Electron-Phonon Coupling and Energy Flow in a Simple Metal beyond the Two-Temperature Approximation

Lutz Waldecker,Roman Bertoni,Jan Vorberger,Ralph Ernstorfer

doi:10.1103/physrevx.6.021003

Lutz Waldecker, Roman Bertoni + Show 2 more

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https://doi.org/10.1103/physrevx.6.021003

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Abstract

The electron-phonon coupling and the corresponding energy exchange was investigated experimentally and by ab initio theory in non-equilibrium states of the free-electron metal aluminium. The temporal evolution of the atomic mean squared displacement in laser-excited thin free-standing films was monitored by femtosecond electron diffraction. The electron-phonon coupling strength was obtained for a range of electronic and lattice temperatures from density functional theory molecular dynamics (DFT-MD) simulations. The electron-phonon coupling parameter extracted from the experimental data in the framework of a two-temperature model (TTM) deviates significantly from the ab initio values. We introduce a non-thermal lattice model (NLM) for describing non-thermal phonon distributions as a sum of thermal distributions of the three phonon branches. The contributions of individual phonon branches to the electron-phonon coupling are considered independently and found to be dominated by longitudinal acoustic phonons. Using all material parameters from first-principle calculations besides the phonon-phonon coupling strength, the prediction of the energy transfer from electrons to phonons by the NLM is in excellent agreement with time-resolved diffraction data. Our results suggest that the TTM is insufficient for describing the microscopic energy flow even for simple metals like aluminium and that the determination of the electron-phonon coupling constant from time-resolved experiments by means of the TTM leads to incorrect values. In contrast, the NLM describing transient phonon populations by three parameters appears to be a sufficient model for quantitatively describing electron-lattice equilibration in aluminium. We discuss the general applicability of the NLM and provide a criterion for the suitability of the two-temperature approximation for other metals.

Highlights

The interaction between electrons and lattice vibrations is central to both ground state as well as out-of-equilibrium properties of solids
We report a combined experimental and theoretical study of the energy transfer from photoexcited electrons to the lattice in the quasi-free-electron metal aluminium by femtosecond electron diffraction and density functional theory (DFT)
V, we introduce a nonthermal lattice model (NLM) allowing for an approximate description of nonequilibrium phonon distributions

Summary

INTRODUCTION

The interaction between electrons and lattice vibrations is central to both ground state as well as out-of-equilibrium properties of solids. For the case of metals, Anisimov et al introduced an empirical two-temperature model (TTM) describing the energy transfer from the excited electrons to the lattice with a single electron-phonon coupling parameter [3,4]. The coupling of electrons to phonons is given by the Eliashberg function and is strongest for the high-energy phonons, whose occupation is the lowest in a thermal state This implies that energy transfer between electrons and lattice in nonequilibrium states leads to transient nonthermal phonon distributions. V, we introduce a nonthermal lattice model (NLM) allowing for an approximate description of nonequilibrium phonon distributions The predictions of this model are compared to the experimentally observed atomic mean-squared displacements (MSD) and a quantitative agreement of DFT calculations and measurements is found

EXPERIMENTAL METHODS

THEORY

TWO-TEMPERATURE MODEL

NONTHERMAL LATTICE MODEL

Findings

DISCUSSION AND CONCLUSION