Direct Observation of Enhanced Electron-Phonon Coupling in Copper Nanoparticles in the Warm-Dense Matter Regime.

Warm dense matter (WDM) represents a highly excited state that lies at the intersection of solids, plasmas, and liquids and that cannot be described by equilibrium theories. The transient nature of this state when created in a laboratory, as well as the difficulties in probing the strongly coupled interactions between the electrons and the ions, make it challenging to develop a complete understanding of matter in this regime. In this work, by exciting isolated ∼8 nm copper nanoparticles with a femtosecond laser below the ablation threshold, we create uniformly excited WDM. Using photoelectron spectroscopy, we measure the instantaneous electron temperature and extract the electron-ion coupling of the nanoparticle as it undergoes a solid-to-WDM phase transition. By comparing with state-of-the-art theories, we confirm that the superheated nanoparticles lie at the boundary between hot solids and plasmas, with associated strong electron-ion coupling. This is evidenced both by a fast energy loss of electrons to ions, and a strong modulation of the electron temperature induced by strong acoustic breathing modes that change the nanoparticle volume. This work demonstrates a new route for experimental exploration of the exotic properties of WDM.

Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations.

Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data as well as particle insertions are avoided. Furthermore, no simulations at "uninteresting" state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semigrand canonical ensemble (NPTΔµ). We describe this Monte Carlo-based Clapeyron integration method, including its basic physical and numerical principles, our extension to electron-ion plasmas, and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense carbon-oxygen plasmas under conditions relevant for the cores of white dwarf stars and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles.

Friction force in strongly magnetized plasmas.

A charged particle moving through a plasma experiences a friction force that commonly acts antiparallel to its velocity. It was recently predicted that in strongly magnetized plasmas, in which the plasma particle gyrofrequency exceeds the plasma frequency, the friction also includes a transverse component that is perpendicular to both the velocity and Lorentz force. Here, this prediction is confirmed using molecular-dynamics simulations, and it is shown that the relative magnitude of the transverse component increases with plasma coupling strength. This result influences single-particle motion and macroscopic transport in strongly magnetized plasmas found in a broad range of applications.

Nature of Non-Adiabatic Electron-Ion Forces in Liquid Metals.

An accurate description of electron-ion interactions in materials is crucial for our understanding of their equilibrium and nonequilibrium properties. Here we assess the properties of frictional forces experienced by ions in noncrystalline metallic systems, including liquid metals and warm dense plasmas, that arise from electronic excitations driven by the nuclear motion due to the presence of a continuum of low-lying electronic states. To this end, we perform detailed ab initio calculations of the full friction tensor that characterizes the set of friction forces. The non-adiabatic electron-ion interactions introduce hydrodynamic couplings between the ionic degrees of freedom, which are sizable between nearest neighbors. The friction tensor is generally inhomogeneous, anisotropic, and nondiagonal, especially at lower densities.

Calculation of electron-ion temperature equilibration rates and friction coefficients in plasmas and liquid metals using quantum molecular dynamics.

We discuss a method to calculate with quantum molecular dynamics simulations the rate of energy exchanges between electrons and ions in two-temperature plasmas, liquid metals, and hot solids. Promising results from this method were recently reported for various materials and physical conditions [Simoni and Daligault, Phys. Rev. Lett. 122, 205001 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.205001]. Like other ab initio calculations, the approach offers a very useful comparison with the experimental measurements and permits an extension into conditions not covered by the experiments. The energy relaxation rate is related to the friction coefficients felt by individual ions due to their nonadiabatic interactions with electrons. Each coefficient satisfies a Kubo relation given by the time integral of the autocorrelation function of the interaction force between an ion and the electrons. These Kubo relations are evaluated using the output of quantum molecular dynamics calculations in which electrons are treated in the framework of finite-temperature density functional theory. The calculation presents difficulties that are unlike those encountered with the Kubo formulas for the electrical and thermal conductivities. In particular, the widely used Kubo-Greenwood approximation is inapplicable here. Indeed, the friction coefficients and the energy relaxation rate diverge in this approximation since it does not properly account for the electronic screening of electron-ion interactions. The inclusion of screening effects considerably complicates the calculations. We discuss the physically motivated approximations we applied to deal with these complications in order to investigate a widest range of materials and physical conditions. Unlike the standard method used for the electronic conductivities, the Kubo formulas are evaluated directly in the time domain and not in the energy domain, which spares one from needing to introduce an extraneous undetermined numerical parameter to account for the discrete character of the numerical density of states. We highlight interesting properties of the energy relaxation rate not shared by other electronic properties, in particular its self-averaging character. We then present a detailed parametric and convergence study with the numerical parameters, including the system size, the number of bands and k points, and the physical approximations for the dielectric function and the exchange-correlation energy.

Theory of the electron-ion temperature relaxation rate spanning the hot solid metals and plasma phases.

We present a theory for the rate of energy exchange between electrons and ions-also known as the electron-ion coupling factor-in physical systems ranging from hot solid metals to plasmas, including liquid metals and warm dense matter. The paper provides the theoretical foundations of a recent work [J. Simoni and J. Daligault, Phys. Rev. Lett. 122, 205001 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.205001], where first-principles quantum molecular dynamics calculations based on this theory were presented for representative materials and conditions. We first derive a general expression for the electron-ion coupling factor that includes self-consistently the quantum mechanical and statistical nature of electrons, the thermal and disorder effects, and the correlations between particles. The electron-ion coupling is related to the friction coefficients felt by individual ions due to their nonadiabatic interactions with the electrons. Each coefficient satisfies a Kubo relation given by the time integral of the autocorrelation function of the interaction force of an ion with the electrons. Exact properties and different representations of the general expressions are discussed. We then show that our theory reduces to well-known models in limiting cases. In particular, we show that it simplifies to the standard electron-phonon coupling formula in the limit of hot solids with lattice and electronic temperatures much greater than the Debye temperature, and that it extends the electron-phonon coupling formula beyond the harmonic phonon approximation. For plasmas, we show that the theory readily reduces to the well-known Spitzer formula in the hot plasma limit, to the Fermi "golden rule" formula in the limit of weak electron-ion interactions, and to other models proposed to go beyond the latter approximation. We explain that the electron-ion coupling is particularly well adapted to average atom models, which offer an effective way to include nonideal interaction effects to the standard models and at a much reduced computational cost in comparison to first-principles quantum molecular dynamics simulations.

First-Principles Determination of Electron-Ion Couplings in the Warm Dense Matter Regime.

We present first-principles calculations of the rate of energy exchanges between electrons and ions in nonequilibrium warm dense plasmas, liquid metals, and hot solids, a fundamental property for which various models offer diverging predictions. To this end, a Kubo relation for the electron-ion coupling parameter is introduced, which includes self-consistently the quantum, thermal, nonlinear, and strong coupling effects that coexist in materials at the confluence of solids and plasmas. Most importantly, like other Kubo relations widely used for calculating electronic conductivities, the expression can be evaluated using quantum molecular dynamics simulations. Results are presented and compared to experimental and theoretical predictions for representative materials of various electronic complexity, including aluminum, copper, iron, and nickel.

Effective potential theory for diffusion in binary ionic mixtures.

Self-diffusion and interdiffusion coefficients of binary ionic mixtures are evaluated using the effective potential theory (EPT), and the predictions are compared with the results of molecular dynamics simulations. We find that EPT agrees with molecular dynamics from weak coupling well into the strong-coupling regime, which is a similar range of coupling strengths as previously observed in comparisons with the one-component plasma. Within this range, typical relative errors of approximately 20% and worst-case relative errors of approximately 40% are observed. We also examine the Darken model, which approximates the interdiffusion coefficients based on the self-diffusion coefficients.

Crossover from Classical to Fermi Liquid Behavior in Dense Plasmas.

We explore the crossover from classical plasma to quantum Fermi liquid behavior of electrons in dense plasmas. To this end, we analyze the evolution with density and temperature of the momentum lifetime of a test electron introduced in a dense electron gas. This allows us (1) to determine the boundaries of the crossover region in the temperature-density plane and to shed light on the evolution of scattering properties across it, (2) to quantify the role of the fermionic nature of electrons on electronic collisions across the crossover region, and (3) to explain how the concept of the Coulomb logarithm emerges at a high enough temperature but disappears at a low enough temperature.

Transport regimes spanning magnetization-coupling phase space.

The manner in which transport properties vary over the entire parameter-space of coupling and magnetization strength is explored. Four regimes are identified based on the relative size of the gyroradius compared to other fundamental length scales: the collision mean free path, Debye length, distance of closest approach, and interparticle spacing. Molecular dynamics simulations of self-diffusion and temperature anisotropy relaxation spanning the parameter space are found to agree well with the predicted boundaries. Comparison with existing theories reveals regimes where they succeed, where they fail, and where no theory has yet been developed.

Ionic Transport Coefficients of Dense Plasmas without Molecular Dynamics.

We present a theoretical model that allows a fast and accurate evaluation of ionic transport properties of realistic plasmas spanning from warm and dense to hot and dilute conditions, including mixtures. This is achieved by combining a recent kinetic theory based on effective interaction potentials with a model for the equilibrium radial density distribution based on an average atom model and the integral equations theory of fluids. The model should find broad use in applications where nonideal plasma conditions are traversed, including inertial confinement fusion, compact astrophysical objects, solar and extrasolar planets, and numerous present-day high energy density laboratory experiments.

Modified Enskog kinetic theory for strongly coupled plasmas.

Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling (Γ≳30). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.

Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory.

We validate the application of our recent orbital-free density functional theory (DFT) approach [Phys. Rev. Lett. 113, 155006 (2014);] for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion coefficient, the viscosity coefficient, the electrical and thermal conductivities, and the reflectivity coefficient of hydrogen and aluminum plasmas. Very good agreement is found with orbital-based Kohn-Sham DFT calculations at lower temperatures. Because the computational costs of the method do not increase with temperature, we can produce results at much higher temperatures than is accessible by the Kohn-Sham method. Our results for warm dense aluminum at solid density are inconsistent with the recent experimental results reported by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)].

Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes.

We develop and implement a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density functional theory. The results for hydrogen and aluminum are in very good agreement with Kohn-Sham (orbital-based) density functional theory and path integral Monte Carlo calculations for microscopic features such as the electron density as well as the equation of state. The present approach does not scale with temperature and hence extends to higher temperatures than is accessible in the Kohn-Sham method and lower temperatures than is accessible by path integral Monte Carlo calculations, while being significantly less computationally expensive than either of those two methods.

Determination of the shear viscosity of the one-component plasma.

The shear viscosity coefficient of the one-component plasma is calculated with unprecedented accuracy using equilibrium molecular dynamics simulations and the Green-Kubo relation. Numerical and statistical uncertainties and their mitigation for improving accuracy are analyzed. In the weakly coupled regime, our results agree with the Landau-Spitzer prediction. In the moderately and strongly coupled regimes, our results are found in good agreement with recent results obtained for the Yukawa one-component plasma using nonequilibrium molecular dynamics. A practical formula is provided for evaluating the viscosity coefficient across coupling regimes, from the weakly coupled regime to solidification threshold. The results are used to test theoretical predictions of the viscosity coefficients found in the literature.

Effective potential theory for transport coefficients across coupling regimes.

A plasma transport theory that spans weak to strong coupling is developed from a binary collision picture, but where the interaction potential is taken to be an effective potential that includes correlation effects and screening self-consistently. This physically motivated approach provides a practical model for evaluating transport coefficients across coupling regimes. The theory is shown to compare well with classical molecular dynamics simulations of temperature relaxation in electron-ion plasmas as well as simulations and experiments of self-diffusion in one-component plasmas. The approach is versatile and can be applied to other transport coefficients as well.

Practical model for the self-diffusion coefficient in Yukawa one-component plasmas.

A practical physically motivated interpolation formula is presented for the self-diffusion coefficient in Yukawa one-component plasmas that is valid for a wide range of inverse screening lengths and over the entire fluid region.

Diffusion in ionic mixtures across coupling regimes.

Molecular dynamics simulations are used to investigate the diffusion properties of one-component plasmas and binary ionic mixtures from the weakly to the strongly coupled regimes. A physically motivated model for the diffusivities is proposed that reproduces the simulation data and gives insight into the nature of ionic motions and interactions in plasmas across the coupling regimes. The model extends the widely used Chapman-Spitzer theory from the weakly to the moderately coupled regime. In the strongly coupled regime, diffusion is modeled in terms of thermally activated jumps between equilibrium positions separated by an energy barrier. The basic ideas discussed are applicable to the study of other transport coefficients.

Comparative merits of the memory function and dynamic local-field correction of the classical one-component plasma.

The complementarity of the liquid and plasma descriptions of the classical one-component plasma is explored by studying wave number and frequency dependent dynamical quantities: the dynamical structure factor (DSF) and the dynamic local field correction (LFC). Accurate molecular dynamics (MD) simulations are used to validate and test models of the DSF and LFC. Our simulations, which span the entire fluid regime (Γ=0.1-175), show that the DSF is very well represented by a simple and well known memory function model of generalized hydrodynamics. On the other hand, the LFC, which we have computed using MD for the first time, is not well described by existing models.

Density fluctuations in the Yukawa one-component plasma: an accurate model for the dynamical structure factor.

Using numerical simulations, we investigate the equilibrium dynamics of a single-component fluid with Yukawa interaction potential. We show that, for a wide range of densities and temperatures, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. Since the Yukawa potential can describe the ion-ion interactions in a plasma, our results have significant applicability for both analyzing and interpreting the results of x-ray scattering data from high-power lasers and fourth-generation light sources.