Abstract
The propagator of a dynamically screened Coulomb interaction W in a sandwichlike structure consisting of two graphene layers separated by a slab of Al2O3 (or vacuum) is derived from single-layer graphene response functions and by using a local dielectric function for the bulk Al2O3. The response function of graphene is obtained using two approaches within the random phase approximation (RPA): an ab initio method that includes all electronic bands in graphene and a computationally less demanding method based on the massless Dirac fermion (MDF) approximation for the low-energy excitations of electrons in the π bands. The propagator W is used to derive an expression for the effective dielectric function of our sandwich structure, which is relevant for the reflection electron energy loss spectroscopy of its surface. Focusing on the range of frequencies from THz to mid-infrared, special attention is paid to finding an accurate optical limit in the ab initio method, where the response function is expressed in terms of a frequency-dependent conductivity of graphene. It was shown that the optical limit suffices for describing hybridization between the Dirac plasmons in graphene layers and the Fuchs-Kliewer phonons in both surfaces of the Al2O3 slab, and that the spectra obtained from both the ab initio method and the MDF approximation in the optical limit agree perfectly well for wave numbers up to about 0.1 nm−1. Going beyond the optical limit, the agreement between the full ab initio method and the MDF approximation was found to extend to wave numbers up to about 0.3 nm−1 for doped graphene layers with the Fermi energy of 0.2 eV.
Highlights
Even though graphene is just a one-atom-thick layer of carbon, it supports a variety of electronic excitations, ranging from the high-energy π and π + σ transitions, which lie in the ultraviolet (UV) to the far-ultraviolet (FUV) frequency range, down to the low-energy excitations within the π electronic bands in doped graphene, lying in the range of terahertz (THz) to infrared (IR) frequencies [1,2,3,4]
The response function of graphene is obtained using two approaches within the random phase approximation (RPA): an ab initio method that includes all electronic bands in graphene and a computationally less demanding method based on the massless Dirac fermion (MDF) approximation for the low-energy excitations of electrons in the π bands
We have presented an ab initio calculation of the dynamic response function of single-layer graphene at the level of random phase approximation (RPA) that includes all electronic transitions within and between σ and π bands and covers a broad range of wave vectors [4]
Summary
Even though graphene is just a one-atom-thick layer of carbon, it supports a variety of electronic excitations, ranging from the high-energy π and π + σ transitions, which lie in the ultraviolet (UV) to the far-ultraviolet (FUV) frequency range, down to the low-energy excitations within the π electronic bands in doped graphene, lying in the range of terahertz (THz) to infrared (IR) frequencies [1,2,3,4]. Graphene layers typically appear in stacks [12,15] or sandwichlike structures [16] with insulating spacers between them made of polar materials, which often support strong Fuchs-Kliewer (FK), or surface optical phonon modes in the THz to mid-IR frequency range [17] Those surface phonons strongly interact with longitudinal plasmon modes, and may completely change the dispersion and damping of the Dirac plasmons in graphene [18,19,20,21], thereby seriously affecting its tunability for optoelectronic [12,17,20,21,22] and plasmonic [23,24,25] applications in the range of frequencies of technological interest. Such excitation could occur indirectly, for example, when light is used first to excite a Mie resonance in a metallic tip placed in the vicinity of a graphene/insulator interface
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