Charge-charge Correlation Function Research Articles

Two-dimensional t−t′ Holstein model

The competition and interplay between charge-density wave and superconductivity have become a central subject for quasi-2D compounds. Some of these materials, such as the transition-metal dichalcogenides, exhibit strong electron-phonon coupling, an interaction that may favor both phases, depending on the external parameters, such as hydrostatic pressure. In view of this, here we analyze the single-band $t$-$t^{\prime}$ Holstein model in the square lattice, adding a next-nearest neighbor hopping $t^{\prime}$ in order to play the role of the external pressure. To this end, we perform unbiased quantum Monte Carlo simulations with an efficient inversion sampling technique appropriately devised for this model. Such a methodology drastically reduces the autocorrelation time, and increases the efficiency of the Monte Carlo approach. By investigating the charge-charge correlation functions, we obtain the behavior of the critical temperature as a function of $t^{\prime}$, and from compressibility analysis, we show that a first-order metal-to-insulator phase transition occurs. We also provide a low-temperature phase diagram for the model.

Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation.

Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction.

Underscreening and hidden ion structures in large scale simulations of concentrated electrolytes.

The electrostatic screening length predicted by Debye-Hückel theory decreases with increasing ionic strength, but recent experiments have found that the screening length can instead increase in concentrated electrolytes. This phenomenon, referred to as underscreening, is believed to result from ion-ion correlations and short-range forces such as excluded volume interactions among ions. We use Brownian Dynamics to simulate a version of the Restrictive Primitive Model for electrolytes over a wide range of ion concentrations, ionic strengths, and ion excluded volume radii for binary electrolytes. We measure the decay of the charge-charge correlation among ions in the bulk and compare it against scaling trends found experimentally and determined in certain weak coupling theories of ion-ion correlation. Moreover, we find that additional large scale ion structures emerge at high concentrations. In this regime, the frequency of oscillations computed from the charge-charge correlation function is not dominated by electrostatic interactions but rather by excluded volume interactions and with oscillation periods on the order of the ion diameter. We also find the nearest neighbor correlation of ions sharing the same charge transitions from negative at small concentrations to positive at high concentrations, representing the formation of small, like-charge ion clusters. We conclude that the increase in local charge density due to the formation of these clusters and the topological constraints of macroscopic charged surfaces can help explain the degree of underscreening observed experimentally.

Screening length for finite-size ions in concentrated electrolytes.

The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function. By going beyond DH theory, we predict the effects of ion size on the charge-charge correlation function. A simple modification of the Coulomb interaction kernel to account for the excluded volume of neighboring ions yields a nonmonotonic dependence of the screening length (correlation length) on the ionic concentration, as well as damped charge oscillations for high concentrations.

Self-diffusion and structure of monovalent ions in two dimensions: A molecular dynamics study

The knowledge of the self-diffusion coefficient is indispensable for different processes in chemical engineering and in the design of new materials, which sometimes occur in restricted or confined geometries. In this work we studied the self-diffusion and structural properties of monovalent ions moving in two dimensions. The two-dimensional soft primitive model was used to describe the interaction between ions and molecular dynamics simulations of the electroneutral mixture were performed to calculate the properties. Radial distribution functions, density-density and charge-charge correlation functions as well as the mean square displacement, the velocity autocorrelation function and the diffusion coefficient were evaluated at supercritical conditions. For the lowest reduced temperature, the formation of clusters, chains and rings of ions influenced the cation-anion radial distribution function, particularly at low densities, where very high values of the first maximum were observed. Clusters and free ions were evaluated. These arrays also influence the density-density and charge-charge correlation functions. Concerning the self-diffusion, it increases as temperature is higher and decreases when density increases, as physically expected. The behavior of the self-diffusion coefficient was analyzed by trying different fitting models. We found that the density dependence is well described by a third-degree polynomial or a linear-logarithmic fit. When the simultaneous dependence with density and temperature is considered, we found that the diffusion is a unique function of the variable ργ/T, where the exponent γ is about 1.7, in contrast with three-dimensional m − 6 Lennard-Jones fluids, where it has been found to be in the range 3.4–13.5. We also investigated the type of diffusive motion. The features observed in both, the velocity autocorrelation function and the mean square displacement, indicated that the diffusion of the ions takes place as normal diffusion, in contrast with other two-dimensional fluids, where superdiffusive and subdiffusive motion have been observed.

Engineering the Floquet spectrum of superconducting multiterminal quantum dots

Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Stark ladder spectra, we have developed an analytical model relying on the sharpness of the resonances. The charge-charge correlation function is obtained as a factorized form of the Floquet wave-function on the dot and the superconducting reservoir populations. We confirm these findings by Keldysh Green's function calculations, in particular regarding the voltage and frequency dependence of the resonance peaks in the current-current correlations. Our results open up a road-map to quantum correlations and coherence in the Floquet dynamics of superconducting devices.

Fate of the open-shell singlet ground state in the experimentally accessible acenes: A quantum Monte Carlo study.

By means of the Jastrow correlated antisymmetrized geminal power (JAGP) wave function and quantum Monte Carlo (QMC) methods, we study the ground state properties of the oligoacene series, up to the nonacene. The JAGP is the accurate variational realization of the resonating-valence-bond (RVB) ansatz proposed by Pauling and Wheland to describe aromatic compounds. We show that the long-ranged RVB correlations built in the acenes' ground state are detrimental for the occurrence of open-shell diradical or polyradical instabilities, previously found by lower-level theories. We substantiate our outcome by a direct comparison with another wave function, tailored to be an open-shell singlet (OSS) for long-enough acenes. By comparing on the same footing the RVB and OSS wave functions, both optimized at a variational QMC level and further projected by the lattice regularized diffusion Monte Carlo method, we prove that the RVB wave function has always a lower variational energy and better nodes than the OSS, for all molecular species considered in this work. The entangled multi-reference RVB state acts against the electron edge localization implied by the OSS wave function and weakens the diradical tendency for higher oligoacenes. These properties are reflected by several descriptors, including wave function parameters, bond length alternation, aromatic indices, and spin-spin correlation functions. In this context, we propose a new aromatic index estimator suitable for geminal wave functions. For the largest acenes taken into account, the long-range decay of the charge-charge correlation functions is compatible with a quasi-metallic behavior.

Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling

In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green's functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J>0) and anti-ferro (J<0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.

Mean-field theory of the phase diagram of ultrasoft, oppositely charged polyions in solution

We investigate the phase separation of the "ultrasoft restricted primitive model" (URPM), a coarse-grained representation of oppositely charged, interpenetrating polyelectrolytes, within a mean-field description based on the "chemical picture." The latter distinguishes between free ions and dimers of oppositely charged ions (Bjerrum pairs) which are in chemical equilibrium governed by a law of mass action. Interactions between ions, and between ions and dimers are treated within linearized Poisson-Boltzmann theory, at four levels of approximation corresponding to increasingly refined descriptions of the interactions. The URPM is found to phase separate into a dilute phase of dimers, and a concentrated phase of mostly free (unpaired) ions below a critical temperature T(c). The phase diagram differs, however, considerably from the predictions of recent simulations; T(c) is about three times higher, and the critical density is much lower than the corresponding simulation data [D. Coslovich, J. P. Hansen, and G. Kahl, Soft Matter 7, 1690 (2011)]. Possible reasons for this unexpected failure of mean-field theory are discussed. The Kirkwood line, separating the regimes of monotonically decaying and damped oscillatory decay of the charge-charge correlation function at large distances is determined within the random phase approximation.

The c-axis charge traveling wave in a coupled system of Josephson junctions

We demonstrate a manifestation of the charge traveling wave along the c-axis (TW) in current voltage characteristics of coupled Josephson junctions in high-$T_c$ superconductors. The branches related to the TW with different wavelengths are found for the stacks with different number of Josephson junctions at different values of system's parameters. Transitions between the TW branches and the outermost branch are observed. Time dependence of the electric charge in the superconducting layers and charge-charge correlation functions for TW and outermost branches show different behavior with bias current. We propose an experimental testing of the TW by microwave irradiation.

COLLECTIVE EXCITATIONS IN SUPERCONDUCTORS AND SEMICONDUCTORS IN THE PRESENCE OF A CONDENSED PHASE

We first study the spectrum of the excitonic polaritons in semiconductors in the presence of a condensed phase. With the help of the Hubbard-Stratonovich transformation we propose an exact mapping of the extended Hubbard model onto an excitonic-polariton model describing the light propagation in semiconductors. This approach allows us to derive exact formulas for spin-spin and charge-charge correlation functions for spin-triplet superconductivity.

Small-Signal Circuit Elements of MIS-Type Nanostructures

Starting from a mean field calculation for the static capacitance of a MIS-nanostructure with a near back gate [P.N. Racec, E. R. Racec and U. Wulf, Phys. Rev. B 65, 193314, (2002)] we develop an approach to determine the equivalent small-signal circuit. The analyzed system has an open character, taken into account in the Landauer-Büttiker formalism. The Coulomb interaction is treated in Hartree approximation. Consistent with our static calculations we determine the charge-charge correlation function in the random phase approximation to find the ac-admittances. The small-signal circuit consists of a voltage-dependent capacitance and a resistance in series. Beyond a characteristic frequency c ν they become frequency dependent. The characteristic frequency is given by the life time of specific resonance which develops in the system.

Electronic Raman scattering in a multiband model for cuprate superconductors

Charge-charge, current-current, and Raman correlation functions are derived in a consistent way using the unified response theory. The theory is based on the improved description of the conduction electron coupling to the external electromagnetic fields, distinguishing further the direct and indirect (assisted) scattering on the quasistatic disorder. The two scattering channels are distinguished in terms of the energy and momentum conservation laws. The theory is illustrated on the Emery three-band model for the normal state of the underdoped high-${T}_{c}$ cuprates which includes the incoherent electron scattering on the disorder associated with the quasistatic fluctuations around the static antiferromagnetic (AF) ordering. It is shown, for the first time consistently, that the incoherent indirect processes dominate the low-frequency part of the Raman spectra, while the long-range screening which is dynamic removes the long-range forces in the ${A}_{1g}$ channel. In the mid-infrared frequency range the coherent AF processes are dominant. In contrast to the nonresonant ${B}_{1g}$ response, which is large by itself, the resonant interband transitions enhance both the ${A}_{1g}$ and ${B}_{1g}$ Raman spectra to comparable values, in good agreement with experimental observation. It is further argued that the AF correlations give rise to the mid-infrared peak in the ${B}_{1g}$ Raman spectrum, accompanied by a similar peak in the optical conductivity. The doping behavior of these peaks is shown to be correlated with the linear doping dependence of the Hall number, as observed in all underdoped high-${T}_{c}$ compounds.

Admittance of planar two-terminal quantum systems

We develop an approach to calculate the admittance of effectively one-dimensional open quantum systems in random phase approximation. The stationary, unperturbed system is described within the Landauer-B\"uttiker formalism taking into account the Coulomb interaction in the Hartree approximation. The dynamic changes in the effective potential are calculated microscopically from the charge-charge correlation function resulting from the stationary scattering states. We provide explicit RPA-expressions for the quantum admittance. As a first example the case of a quantum capacitor is considered where we can derive a small-frequency expansion for the admittance which lends itself to an experimental testing of the theory. A comparison of the low-frequency expansion with the complete RPA-expression shows that for a quantum capacitor a simple classical equivalent circuit with frequency-independent elements does not describe satisfactorily the quantum-admittance with increasing the frequency.

Correlation exponentKρof the one-dimensional Kondo lattice model

We present results for the correlation exponent K_rho of the Tomonaga-Luttinger liquid description of the one-dimensional Kondo lattice as a function of conduction electron density and coupling constant. It is obtained from the first derivative of the Fourier transform of the charge-charge correlation function. We also show that the spin correlation function can only be described in this picture if we include logarithmic corrections, a feature that had been previously overlooked. A consistent description of both charge and spin sectors is then obtained. Finally, we show evidence that the spin sector of the dimerized phase at quarter-filling is gapless.

Field theoretical approach to inhomogeneous ionic systems: thermodynamic consistency with the contact theorem, Gibbs adsorption and surface tension

Using a statistical field approach we investigate the structure of an electrolyte solution in contact with a neutral impenetrable wall. The Hamiltonian contains the Coulomb interaction and the ideal entropy. At the level of the quadratic approximation, the Hamiltonian yields the Debye-Hückel theory in the bulk. Analytic expressions of the charge-charge and potential-potential inhomogeneous correlation functions are obtained. Exact asymptotic results for point ion charge correlation functions are obtained and the profile for the fluctuation of the electric potential is calculated. We also consider the term beyond the quadratic expansion of the ideal entropy in the Hamiltonian. With this term a higher order coupling between charge density and number density produces a non-trivial profile for the total ion density. This density profile is consistent with the contact theorem and the related surface tension calculated from the Gibbs adsorption isotherm.

Inhomogeneous Gutzwiller approximation with random phase fluctuations for the Hubbard model

We present a detailed study of the time-dependent Gutzwiller approximation for the Hubbard model. The formalism, labelled GA+RPA, allows us to compute random-phase approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). No restrictions are imposed on the charge and spin configurations which makes the method suitable for the calculation of linear excitations around symmetry-broken solutions. Well-behaved sum rules are obeyed as in the Hartree-Fock (HF) plus RPA approach. Analytical results for a two-site model and numerical results for charge-charge and current-current dynamical correlation functions in one and two dimensions are compared with exact and HF+RPA results, supporting the much better performance of GA+RPA with respect to conventional HF+RPA theory.

Effect of a nearby charge-ordered phase on correlation functions in ionic systems

The charge–charge and number–number correlation functions are investigated using a mean-field density functional for the restricted primitive model (hard-sphere and Coulomb interactions) supplemented with short-ranged attractive forces. The system exhibits phase separation into ion-dilute and ion-dense phases, and the latter phase becomes unstable with respect to charge-ordering along the λ-line. In mean field approximation both the range and the amplitude of the charge-charge correlation function increase as (S−Sλ)−1/2 on the approach to the λ-line, where S=T*/ρ0* and Sλ is the value of S at the λ-line (T* is the reduced temperature and ρ0* is the dimensionless density). The line dividing the phase diagram into regions where the range of charge–charge correlations is longer (shorter) than the range of the number–number correlations is also determined. We argue that the large range and large amplitude of the charge–charge correlation function is consistent with the formation of aggregates (living polymers) observed in simulations of ionic systems.

Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model

We have carried out symmetrized density-matrix renormalization-group calculations to study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople Hamiltonian. We have used the ${C}_{2}$ symmetry, the electron-hole symmetry, and the spin parity of the system in our calculations. We find that there is a crossover in the lowest dipole forbidden two-photon state and the lowest dipole allowed excited state with size of the oligomer. In the long system limit, the two-photon state lies below the lowest dipole allowed excited state. The triplet state lies well below the two-photon state and energetically does not correspond to its description as being made up of two triplets. These results are in agreement with the general trends in linear conjugated polymers. However, unlike in linear polyenes wherein the two-photon state is a localized excitation, we find that in polyacenes, the two-photon excitation is spread out over the system. We have doped the systems with a hole and an electron and have calculated the charge excitation gap. Using the charge gap and the optical gap, we estimate the binding energy of the ${1}^{1}{B}^{\ensuremath{-}}$ exciton to be 2.09 eV. We have also studied doubly doped polyacenes and find that the bipolaron in these systems, to be composed of two separated polarons, as indicated by the calculated charge-density profile and charge-charge correlation function. We have studied bond orders in various states in order to get an idea of the excited state geometry of the system. We find that the ground state, the triplet state, the dipole allowed state, and the polaron excitations correspond to lengthening of the rung bonds in the interior of the oligomer while the two-photon excitation corresponds to the rung bond lengths having two maxima in the system.

Charge-charge correlation functions in the Emery three-band model

The influence of the long-range Coulomb forces on the charge-charge correlation functions has been examined in the Emery three-band model. The ${U}_{d}=0$ limit and the mean-field approximation of the ${U}_{d}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit have been studied. The intraband and interband contributions to the dynamically screened correlation functions are found both for the intercell (monopole) and intracell (quadrupole) charge fluctuations. It appears that the interband monopole processes are responsible for the optical interband transitions. For strong local correlations ${(U}_{d}\ensuremath{\rightarrow}\ensuremath{\infty}),$ the threshold energy of these processes is found to be only slightly dependent on the bare hybridization parameter ${t}_{\mathrm{pd}}^{0}/{\ensuremath{\Delta}}_{\mathrm{pd}}^{0}.$ The value of the threshold energy is comparable with the bare first-neighbor overlap energy ${t}_{\mathrm{pd}}^{0}.$ As expected from experimental observations and previous static, symmetry-based theoretical considerations, the oxygen-oxygen charge correlation function is not screened in the tetragonal lattices, in contrast to the oxygen-copper $(\mathrm{pd})$ charge correlation function. The intraband coupling of the Raman-active phonons to the $\mathrm{pd}$ intracell charge fluctuations becomes thus substantially screened, but does not vanish, at variance with the predictions of the static-screening models. It is also found that the mean-field approximation of the ${U}_{d}\ensuremath{\rightarrow}\ensuremath{\infty}$ case can explain the measured magnitude of the plasma frequency, as well as its dependence on doping, but only in the overdoped high-${T}_{c}$ superconductors.