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The immiscibility of hydrogen-helium mixture under the temperature and pressure conditions of planetary interiors is crucial for understanding the structures of gas giant planets (e.g., Jupiter and Saturn). While the experimental probe at such extreme conditions is challenging, theoretical simulation is heavily relied in an effort to unravel the mixing behavior of hydrogen and helium. Here we develop a method via a machine learning accelerated molecular dynamics simulation to quantify the physical separation of hydrogen and helium under the conditions of planetary interiors. The immiscibility line achieved with the developed method yields substantially higher demixing temperatures at pressure above 1.5 Mbar than earlier theoretical data, but matches better to the experimental estimate. Our results suggest a possibility that H-He demixing takes place in a large fraction of the interior radii of Jupiter and Saturn, i.e., 27.5% in Jupiter and 48.3% in Saturn. This indication of an H-He immiscible layer hints at the formation of helium rain and offers a potential explanation for the decrease of helium in the atmospheres of Jupiter and Saturn., Comment: 3 figures, accepted in Nature Communications

Superionic ices with highly mobile protons within the stable oxygen sub-lattice occupy an important proportion of the phase diagram of ice and widely exist in the interior of icy giants and throughout the universe. Understanding the thermal transport in superionic ice is vital for the thermal evolution of icy planets. However, it is highly challenging due to the extreme thermodynamic conditions and dynamical nature of protons, beyond the capability of the traditional lattice dynamics and empirical potential molecular dynamics approaches. In this work, by utilizing the deep potential molecular dynamics approach, we investigate the thermal conductivity of ice-VII and superionic ice-VII" along the isobar of $p = 30\ \rm{GPa}$. A non-monotonic trend of thermal conductivity with elevated temperature is observed. Through heat flux decomposition and trajectory-based spectra analysis, we show that the thermally-activated proton diffusion in ice-VII and superionic ice-VII" contribute significantly to heat convection, while the broadening in vibrational energy peaks and significant softening of transverse acoustic branches lead to a reduction in heat conduction. The competition between proton diffusion and phonon scattering results in anomalous thermal transport across the superionic transition in ice. This work unravels the important role of proton diffusion in the thermal transport of high-pressure ice. Our approach provides new insights into modeling the thermal transport and atomistic dynamics in superionic materials., Comment: 5 figures

The coupling of excited states and ionic dynamics is the basic and challenging point for the materials response at extreme conditions. In laboratory, the intense laser produces transient nature and complexity with highly nonequilibrium states, making it extremely difficult and interesting for both experimental measurements and theoretical methods. With the inclusion of laser-excited states, we extended ab initio method into the direct simulations of whole laser-driven microscopic dynamics from solid to liquid. We constructed the framework of combining the electron-temperaturedependent deep neural network potential energy surface with hybrid atomistic-continuum approach, controlling non-adiabatic energy exchange and atomistic dynamics, which enables consistent interpretation of experimental data. By large scale ab inito simulations, we demonstrate that the nonthermal effects introduced by hot electrons play a dominant role in modulating the lattice dynamics, thermodynamic pathway, and structural transformation. We highlight that the present work provides a path to realistic computational studies of laser-driven processes, thus bridging the gap between experiments and simulations., Comment: 4 figures

The accumulation and circulation of carbon-hydrogen dictate the chemical evolution of ice giant planets. Species separation and diamond precipitation have been reported in carbon-hydrogen systems, verified by static and shock-compression experiments. Nevertheless, the dynamic formation processes for the above-mentioned phenomena are still insufficiently understood. Here, combing deep learning model, we demonstrate that diamonds form through a three-step process involving decomposition, species separation and nucleation procedures. Under shock condition of 125 GPa and 4590 K, hydrocarbons are decomposed to give hydrogen and low-molecular-weight alkanes (CH4 and C2H6), which escape from the carbon chains resulting in C/H species separation. The remaining carbon atoms without C-H bonds accumulate and nucleate to form diamond crystals. The process of diamond growth is found to associated with a critical nucleus size where dynamic energy barrier plays a key role. These dynamic processes for diamonds formation are insightful in establishing the model for ice giant planet evolution., Comment: 5 figures

Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model the dramatic change of both electronic structures and ion dynamics during such dynamic processes, the traditional method faces difficulties. Here, we demonstrate the ability of deep neural network (DNN) to capture the atomic local-environment dependence of electronic density of states (DOS) for both multicomponent system under exoplanet thermodynamic condition and nonequilibrium system during super-heated melting process. Large scale and time-resolved diagnosis of DOS can be efficiently achieved within the accuracy of ab initio method. Moreover, the atomic contribution to DOS given by DNN model accurately reveals the information of local neighborhood for selected atom, thus can serve as robust order parameters to identify different phases and intermediate local structures, strongly highlights the efficacy of this DNN model in studying dynamic processes., Comment: 7 Figures, accepted by PRB

We present a finite-temperature density functional theory investigation of the nonequilibrium transient electronic structure of warm dense Li, Al, Cu, and Au created by laser excitation. Photons excite electrons either from the inner shell orbitals or from the valence bands according to the photon energy, and give rise to isochoric heating of the sample. Localized states related to the 3d orbital are observed for Cu when the hole lies in the inner shell 3s orbital. The electrical conductivity for these materials at nonequilibrium states is calculated using the Kubo-Greenwood formula. The change of the electrical conductivity, compared to the equilibrium state, is different for the case of holes in inner shell orbitals or the valence band. This is attributed to the competition of two factors: the shift of the orbital energies due to reduced screening of core electrons, and the increase of chemical potential due to the excitation of electrons. The finite temperature effect of both the electrons and the ions on the electrical conductivity is discussed in detail. This work is helpful to better understand the physics of laser excitation experiments of warm dense matter., Comment: 111 pages, 9 figures

The dynamic electron-ion collisions play an important rolein determining the static and transport properties of warmdense matter (WDM). Electron force field (eFF) method is applied to study the ionic transport properties of warm densehydrogen. Compared with the results from quantum moleculardynamics and orbital-free molecular dynamics, the ionicdiffusions are largely reduced by involving the dynamic collisions of electrons and ions. This physics is verified by quantum Langevin molecular dynamics (QLMD) simulations, which includes electron-ion collisions induced friction(EI-CIF) into the dynamic equation of ions. Based on these new results, we proposed a model including the correctionof collisions induced friction of the ionic diffusion. The CIF model has been verified to be valid at a wide range ofdensity and temperature. We also compare the results with the Yukawa one component plasma (YOCP) model andEffective OCP (EOCP) model. We proposed to calculate the self-diffusion coefficients using the EOCP model modifiedby the CIF model to introduce the dynamic electron-ion collisions effect., Comment: accepted by POP

A detailed understanding of the material response to rapid compression is challenging and demanding. For instance, the element gold under dynamic compression exhibits complex phase transformations where there exist some large discrepancies between experimental and theoretical studies. Here, we combined large-scale molecular dynamics simulations with a deep potential to elucidate the dynamic compression processes of gold from an atomic level. The potential is constructed by accurately reproducing the free energy surfaces of density-functional-theory calculations for gold, from ambient conditions to 15 500 K and 500 GPa. Within this framework, we extend the simulations up to 200 000 atoms size, and found a much lower pressure threshold for phase transitioning from face-centered cubic (FCC) to body-centered (BCC), as compared to previous calculations. Furthermore, the transition pressure is strongly dependent on the shock direction, namely 159 GPa for (100) orientation and 219 GPa for (110) orientation, respectively. Most importantly, the accurate atomistic perspective presents that the shocked BCC structure contains unique features of medium-range and short-range orders, which is named disorders here. We propose a model and demonstrate that the existence of disorders significantly reduces the Gibbs free energies of shocked structures, therefore leading to the lowering of the phase transition pressure. The present study provides a new path to understand the structure dynamics under extreme conditions., Comment: 6 pages, 3 figures

For a long time, there have been huge discrepancies between different models and experiments concerning the liquid-liquid phase transition (LLPT) in dense hydrogen. In this work, we present the results of extensive calculations of the LLPT in dense hydrogen using the most expensive first-principle path-integral molecular dynamics simulations available. The nonlocal density functional rVV10 and hybrid functional PBE0 are used to improve the description of the electronic structure of hydrogen. Of all the density functional theory calculations available, we report the most consistent results through quantum Monte Carlo simulations and coupled electron-ion Monte Carlo simulations of the LLPT in dense hydrogen. The critical point of the first-order LLPT is estimated above 2000 K according to the equation of state. Moreover, the metallization pressure obtained from the jump of dc electrical conductivity almost coincides with the plateau of equation of state.

Transport properties of dense liquid helium under the conditions of planet's core and cool atmosphere of white dwarfs have been investigated by using the improved centroid path-integral simulations combined with density functional theory. The self-diffusion is largely higher and the shear viscosity is notably lower predicted with the quantum mechanical description of the nuclear motion compared with the description by Newton equation. The results show that nuclear quantum effects (NQEs), which depends on the temperature and density of the matter via the thermal de Broglie wavelength and the ionization of electrons, are essential for the transport properties of dense liquid helium at certain astrophysical conditions. The Stokes-Einstein relation between diffusion and viscosity in strongly coupled regime is also examined to display the influences of NQEs., Comment: 6 figures

Nuclear quantum effects (NQEs) on the structures and transport properties of dense liquid hydrogen at densities of 10-100 g/cm3 and temperatures of 0.1-1 eV are fully assessed using \textit{ab initio} path-integral molecular dynamics simulations. With the inclusion of NQEs, ionic diffusions are strongly enhanced by the magnitude from 100% to 15% with increasing temperature, while electrical conductivities are significantly suppressed. The analyses of ionic structures and zero-point energy show also the importance of NQEs in these regime. The significant quantum delocalization of ions introduces expressively different scattering cross section between protons compared with classical particle treatments, which can explain the large alterability of transport behaviors. Furthermore, the energy, pressure, and isotope effects are also greatly influenced by NQEs. The complex behaviors show that NQEs can not be neglected for dense hydrogen even in the warm dense regime., Comment: 5 pages, 4 figures

Fe exists abundantly in the universe. In particular, the dynamical structures and transport properties of warm dense Fe are crucial for understanding the evolution and structures of giant planets. In this article, we present the ionic structures, equation of states, diffusion and viscosity of Fe at two typical densities of 33.385 g/cm$^3$ and 45 g/cm$^3$ in the temperature range of 1 eV and 10 eV, giving the data by the first principles calculations using quantum Langevin molecular dynamics (QLMD). Furthermore, the validation of Stokes-Einstein (SE) relation in this regime is discussed, showing the importance of choosing the effective atomic diameter. The results remind us of the careful usage of the SE relation under extreme conditions., Comment: to be published in New Journal of Physics

The complex structures of warm and hot dense matter are essential to understand the behaviors of materials in high energy density physics processes and provide new features of matter constitutions. Here, along a new unified first-principle determined Hugoniot curve of iron from normal condensed condition up to 1 Gbar, the novel structures characterized by the ionic clusters and separated "electron bubbles" are revolutionarily unraveled using newly developed quantum Langevin molecular dynamics (QLMD). Subsistence of complex clusters, with bonds formed by inner shell electrons of neighbor ions, can persist in the time length of 50 femto-seconds dynamically with quantum flowing bubbles, which are produced by the interplay of Fermi electron degeneracy, the ionic coupling and the dynamical nature. With the inclusion of those complicated features in QLMD, the present data could serve as a first-principle benchmark in a wide range of temperatures and densities., Comment: 5 pages, 4 figures