Intraband memory function and memory-function conductivity formula in doped graphene

Kupčić, Ivan

doi:10.1103/physrevb.95.035403

Cited by 9 publications

(3 citation statements)

References 37 publications

(131 reference statements)

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“…Also, δn k,κ (ω) can be represented diagrammatically, as shown in Fig. 2, and calculated by Matsubara method [46,47]. In the next two subsections, the electron-hole operator (3.4) is evaluated under the assumption that the phonon subsystem remains in equilibrium.…”

Section: A Electron-hole Operatormentioning

confidence: 99%

Dynamical conductivity of lithium-intercalated hexagonal boron nitride films: A memory function approach

Rukelj

2020

Phys. Rev. B

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This work is a study of dynamical conductivity of a quasi-two-dimensional heterostructure Li(BN) 8 . The conducting electrons have a free-electron-like parabolic dispersion and are assumed to scatter only on acoustic phonons. The approach used to derive the generalized Drude relation with frequency and temperature dependent relaxation consists of defining the induced current density as a function of the electron-hole operator. This element is proportional to the perturbating electric field and is decomposed into the zeroth and second order of the electron-phonon interaction. The electron-hole operator is then evaluated using the Heisenberg equation. The connection between the electron-hole operator and the memory function is shown. The analytical properties of the imaginary and real part of the frequency and temperature dependent memory function, that describe electron scattering on acoustic and optical phonons, are examined in detail. Finally, the dynamical conductivity of Li(BN) 8 is calculated, with the explanation of all relevant features originating from the memory function.

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Section: A Electron-hole Operatormentioning

confidence: 99%

Dynamical conductivity of lithium-intercalated hexagonal boron nitride films: A memory function approach

Rukelj

2020

Phys. Rev. B

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“…The effects of the electron-phonon interaction are contained in the dynamical renormalization and scattering time parameters, i.e., λ ph (ω) and τ ph (ω), respectively. 24,27,28 These two quantities are related by the Kramers-Kronig relations. In the low-temperature regime (k B T ω) τ ph (ω) can be written as…”

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confidence: 99%

Dopant-Induced Plasmon Decay in Graphene

Novko

2017

Nano Lett.

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Chemically doped graphene could support plasmon excitations up to telecommunication or even visible frequencies. Apart from that, the presence of dopant may influence electron scattering mechanisms in graphene and thus impact the plasmon decay rate. Here I study from first principles these effects in single-layer and bilayer graphene doped with various alkali and alkaline earth metals. I find new dopantactivated damping channels: loss due to out-of-plane graphene and in-plane dopant vibrations, and electron transitions between graphene and dopant states. The latter excitations interact with the graphene plasmon and together they form a new hybrid mode. The study points out a strong dependence of these features on the type of dopants and the number of layers, which could be used as a tuning mechanism in future graphene-based plasmonic devices. Recently, the quantized collective motion of surface electrons, called surface plasmon, has gained renewed attention as the potential mechanism for the confinement of electromagnetic energy, which could reduce the size of optical devices to the desired nanoscale.1 The twodimensional (2D) plasmon of graphene is a most promising framework to investigate these confinement effects, 2 as a result of its relatively long lifetime 3-5 and its tunability through an electrostatic gating 6,7 or chemical doping. [8][9][10] Angle-resolved photoemission (ARPES) studies show that chemical doping by deposition of alkali and alkaline earth metal (X) atoms on graphene introduces much higher concentrations of conducting electrons than the standard electrostatic gating techniques. 8,11,12 In fact, two recent theoretical studies point out that lithium-doped single-and few-layer graphene can support plasmons ranging from nearinfrared to possibly visible energies due to a high level of doping. 9,10 This opens new possibilities to extend the application of graphene plasmonics to telecommunication technologies,photodetectors, 13 or photovoltaic systems. 14The underlying physics of dopant-induced plasmon decay in graphene, i.e., how dopants affect the electron scattering processes, is not understood yet. The largest contribution consists of interband electron-hole pair excitations between occupied and unoccupied π bands 3 (i.e., Landau damping), which are suppressed due to Pauli blocking below the value of two times the Fermi energy, 2ε F . Since the value of ε F in X-doped graphene shifts up to ∼ 1.5 eV, 8,11,12 this damping channel is diminished within a large energy window. Nevertheless, the 2D plasmon in doped graphene can still show substantial decay rates below the interband gap because of higher-order processes: electron-phonon, 3,4,15,16 electron-impurity, 17and electron-electron 18,19 scatterings. For the case of dopant-free graphene it is widely accepted that the first decay channel is a major contributor to the plasmon decay rate, but only when the plasmon energy exceeds the energy of intrinsic optical phonon of graphene (ω op ≈ 0.2 eV). 3,4 On the other hand, when the plasmon ene...

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“…26, whereby ∆Σ(k, q, ω, ǫ k / ) is approximated by its average over the Fermi surface in the optical limit (q → 0). Within these approximations, the polarization can be expressed as: 62,63…”

Section: Approximate Treatment Of Electron-phonon Interactionmentioning

confidence: 99%

Phonon-assisted damping of plasmons in three- and two-dimensional metals

2018

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We investigate the effects of crystal lattice vibrations on the dispersion of plasmons. The loss function of the homogeneous electron gas (HEG) in two and three dimensions is evaluated numerically in presence of electronic coupling to an optical phonon mode. Our calculations are based on many-body perturbation theory for the dielectric function as formulated by the Hedin-Baym equations in the Fan-Migdal approximation. The coupling to phonons broadens the spectral signatures of plasmons in the electron-energy loss spectrum (EELS) and it induces the decay of plasmons on timescales shorter than 1 ps. Our results further reveal the formation of a kink in the plasmon dispersion of the 2D HEG, which marks the onset of plasmon-phonon scattering. Overall, these features constitute a fingerprint of plasmon-phonon coupling in the EELS of simple metals. It is shown that these effects may be accounted for by resorting to a simplified treatment of the electron-phonon interaction which is amenable to first-principles calculations.

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Intraband memory function and memory-function conductivity formula in doped graphene

Cited by 9 publications

References 37 publications

Dynamical conductivity of lithium-intercalated hexagonal boron nitride films: A memory function approach

Dynamical conductivity of lithium-intercalated hexagonal boron nitride films: A memory function approach

Dopant-Induced Plasmon Decay in Graphene

Phonon-assisted damping of plasmons in three- and two-dimensional metals

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