[Paper Review] How long, and why, do Photoexcited Electrons in a Metal Remain Hot?

Richard B. Wilson, Sinisa Coh|arXiv (Cornell University)|Jun 27, 2019

Quantum and electron transport phenomena57 references4 citations

TL;DR

This paper reveals that electron-electron (e-e) interactions dominantly control the lifetime of hot electrons in metals, despite electron-phonon (e-p) interactions being the primary energy sink. Surprisingly, the occupation time of high-energy electron states depends only on e-e coupling strength, while energy relaxation rates are governed by the interplay of both e-e and e-p interactions—especially in metals with strong e-p coupling.

ABSTRACT

. Calculations are presented to show how dynamics of photoexcited electrons depend on electron-electron (e-e) and electron-phonon (e-p) interaction strengths. The observed dependence is universal to most metals, and is also somewhat counterintuitive. For example, the time that high energy electron states remain occupied depends only on the strength of e-e interactions, even if e-p interactions are much stronger. Furthermore, even though only e-p interactions can reduce the total energy stored by hot electrons, the time it takes for energy to leave the electronic subsystem is governed by both e-e and e-p interactions. Finally, the effect of e-e interactions on energy-relaxation is largest in metals where e-p interactions are strongest. We report simple expressions that accurately capture the interplay of e-e and e-p interactions on relaxation rates of the hot electron distribution. These findings are important for understanding ultrafast electron dynamics in a diverse range of fields, e.g. ultrafast magnetism, photocatalysis, plasmonics, and others.

Motivation & Objective

• To understand the relative roles of electron-electron (e-e) and electron-phonon (e-p) interactions in determining the relaxation dynamics of photoexcited electrons in metals.
• To resolve the counterintuitive observation that e-e interactions govern the lifetime of hot electron states even when e-p interactions are stronger.
• To derive universal expressions that accurately describe the interplay between e-e and e-p interactions in hot electron relaxation.
• To clarify why e-e interactions have the largest effect on energy relaxation in metals with the strongest e-p coupling.
• To provide a theoretical framework applicable to ultrafast processes in plasmonics, photocatalysis, and ultrafast magnetism.

Proposed method

• Using many-body perturbation theory to model electron dynamics following photoexcitation in metals.
• Calculating relaxation rates by incorporating both electron-electron and electron-phonon scattering processes.
• Deriving analytical expressions that capture the universal dependence of relaxation on e-e and e-p interaction strengths.
• Analyzing the time evolution of the electron distribution function under varying e-e and e-p coupling strengths.
• Demonstrating that the occupation time of high-energy states is independent of e-p coupling but dependent solely on e-e interactions.
• Quantifying how the energy relaxation time emerges from the combined influence of both e-e and e-p scattering mechanisms.

Experimental results

Research questions

• RQ1 Why does the lifetime of photoexcited electrons in high-energy states depend only on electron-electron interactions, even when electron-phonon interactions are stronger?
• RQ2 How do electron-electron and electron-phonon interactions jointly determine the energy relaxation time of the electronic subsystem?
• RQ3 What explains the counterintuitive result that electron-electron interactions have the strongest influence on energy relaxation in metals with the strongest electron-phonon coupling?
• RQ4 To what extent can the relaxation dynamics of hot electrons be universally described across different metals using a single framework?
• RQ5 What are the quantitative expressions that accurately model the interplay between e-e and e-p interactions in hot electron relaxation?

Key findings

• The time during which high-energy electron states remain occupied depends exclusively on the strength of electron-electron interactions, regardless of electron-phonon coupling strength.
• Although electron-phonon interactions are responsible for energy dissipation, the rate at which energy leaves the electronic subsystem is governed by both electron-electron and electron-phonon interactions.
• Electron-electron interactions exert the largest influence on energy relaxation in metals with the strongest electron-phonon coupling, contrary to intuitive expectations.
• The derived expressions accurately capture the interplay between e-e and e-p interactions across a wide range of metallic systems.
• The observed relaxation dynamics are universal across most metals, indicating a common underlying mechanism.
• The findings provide a unified theoretical description of hot electron relaxation that is relevant to applications in ultrafast magnetism, photocatalysis, and plasmonics.