Warm Dense Matter Conditions Research Articles

Ultrafast Heating-Induced Suppression of d-Band Dominance in the Electronic Excitation Spectrum of Cuprum.

The combination of isochoric heating of solids by free-electron lasers (FELs) and in situ diagnostics by X-ray Thomson scattering (XRTS) allows for measurements of material properties at warm dense matter (WDM) conditions relevant for astrophysics, inertial confinement fusion, and materials science. In the case of metals, the FEL beam pumps energy directly into electrons with the lattice structure of ions being nearly unaffected. This leads to a unique transient state that gives rise to a set of interesting physical effects, which can serve as a reliable testing platform for WDM theories. In this work, we present extensive linear-response time-dependent density functional theory (TDDFT) results for the electronic dynamic structure factor of isochorically heated copper with a face-centered cubic lattice. At ambient conditions, the plasmon is heavily damped due to the presence of d-band excitations, and its position is independent of the wavenumber. In contrast, the plasmon feature starts to dominate the excitation spectrum and has a Bohm-Gross-type plasmon dispersion for temperatures T ≥ 4 eV, where the quasi-free electrons in the interstitial region are in the WDM regime. In addition, we analyze the thermal changes in the d-band excitations and outline the possibility to use future XRTS measurements of isochorically heated copper as a controlled testbed for WDM theories.

DC electrical conductivity measurements of warm dense matter using ultrafast THz radiation

We describe measurements of the DC electrical conductivity of warm dense matter using ultrafast terahertz (THz) pulses. THz fields are sufficiently slowly varying that they behave like DC fields on the timescale of electron–electron and electron–ion interactions and hence probe DC-like responses. Using a novel single-shot electro-optic sampling technique, the electrical conductivity of the laser-generated warm dense matter was determined with <1 ps temporal resolution. We present the details of the single-shot THz detection methodology as well as considerations for warm dense matter experiments. We, then, provide proof-of-concept studies on aluminum driven to the warm dense matter regime through isochoric heating and shock compression. Our results indicate a decrease in the conductivity when driven to warm dense matter conditions and provide a platform for future warm dense matter studies.

Electronic density response of warm dense hydrogen on the nanoscale.

The properties of hydrogen at warm dense matter (WDM) conditions are of high importance for the understanding of astrophysical objects and technological applications such as inertial confinement fusion. In this work, we present extensive ab initio path integral Monte Carlo results for the electronic properties in the Coulomb potential of a fixed ionic configuration. This gives us unique insights into the complex interplay between the electronic localization around the protons with their density response to an external harmonic perturbation. We find qualitative agreement between our simulation data and a heuristic model based on the assumption of a local uniform electron gas model, but important trends are not captured by this simplification. In addition to being interesting in their own right, we are convinced that our results will be of high value for future projects, such as the rigorous benchmarking of approximate theories for the simulation of WDM, most notably density functional theory.

Generalized chemical model for plasmas with application to the ionization potential depression

On the basis of the generalized Poisson–Boltzmann equation derived from the Bogolyubov chain of equations for the equilibrium distribution functions in the pair correlation approximation, a general expression is proposed for the Helmholtz free energy of a system that contains any number of components and whose particles interact via arbitrary potentials. This opens up an extraordinary opportunity to simultaneously treat a whole range of physical effects including partial ionization, quantum effects of diffraction and electron degeneracy, short- and long-range interactions of charged particles with neutrals, finite size effects, etc. It is shown that all medium constituents are tied together in a single screening matrix, whose determinant and trace determine the excess contribution to the free energy. The approach developed is then applied to the problem of the ionization potential depression (IPD) leading to quite simple analytical expressions, which turn out to be useful for various practical purposes. In particular, for a single ionization from the neutral state the IPD is shown to significantly depend on the ionization degree such that it consists of the difference of charged and neutral contributions for a fully ionized plasma and turns non-zero for an almost neutral medium. On the other hand, for a multiple ionization process finite size effects of atoms and ions are demonstrated to be of great importance and accounted for in order to achieve good agreement with experimental data on the IPD under warm dense matter conditions.

Toward using collective x-ray Thomson scattering to study C–H demixing and hydrogen metallization in warm dense matter conditions

The insulator–metal transition in liquid hydrogen is an important phenomenon to understand the interiors of gas giants, such as Jupiter and Saturn, as well as the physical and chemical behavior of materials at high pressures and temperatures. Here, the path toward an experimental approach is detailed based on spectrally resolved x-ray scattering, tailored to observe and characterize hydrogen metallization in dynamically compressed hydrocarbons in the regime of carbon–hydrogen phase separation. With the help of time-dependent density functional theory calculations and scattering spectra from undriven carbon samples collected at the European x-ray Free-Electron Laser Facility (EuXFEL), we demonstrate sufficient data quality for observing C–H demixing and investigating the presence of liquid metallic hydrogen in future experiments using the reprated drive laser systems at EuXFEL.

The Influence of the Effects of the Bound Electrons on the Ion Structural and Thermodynamic Properties

In this article, a strongly coupled one-component plasma (OCP), where ions interact with a background of weakly coupled electrons, is considered. The thermodynamic properties of this plasma were studied on the basis of three types of interaction potentials. The first potential with ionic core obtained from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ab initio$ </tex-math></inline-formula> simulations takes into account the effects of the bound electrons, the second is the well-known Yukawa potential, and the third is the effective potential derived by the method of dielectric response function taking into account electron screening and quantum-mechanical diffraction effect of electrons. The radial distribution functions (RDFs) were calculated for the first potential using molecular dynamics (MD) simulations and were additionally compared with the RDFs obtained for all three potentials by solving the integral Ornstein–Zernike equation in the hypernetted chain (HNC) approximation and show that the use of the effective potential is not applicable at warm dense matter (WDM) conditions, when the ion core is significant.

Metallic water: Transient state under ultrafast electronic excitation.

The modern means of controlled irradiation by femtosecond lasers or swift heavy ion beams can transiently produce such energy densities in samples that reach collective electronic excitation levels of the warm dense matter state, where the potential energy of interaction of the particles is comparable to their kinetic energies (temperatures of a few eV). Such massive electronic excitation severely alters the interatomic potentials, producing unusual nonequilibrium states of matter and different chemistry. We employ density functional theory and tight binding molecular dynamics formalisms to study the response of bulk water to ultrafast excitation of its electrons. After a certain threshold electronic temperature, the water becomes electronically conducting via the collapse of its bandgap. At high doses, it is accompanied by nonthermal acceleration of ions to a temperature of a few thousand Kelvins within sub-100fs timescales. We identify the interplay of this nonthermal mechanism with the electron-ion coupling, enhancing the electron-to-ions energy transfer. Various chemically active fragments are formed from the disintegrating water molecules, depending on the deposited dose.

Ab Initio Static Exchange-Correlation Kernel across Jacob's Ladder without Functional Derivatives.

The electronic exchange─correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an external perturbation. In this work, we present a formally exact methodology for the computation of the system specific static XC kernel exclusively within the framework of density functional theory (DFT) and without employing functional derivatives─no external input apart from the usual XC-functional is required. We compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model under both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC functionals, and it has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects. The observed excellent agreement to the QMC reference data demonstrates that presented framework is capable to capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers.

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics.

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equationof state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions.

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [Böhme et al., Phys. Rev. Lett. 129, 066402 (2022)0031-900710.1103/PhysRevLett.129.066402]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair potential. We find very favorable convergence behavior towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are afflicted with the notorious fermion sign problem, which we analyze in detail. While computationally demanding, our results constitute an exact benchmark for other methods and approximations within DFT. Our setup gives us the unique capability to study important properties of warm dense hydrogen such as the electronic static density response and exchange-correlation kernel without any model assumptions, which will be very valuable for a variety of applications such as the interpretation of experiments and the development of new XC functionals.

Spin-resolved density response of the warm dense electron gas

We present extensive ab initio path integral Monte Carlo (PIMC) results for the spin-resolved density response of the uniform electron gas at warm dense matter conditions. This allows us to unambiguously assess the accuracy of previous theoretical approximations, thereby providing valuable insights for the future development of dielectric schemes. From a physical perspective, we observe a nontrivial manifestation of an effective electron-electron attraction that emerges in the spin-offdiagonal static density response function at strong coupling, ${r}_{s}\ensuremath{\gtrsim}5$. All PIMC results are freely available online and can be used to benchmark approximations and simulation schemes.

Calculations on the stopping power of the warm dense matter at the Bragg peak

This work aims to be useful for future experiments providing hydrodynamic and stopping power calculations to warm dense matter (WDM) analysis. For this purpose, the hydrodynamic simulations have been carried out using MULTI-fs code. Key plasma parameters - e.g., electron temperature, mass density, ionization, etc- have been studied at different expansion times to show the WDM behavior. Thanks to these data from the hydrodynamic simulations, precise stopping power calculations can be performed. A comparison is made between our present stopping power model with other models in the literature at the Bragg peak. Specifically, proton energy loss is estimated in carbon at a WDM state described by the hydrodynamic simulations. As the Bragg peak is the energy range where most differences arise between theoretical stopping power models, an experiment of the characteristics here described could be useful to differentiate between these models and to test their validity in the WDM regime.

Superionic states formation in group III oxides irradiated with ultrafast lasers

After ultrafast laser irradiation, a target enters a poorly explored regime where physics of a solid state overlaps with plasma physics and chemistry, creating an unusual synergy—a warm dense matter state (WDM). We study theoretically the WDM kinetics and chemistry in a number of group III-metal oxides with highly excited electronic system. We employ density functional theory to investigate a possibility of nonthermal transition of the materials into a superionic state under these conditions. Atomic and electronic properties of the materials are analyzed during the transitions to acquire insights into physical mechanisms guiding such transformations.

Nonlinear interaction of external perturbations in warm dense matter

AbstractWe present extensive new ab initio path integral Monte Carlo (PIMC) results for an electron gas at warm dense matter conditions that is subject to multiple harmonic perturbations. In addition to the previously investigated nonlinear effects at the original wave number (Dornheim et al., Phys. Rev. Lett., 2020, 125, 085001) and the excitation of higher harmonics (Dornheim et al., Phys. Rev. Res., 2021, 3, 033231), the presence of multiple external potentials leads to mode‐coupling effects, which constitute the dominant nonlinear effect and lead to a substantially more complicated density response compared to linear response theory. One possibility to estimate mode‐coupling effects from a PIMC simulation of the unperturbed system is given in terms of generalized imaginary‐time correlation functions that have been recently introduced by Dornheim et al. (J. Chem. Phys., 2021, 155, 054110). In addition, we extend our previous analytical theory of the nonlinear density response of the electron gas in terms of the static local field correction (Dornheim et al., 2020, Phys. Rev. Lett., 125, 235001), which allows for a highly accurate description of the PIMC results with negligible computational cost.

Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter

In a recent letter [Phys. Rev. Lett. 125, 085001 (2020)], Dornheim et al. have presented the first ab initio path integral Monte Carlo (PIMC) results for the nonlinear electronic density response at warm dense matter (WDM) conditions. In the present work, we extend these considerations by exploring the relation between the nonlinear response and three-/four-body correlation functions from many-body theory. In particular, this connection directly implies a comparably increased sensitivity of the nonlinear response to electronic exchange–correlation (XC) effects, which is indeed confirmed by our analysis over the entire relevant range of densities (\(r_{s} = 0.5, \ldots ,10\)) and temperatures (\(\theta = 0.01, \ldots ,4\)). Finally, our work suggests the possibility of deliberately probing the nonlinear regime to experimentally probe three- and potentially even four-body correlation functions in WDM.

Nonlinear electronic density response of the ferromagnetic uniform electron gas at warm dense matter conditions

AbstractIn a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 125, 085001 (2020)], we have presented the first ab initio results for the nonlinear density response of electrons in the warm dense matter (WDM) regime. In the present work, we extend these efforts by carrying out extensive new path integral Monte Carlo simulations of a ferromagnetic electron gas that is subject to an external harmonic perturbation. This allows us to unambiguously quantify the impact of spin‐effects on the nonlinear density response of the warm dense electron gas. In addition to their utility for the description of WDM in an external magnetic field, our results further advance our current understanding of the uniform electron gas as a fundamental model system, which is important in its own right.

Ultrafast visualization of phase transitions in nonequilibrium warm dense matter

Intense ultrafast laser excitation brings materials into highly nonequilibrium states with complex solid–liquid phase transitions. These ultrafast processes yield warm dense matter (WDM) conditions characterized by comparable thermal and Fermi energies, and strong ion–ion coupling. Here, we review recent studies employing mega-electron-volt ultrafast electron diffraction to resolve the structural dynamics of nonequilibrium WDM created by femtosecond laser heating of solids. For the study of warm dense gold, the results showed homogeneous melting that occurs within tens of picoseconds at absorbed energy densities of 0.4–1.4 MJ/kg. These results constrained the electron–ion coupling rate and revealed the melting sensitivity to nucleation seeds. For the study of radiation-damaged tungsten, the results showed a melting transition below the melting temperature. Molecular dynamics simulations suggested that this melting behavior is driven by vacancy defect clusters from radiation damage. These studies provided atomic-level insights into the melting behavior of materials under extreme conditions.

Demonstration of an x-ray Raman spectroscopy setup to study warm dense carbon at the high energy density instrument of European XFEL

We present a proof-of-principle study demonstrating x-ray Raman Spectroscopy (XRS) from carbon samples at ambient conditions in conjunction with other common diagnostics to study warm dense matter, performed at the high energy density scientific instrument of the European x-ray Free Electron Laser (European XFEL). We obtain sufficient spectral resolution to identify the local structure and chemical bonding of diamond and graphite samples, using highly annealed pyrolytic graphite spectrometers. Due to the high crystal reflectivity and XFEL brightness, we obtain signal strengths that will enable accurate XRS measurements in upcoming pump–probe experiments with a high repetition-rate, where the samples will be pumped with high-power lasers. Molecular dynamics simulations based on density functional theory together with XRS simulations demonstrate the potential of this technique and show predictions for high-energy-density conditions. Our setup allows simultaneous implementation of several different diagnostic methods to reduce ambiguities in the analysis of the experimental results, which, for warm dense matter, often relies on simplifying model assumptions. The promising capabilities demonstrated here provide unprecedented insights into chemical and structural dynamics in warm dense matter states of light elements, including conditions similar to the interiors of planets, low-mass stars, and other celestial bodies.

Molecular dynamics investigation of the stopping power of warm dense hydrogen for electrons.

A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400-10000eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.

Real-space Green’s functions for warm dense matter

Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting applications from astrophysics to fusion energy research. Here we explore the real-space Green’s function method as a technique for solving the Kohn–Sham density functional theory equations under warm dense matter conditions. We find the method to be tractable and accurate throughout the density and temperature range of interest, in contrast to other approaches. Good agreement on equation of state is found when comparing to other methods, where they are thought to be accurate.