Dynamical electrical conductivity of graphene

The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and outof-plane conductivities of graphene are expressed via the components of the polarization tensor in (2+1)-dimensional space-time analytically continued to the real frequency axis. Simple analytic expressions for both the real and imaginary parts of the conductivity of graphene are obtained at zero and nonzero temperature. They demonstrate an interesting interplay depending on the values of mass gap and chemical potential. In the local limit, several results obtained earlier using various approximate and phenomenological approaches are reproduced, refined and generalized.The numerical computations of both the real and imaginary parts of the conductivity of graphene are performed to illustrate the obtained results. The analytic expressions for the conductivity of graphene obtained in this paper can serve as a guide in the comparison between different theoretical approaches and between experiment and theory.

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“…[62] Eqs. (35) and (36) were derived for the case of gapped but undoped (µ = 0) graphene using the formalism of the polarization tensor.…”

Section: B Real Part Of Conductivity At Any Temperaturementioning

confidence: 99%

Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential

Mostepanenko

Петров

2017

Phys. Rev. B

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“…For the electron-magnon study, in zero temperature limit (T m , T e → 0) and at lower frequency, we observe that the scattering rate scales as ω 3/2 and at frequency higher than Θ BG it saturates to a constant value. For the case of electron-phonon interaction, in zero temperature behavior and lower frequency regime (ω ω BG ), it is notice that the scattering rate proportional to ω 3 power law in contrast to the simple metal (scales as ω 5 ) [14] and graphene (scales as ω 4 ) [26].…”

Section: Discussionmentioning

confidence: 99%

Hot electron relaxation in normal state of iron pnictides: memory function approach

Rani¹,

Sevik²

2020

Preprint

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This study leads to the investigation of the non-equilibrium electron relaxation in the normal state of iron pnictides. Here we consider the relaxation of electrons due to their coupling with magnons and phonons in the metallic state of iron pnictides using the memory function approach. In the present model, electrons live at a higher temperature than that of the phonon and magnon baths, mimicking a non-equilibrium steady state situation. Further we analyze theoretically the generalized Drude scattering rate within the framework of Two Temperature Model and study the full frequency and temperature behavior for it. In zero frequency regime, the rate of electron-magnon scattering and electron-phonon scattering shows a linear temperature dependence at higher temperature values greater than Bloch-Grüneisen temperature. Whereas at lower temperature values, T ΘBG, corresponding scattering rates follow the temperature behavior as (1/τe−p ∝ T 3 ) and (1/τe−m ∝ T 3/2 ), respectively. In the AC regime, we compute that 1/τ ∝ ω 2 for ω ωBG and for the values greater than the Bloch-Grüneisen frequency, it is ω-independent. Also, in lower frequency and zero temperature limit, we have observed the different frequency scale of electron-magnon and electron-phonon scattering i.e (1/τ ∝ ω 3/2 ) and (1/τ ∝ ω 3 ). These results can be viewed with the pump-probe experimental setting for the normal state of iron pnictides.

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“…surface(k F ) as compared to Debye surface(k D ) [38]. Thus in this system when k F << k D , below the Bloch-Grüneisen temperature, only small number of phonons with wave vector (k ph < 2k F ) can take part in scattering.…”

Section: A Calculation For Generalized Drude Scattering Ratementioning

confidence: 90%

Non-equilibrium electron relaxation in Graphene

Rani,

Bhalla,

Singh

2018

Preprint

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We apply the powerful method of memory function formalism to investigate nonequilibrium electron relaxation in graphene. Within the premises of Two Temperature Model (TTM), explicit expressions of the imaginary part of the Memory Function or generalized Drude scattering rate (1/τ ) are obtained. In the DC limit and in equilibrium case where electron temperature (T e ) is equal to phonon temperature (T), we reproduce the known results (i.e. 1/τ ∝ T 4 when T << Θ BG and 1/τ ∝ T when T >> Θ BG , where Θ BG is the Bloch-Grüneisen temperature). We report several new results for 1/τ where T = T e relevant in pump-probe spectroscopic experiments. In the finite frequency regime we find that 1/τ ∝ ω 2 when ω << ω BG , and for ω >> ω BG it is ω independent and also electron temperature independent. These results can be verified in a typical pump-probe experimental setting for graphene.

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Dynamical electrical conductivity of graphene

Cited by 13 publications

References 32 publications

Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential

Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential

Hot electron relaxation in normal state of iron pnictides: memory function approach

Non-equilibrium electron relaxation in Graphene

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