Theory of electronic relaxation in a metal excited by an ultrashort optical pump

Баранов, В. В.; Kabanov, V. V.

doi:10.1103/physrevb.89.125102

Cited by 56 publications

(60 citation statements)

References 33 publications

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“…On the other hand, Eq. (40) shows that the transition probability is maximal for δE K,q = 0. Both conditions can be fulfilled simultaneously only in the adiabatic limit ω 0 t 0 .…”

Section: Relaxation In the Weak-coupling Regimementioning

confidence: 95%

“…(Note that exact solutions can be obtained in the 1D adiabatic regime and for the linear electronic dispersion [36,37].) Several techniques are also now available to study manyelectron systems beyond the mean-field [38] and Boltzmann approaches [39,40]. For example, the dynamics of electrons coupled to phonons has been studied within the Holstein model using dynamical mean-field theory (DMFT) [41], continuous-time quantum Monte Carlo [42], and Keldysh Green functions within the Migdal approximation [43,44].…”

Section: Introductionmentioning

confidence: 98%

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Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

et al. 2015

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We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the nonequilibrium dynamics in an interacting many-body system where excess energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the nonequilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block-decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines the so-called optimal phonon modes. We discuss their structure in nonequilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.

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“…On the other hand, Eq. (40) shows that the transition probability is maximal for δE K,q = 0. Both conditions can be fulfilled simultaneously only in the adiabatic limit ω 0 t 0 .…”

Section: Relaxation In the Weak-coupling Regimementioning

confidence: 95%

Section: Introductionmentioning

confidence: 98%

Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

et al. 2015

View full text Add to dashboard Cite

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“…This conclusion is based solely on the observation that δR(t) is proportional to δγ ∞ (t)-that is, to the total energy stored in the boson bath-and does not necessarily require an effective thermalization of the charge carriers through direct carrier-carrier collisions 18 . Considering that the elementary time (h/t h ∼ 2 fs) associated with the Cu-O-Cu hole-hopping process inevitably leads to the creation of local AF excitations, AF fluctuations are a candidate as the dominant mediators of the hole interactions on this ultrafast timescale.…”

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confidence: 99%

Snapshots of the retarded interaction of charge carriers with ultrafast fluctuations in cuprates

Conte

Vidmar

Golež

et al. 2014

19th International Conference on Ultrafast Phenomena

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One of the pivotal questions in the physics of high-temperature superconductors is whether the low-energy dynamics of the charge carriers is mediated by bosons with a characteristic timescale. This issue has remained elusive as electronic correlations are expected to greatly accelerate the electron-boson scattering processes, confining them to the very femtosecond timescale that is hard to access even with state-of-the-art ultrafast techniques. Here we simultaneously push the time resolution and frequency range of transient reflectivity measurements up to an unprecedented level, enabling us to directly observe the ∼16 fs build-up of the e ective electron-boson interaction in hole-doped copper oxides. This extremely fast timescale is in agreement with numerical calculations based on the t-J model and the repulsive Hubbard model, in which the relaxation of the photo-excited charges is achieved via inelastic scattering with short-range antiferromagnetic excitations.A fter almost 30 years of intensive experimental and theoretical efforts to understand the origin of high-temperature superconductivity in copper oxides, a consensus about the microscopic process responsible for the superconducting pairing is still lacking. The large Coulomb repulsion U 1 eV between two electrons occupying the same lattice site is believed to have fundamental consequences for the normal state of these systems 1 , and it is not clear whether a BCS-like bosonic glue that mediates the electron interactions and eventually leads to pairing can still be defined [2][3][4] . The fundamental issue can be reduced to the question whether the electronic interactions are essentially unmediated and instantaneous, or whether the low-energy physics, including superconductivity, can be effectively described in terms of interactions among the fermionic charge carriers mediated by the exchange of bosons. The problem can be rationalized by considering the Hubbard model, in which the instantaneous virtual hopping of holes into already occupied sites (with an energy cost of U ) inherently favours an antiferromagnetic (AF) coupling J = 4t 2 h /U between neighbouring sites, where t h is the nearestneighbour hopping energy. As a consequence, antiferromagnetic fluctuations with a high-energy cutoff of 2J U naturally emerge as a candidate 5 for mediating the low-energy electronic interactions, on a characteristic retarded timescale of the order ofh/2J .In principle, time-resolved optical spectroscopy 6 may be used to prove the existence of an effective retarded boson-mediated interaction, provided that the temporal resolution is of the order of the inverse bosonic-fluctuation scale (for example,h/2J for AF fluctuations) and the optical properties are probed over a sufficiently broad frequency range, to extract the dynamics of the electron-boson coupling. Recent advances in ultrafast optical spectroscopy have succeeded in separately fulfilling these requirements. For example, high-temporal-resolution (<15 fs) experiments 7,8 have been carried out to investigate the...

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“…This process is very efficient in metals, since, in contrast to semiconductors, there is no energy gap preventing the generation of secondary particles. These effects are included in the the scattering-in term ( ) G nk in ee of equation (5). Although this term can be obtained from the master equation [39] as well, we choose for computational convenience a simpler treatment in our present study.…”

Section: Relaxation Due To E-e Scatteringmentioning

confidence: 99%

“…In this prevailing view, the role of e-ph interactions already in the early stages of relaxation is usually ignored. However, this simple picture is questioned by studies, both experimental and theoretical [4,5], suggesting overlapping timescales of e-e and e-ph-driven thermalization. Moreover, there is little knowledge how the electrons far above the Fermi level (several tenth of eV) interact with the phonons.…”

Section: Introductionmentioning

confidence: 99%

Relaxation of electrons in quantum-confined states in Pb/Si(111) thin films from master equation with first-principles-derived rates

Kratzer

Zahedifar

2019

New J. Phys.

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Atomically thin films of Pb on Si(111) provide an experimentally tunable system comprising a highly structured electronic density of states. The lifetime of excited electrons in these states is limited by both electron-electron (e-e) and electron-phonon (e-ph) scattering. We employ the description by a master equation for the electronic occupation numbers to analyze the relative importance of both scattering mechanisms. The electronic and phononic band structures, as well as the matrix elements for electron-phonon coupling within deformation potential theory were obtained from density functional calculations, thus taking into account quantum confinement effects. For the relaxation dynamics, the contribution of impact ionization processes to the lifetime is estimated from the imaginary part of the electronic self-energy calculated in the GW approximation. By numerically solving rate equations for the occupations of the Pb-derived electronic states coupled to a phononic heat bath, we are able to follow the distribution of the electronic excitation energy to the various modes of Pb lattice vibrations. While e-e scattering is the dominant relaxation mechanism, we demonstrate that the e-ph scattering is highly phonon-mode-specific, with a large contribution from surface phonons. At electron energies of about 0.3 eV above the Fermi surface, a 'phonon bottleneck' characteristic of relaxation in nanostructures with well-separated electronic states is observed. The time scales extracted from the simulations are compared to data from pump-probe experiments using time-resolved two-photon photoemission.

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Theory of electronic relaxation in a metal excited by an ultrashort optical pump

Cited by 56 publications

References 33 publications

Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

Snapshots of the retarded interaction of charge carriers with ultrafast fluctuations in cuprates

Relaxation of electrons in quantum-confined states in Pb/Si(111) thin films from master equation with first-principles-derived rates

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