Abstract
This paper gives a theoretical formulation of the electromagnetic response of the quasi-two-dimensional (Q2D) crystals suitable for investigation of optical activity and polariton modes. The response to external electromagnetic field is described by current-current response tensor $\Pi_{\mu\nu}$ calculated by solving the Dyson equation in the random phase approximation (RPA), where current-current interaction is mediated by the photon propagator $D_{\mu\nu}$. The irreducible current-current response tensor $\Pi^0_{\mu\nu}$ is calculated from the {\em ab initio} Kohn-Sham (KS) orbitals. The accuracy of $\Pi^0_{\mu\nu}$ is tested in the long wavelength limit where it gives correct Drude dielectric function and conductivity. The theory is applied to the calculation of optical absorption and conductivity in pristine and doped single layer graphene and successfully compared with previous calculations and measurements.
Highlights
Derivation of the current-current response tensorWe will first derive the Dyson equation for the screened current-current response tensor in the Q2D crystal consisting of one or few atomic layers
Understanding the interaction between light and electrons in a crystal has always been an attractive topic, and its extensive study led to the realization of many devices, such as lasers, semiconducting solar cells or LED diodes
In Ref. [31, 32] optical properties and conductivity in graphene are investigated at a high level of accuracy, beyond random phase approximation (RPA), the orbital and band structure are described within the tight binding approximation (TBA)
Summary
We will first derive the Dyson equation for the screened current-current response tensor in the Q2D crystal consisting of one or few atomic layers. A0μ (r, t) , A0ν (r , t ) − Ψ0EM (14) , where Ψ0EM is the photon vacuum (ground state of H0EM), and the operator A0μ is defined as: A0μ (r, t) = eiH0EMtAμ (r) e−iH0EMt. The perturbation expansion of the current-current response tensor Π is diagrammatically presented, where the green wavy line represents the external field Aext, that induces current fluctuations in the crystal. Suppose that the crystal is exposed to the external (classical) electromagnetic field described by the vector potential Aext(r, t) In this case the total Hamiltonian (1) gets an additional term V ext which has the form analogous to (3–5) except that A should be replaced by Aext.
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