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

Mostepanenko, V. M.; Петров, В. М.

doi:10.1103/physrevb.96.235432

Cited by 28 publications

(62 citation statements)

References 79 publications

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“…Calculating the expectation value of the current operator to first order in the vector potential gives us the diamagnetic contribution in the conductivity formula: σ dia = −ρe 2 v 2 /(iΩ). This is akin to the origin of a diamagnetic term in graphene where the energy dispersion is also linear 43,44 .…”

Section: Conductivity Along the Edgementioning

confidence: 95%

Collective modes for helical edge states interacting with quantum light

Gulácsi

Dóra

2019

Phys. Rev. B

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We investigate the light-matter interaction between the edge state of a 2D topological insulator and quantum electromagnetic field. The interaction originates from the Zeeman term between the spin of the edge electrons and the magnetic field, and also through the Peierls substitution. The continuous U(1) symmetry of the system in the absence of the vector potential reduces into discrete time reversal symmetry in the presence of the vector potential. Due to light-matter interaction, a superradiant ground state emerges with spontaneously broken time reversal symmetry, accompanied by a net photocurrent along the edge, generated by the vector potential of the quantum light. The spectral function of the photon field reveals polariton continuum excitations above a threshold energy, corresponding to a Higgs mode and another low energy collective mode due to the phase fluctuations of the ground state. This collective mode is a zero energy Goldstone mode that arises from the broken continuous U(1) symmetry in the absence of the vector potential, and acquires finite a gap in the presence of the vector potential. The optical conductivity of the edge electrons is calculated using the random phase approximation by taking the fluctuation of the order parameter into account. It contains the collective modes as a Drude peak with renormalized effective mass, which moves to finite frequencies as the symmetry of the system is lowered by the inclusion of the vector potential.

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Section: Conductivity Along the Edgementioning

confidence: 95%

Collective modes for helical edge states interacting with quantum light

Gulácsi

Dóra

2019

Phys. Rev. B

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“…2(b), as compared to Figs. 1 and 2(a), is the presence of small peaks at ω = 2µ just after the points of each minimum of R. These peaks arise for the reason that at zero temperature Imσ → ∞ when ω → 2µ resulting in an unphysically narrow maximum R = 1 [52].…”

Section: Impact Of Chemical Potential In the Case Of Gapless Gramentioning

confidence: 99%

“…It is well known that the polarization tensor is closely related to the in-plane and out-ofplane nonlocal conductivities of graphene [37,44,45,47,52]…”

Section: Modelmentioning

confidence: 99%

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Impact of chemical potential on the reflectance of graphene in the infrared and microwave domains

Mostepanenko

Петров

2018

Phys. Rev. A

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The reflectance of graphene is investigated in the framework of the Dirac model with account of its realistic properties, such as nonzero chemical potential and band gap, at any temperature. For this purpose, the exact reflection coefficients of the electromagnetic waves on a graphene sheet expressed via the polarization tensor and ultimately via the electrical conductivity of graphene have been used. The reflectance of graphene is computed as a function of frequency and chemical potential at different temperatures and values of the band-gap parameter. The minimum values of the reflectance are found which are reached in the infrared domain at the points of vanishing imaginary part of the conductivity of graphene. For a gapped graphene, the maximum reflectance equal to unity is reached at the points where the imaginary part of conductivity diverges. The computational results demonstrate an interesting interplay between the band gap and chemical potential in their combined effect on the reflectance. Specifically, there are wide frequency intervals where the reflectance of graphene increases with increasing chemical potential and decreasing band gap. The numerical computations are found to be in good agreement with the analytic asymptotic expressions in the regions of their applicability. Several technological areas, where the obtained results could be used, are listed.

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“…Note that the polarization tensor of graphene is closely connected with the in-plane conductivity of graphene [25][26][27]35] Π 00 (ω, k) = 4πi k 2 ω σ(ω, k).…”

Section: Coated Filmsmentioning

confidence: 99%

Maximum reflectance and transmittance of films coated with gapped graphene in the context of the Dirac model

Mostepanenko

2018

Phys. Rev. A

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The analytic expressions for the maximum and minimum reflectance of optical films coated with gapped graphene are derived in the application region of the Dirac model with account of multiple reflections. The respective film thicknesses are also found. In so doing the film material is described by the frequency-dependent index of refraction and graphene by the polarization tensor defined along the real frequency axis. The developed formalism is illustrated by an example of the graphene-coated film made of amorphous silica. Numerical computations of the maximum and minimum reflectances and respective film thicknesses are performed at room temperature in two frequency regions belonging to the near-infrared and far-infrared domains. It is shown that in the far-infrared domain the graphene coating makes a profound effect on the values of maximum reflectance and respective film thickness leading to a relative increase of their values by up to 65% and 50%, respectively. The maximum transmittance of a graphene-coated film of appropriately chosen thickness is shown to exceed 90%. Possible applications of the obtained results are discussed.

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

Cited by 28 publications

References 79 publications

Collective modes for helical edge states interacting with quantum light

Collective modes for helical edge states interacting with quantum light

Impact of chemical potential on the reflectance of graphene in the infrared and microwave domains

Maximum reflectance and transmittance of films coated with gapped graphene in the context of the Dirac model

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