacting GaAs bilayer hole systems in the limit of no interlayer tunneling. These systems exhibit a reentrant insulating phase near the many-body quantum Hall state (QHS) at total filling factor , when both layers have the same density. The diffusion thermopower is expected to diverge as in the presence of an energy gap (Wigner crystal) or to vanish in the case of a disordered induced mobility gap. Our results show that, as the temperature is decreased, the diffusion thermopower exhibits a dependence in the insulating phase around . This behavior clearly indicates the opening of an energy gap at low temperature, in agreement with the formation of a pinned Wigner solid. Finally, we report on the T-dependence of the thermopower at . [Copyright &y& Elsevier]

Abstract: Our recent broadband microwave and RF spectroscopic measurements of two-dimensional electron systems at Landau level filling are reviewed. Resonances in the spectrum of diagonal conductivity in many discrete regions of allow us to identify and study the pinned electron solids. [Copyright &y& Elsevier]

Abstract: We quantize the electromagnetic field in a polar medium starting with the fundamental equations of motion. In our model the medium is described by a Lorenz-type dielectric function appropriate e.g. for ionic crystals, metals and inert dielectrics. There are no restrictions on the spatial behavior of the dielectric function, i.e. there can be many different polar media with arbitrary shapes. We assume no losses in our system so the dielectric function for the whole space is assumed as real. The quantization procedure is based on an expansion of the total field (transverse and longitudinal) in terms of the coupled (polariton) eigenmodes, so our theory gives the Hamiltonian of polaritons of dispersive dielectric media. We pay particular attention to the derivation of the fundamental (equal-time) commutation relations between the conjugate field operators. As an example, we apply our theory to the quasi-two-dimensional Wigner crystal, formed by electrons at very low temperature. We discuss the influence of the quantized electromagnetic field on the dynamics of Wigner electrons, i.e., on the dispersion relation of Wigner phonons. We expect a significant influence in the case when frequencies of (surface) polaritons and Wigner phonons coincide, and we discuss the energy spectrum of such a system. [Copyright &y& Elsevier]

Abstract: Victor Emery made seminal contributions to the theory of one-dimensional electronic systems and to its applications to organic metals. His inventions became illuminated recently when the joint effect of the ferroelectricity and the charge disproportionation has been discovered in (TMTTF)2X compounds and beyond. Several of his contributions came to agenda at once: separate gaps in spin/charge channels and the route to solitons, 4kF anomaly, dimerization gap, role of ionic transitions. New phenomena unify an unusual variety of concepts: ferroelectricity of good conductors, structural instability towards Mott-Hubbard state, Wigner crystallization in a dense electronic system, ordered 4kF density wave, richness of physics of solitons, interplay of structural and electronic symmetries. The ferroelectric state gives rise to several types of solitons carrying the electron charge, a noninteger charge, spin or both the spin and the charge in special cases. They are clearly observed via conductivity, electric and magnetic susceptibilities. Solitons are challenging for optics where they already seem to determine the pseudogap in adsorption. Various features also appear, or are expected, from collective electronic and coupled electron-phonon modes. The last topic, as well as some aspects of physics of solitons, recalls also the contributions of M.J. Rice. Moreover, the observation of Mott-Hubbard states refers to classical results of A. A. Ovchinnikov. [Copyright &y& Elsevier]

We argue that, due to the specific form of the interaction potential between electronic guiding centers, a bubble crystal (BC) with basis may be energetically more favorable than the usual bubble solid. This new BC has well-defined normal eigenmodes, and remains energetically favorable when the effects of finite sample thickness and of screening by electrons in lower LLs are taken into account. [ABSTRACT FROM AUTHOR]

We study the effect of the pair interactions range on the density–density correlations of Luttinger model in the presence of an external field. If long range interactions are considered, then the Wigner crystal structure, characteristic of the field-free system, is not substantially modified. [Copyright &y& Elsevier]

We study the effect of the interaction between two parallel wires on the electronic correlations and the conductivity of one of them. If the interactions are not singular and the wires are near enough, then we found that the correlations are quickly damped and a divergence in the conductivity at zero temperature appears. On the other hand, if the interactions are singular, then the correlations in each wire is not affected by the coupling with the other one. [Copyright &y& Elsevier]

The cyclotron resonance of the correlated two-dimensional electrons on liquid helium in high magnetic fields is investigated on the basis of the newly developed theory. Electrons are assumed to form a Wigner crystal, and the electron correlation effect is taken into account through the self-consistently determined Wigner phonons, where the electron–electron interaction, the electron–ripplon and electron–vapor atom scatterings are considered on the same footing. The numerical calculations show a very good agreement with experiments without any fitting parameters. [Copyright &y& Elsevier]

The ground state of a quasi-two-dimensional electron gas (Q-2DEG) is investigated within a framework of the local spin density approximation (LSDA) with Perdew–Zunger type exchange-correlation energy. The ground state in a Q-2DEG is given as a function of film thickness and electron density. The Wigner rod ground state in a very thin film with low electron areal density is discussed in detail. In addition, the ground state of a two-dimensional electron gas (2DEG) is investigated using the LSDA with Tanatar–Ceperley and Attaccalite–Moroni–Georgi–Bachelet types of exchange-correlation energy. The ground state is found to show a phase transition from a nonmagnetic fluid to a spin-fully-polarized ferromagnetic Wigner ribbon with decreasing areal density. The difference between a 2DEG and a Q-2DEG with infinitesimal film thickness is discussed. [Copyright &y& Elsevier]