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

Quynh L. D. Nguyen, Jacopo Simoni, Kevin M. Dorney, Xun Shi, Jennifer L. Ellis, Nathan J. Brooks, Daniel D. Hickstein, Amanda G. Grennell, Sadegh Yazdi, Eleanor E. B. Campbell, Liang Z. Tan, David Prendergast, Jerome Daligault, Henry C. Kapteyn, and Margaret M. Murnane

Phys. Rev. Lett. 131, 085101 – Published 21 August 2023

Abstract

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 $\sim 8 nm$ 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.

Received 20 December 2021
Revised 27 June 2022
Accepted 26 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.085101

Physics Subject Headings (PhySH)

High-energy-density plasmas

Warm-dense matter

First-principles calculations in plasma physics Molecular dynamics Optical plasma measurements Optical spectroscopy Photoionization

Plasma Physics

Authors & Affiliations

Quynh L. D. Nguyen ^1,*, Jacopo Simoni^2,8, Kevin M. Dorney ¹, Xun Shi¹, Jennifer L. Ellis¹, Nathan J. Brooks¹, Daniel D. Hickstein ³, Amanda G. Grennell⁴, Sadegh Yazdi ⁵, Eleanor E. B. Campbell ^6,7, Liang Z. Tan ⁸, David Prendergast ⁸, Jerome Daligault², Henry C. Kapteyn ^1,3, and Margaret M. Murnane¹

¹JILA, Department of Physics, University of Colorado and NIST, Boulder, Colorado 80309, USA
²Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
³Kapteyn-Murnane Laboratories Inc., 4775 Walnut St #102, Boulder, Colorado 80301, USA
⁴Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309 80309, USA
⁵Renewable and Sustainable Energy Institute, University of Colorado Boulder, Boulder, Colorado 80309, USA
⁶EaStCHEM, School of Chemistry, Edinburgh University, David Brewster Road, Edinburgh EH9 3FJ, United Kingdom
⁷Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
⁸Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*Quynh.L.Nguyen@colorado.edu Present address: Stanford PULSE Institute and Linac Coherent Light Source, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA.

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Issue

Vol. 131, Iss. 8 — 25 August 2023

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Images

Figure 1
Exciting and probing dynamics of warm dense Cu Nanoparticles (CuNPs). (a) After excitation by a 790-nm pulse, hot electrons thermalize on timescales $< 50 fs$ . This is followed by energy transfer from the electron bath to the lattice on timescales up to 2 ps [23, 24, 25]. The electron Fermi distribution (electron density ( $ρ$ ) versus energy (E)) is shown, where $E_{F}$ is the Fermi energy. (b) Experimental apparatus for in vacuo ultrafast photoelectron spectroscopy of CuNPs. A modified magnetron sputtering source produces monodisperse, highly pure CuNPs. Subsequently, they fly through a series of differential pumping stages and enter the interaction region where they interact with an infrared laser excitation pulse. A time-delayed blue probe pulse is then used to probe the hot electron distribution.
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Figure 2
Evolution of the hot electron temperature. (a) Photoelectron energy as a function of pump-probe delay for pump laser fluence of $120 mJ / {cm}^{2}$ . Dashed colored lines indicate the photoelectron spectra (PES) at different time delays. The horizontal dashed white lines indicate the energy range for the fitting. (b) PES at time delays that correspond to the colored-dashed lines in panel (a) on a semilog-scale. The solid black lines show numerical fits of the data to thermal distributions, which are used to extract the electron temperature at each time delay. (c) $T_{e}$ profiles as a function of time delay for pump fluences around $F_{melt} = 107 mJ / {cm}^{2}$ .
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Figure 3
Electron-ion (phonon) couplings in warm-dense CuNPs. (a) Simple-TTM (without pressure) fit applied to the $T_{e}$ profile at $120 mJ / {cm}^{2}$ to extract $G_{e i}$ . $T_{e}$ (red) and $T_{i}$ (green) are the fits obtained for the electron and ion temperature profiles, where the error bars for $T_{e}$ are in shaded blue. The magenta solid line indicates the melting temperature for CuNPs, $T_{m e l t} = 1100 K$ . The peak- $T_{e}$ (red circle) and equilibrium electron-ion temperature $T_{e - i}$ (green circle) are determined from the $T_{e}$ and $T_{i}$ fits. Note that the pump-probe delay time of 0 fs does not reflect the arrival time, which is closer to around $- 0.5$ ps. This was done for the purposes of the curve fitting. (b) The extracted peak- $T_{e}$ and $T_{e - i}$ are shown for $F = 80$ to $147 mJ / {cm}^{2}$ , where the lattice temperature exceeds $T_{m e l t}$ at $F_{m e l t} = 107 mJ / {cm}^{2}$ . The solid and WDM regimes are separated by a turquoise vertical line, where the blue region represents $T_{i} < T_{m e l t}$ and white region shows $T_{i} > T_{m e l t}$ . We use this same notation in panel (c). (c) $G_{e i}$ fitted from the simple-TTM and displayed as a function of the peak- $T_{e}$ corresponding to each fluence. Theoretical $G_{e i}$ are calculated using $Lin + Simoni$ (blue), and Simoni (green) models [42]. The measurements for flat-CuWDM (purple) [43] and solid Cu [44] (black) are included for comparison. (d) The obtained $G_{e i}$ from simple-TTM and measured phonon mode (1.9 THz) are implemented into the modified-TTM for the same data shown in panel (a). $T_{e}$ (red) and $T_{i}$ (green) profiles are predicted using the semi-empirical modified-TTM. The error bars in all panels indicate 95% confidence interval.
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Figure 4
Hot electron dynamics of CuNPs. Extracted temporal evolution of $T_{e}$ at pump fluences of (a) $94 mJ / {cm}^{2}$ (below $F_{m e l t}$ ) and (b) $120 mJ / {cm}^{2}$ (above $F_{m e l t}$ ) to compare the volume-surface effects for CuNPs crossing the phase transition temperature. The solid black lines represent a fit to the data convoluted with the IRF of $99 \pm 1 fs$ (see Supplemental Material, S12), and are used to determine $τ_{e i}$ . The magenta solid horizontal line indicates $T_{m e l t}$ for CuNPs. (c) Extracted $τ_{e i}$ for all pump fluences with error bars within 95% confidence intervals. The turquoise vertical line indicates $F_{m e l t}$ at $107 mJ / {cm}^{2}$ .
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Figure 5
Cu electronic pressure. The calculated electronic pressures for zero temperature solid FCC Cu (blue), liquid Cu at $T_{melt} = 1356 K$ (green) and 2000 K (red) at varying densities.
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Figure 6
Time- and temperature variation of the surface electron density for solid and liquid Cu NPs calculated using a slab model at (a) $0.2 T$ and (b) $0.34 T$ for solid, and at (c) 0.004 ps (zoom in (d)) for liquid Cu. $T$ is the period of the acoustic phonon mode at 1.9 THz. The variation in the electron density at different times is due to fluctuations in the atomic positions. In both systems, the magnitude of the charge density migrates further away from the surface at higher electronic temperatures. Particularly in liquid, at higher electronic temperatures it increases in magnitude.
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