Anisotropic Eliashberg function and electron-phonon coupling in doped graphene

Abstract

We investigate, with high-resolution angle-resolved photoemission spectroscopy, the spectral function of potassium-doped quasi-free-standing graphene on Au. Angle-dependent x-ray photoemission and density functional theory calculations demonstrate that potassium intercalates into the graphene/Au interface, leading to an upshift of the K-derived electronic band above the Fermi level. This empty band is what makes this system perfectly suited to disentangle the contributions to electron-phonon coupling coming from the π band and K-derived bands. From a self-energy analysis we find an anisotropic electron-phonon coupling strength λ of 0.1 (0.2) for the K (KM) high-symmetry directions in momentum space, respectively. Interestingly, the high-energy part of the Eliashberg function which relates to graphene's optical phonons is equal in both directions but only in KM does an additional low-energy part appear.

Observation of a universal donor-dependent vibrational mode in graphene

“…Hence, the Eliashberg function a 2 F(o, E, k) contains all we need to predict T c . It has been shown for Be 26 and also for graphene 27 that a 2 F(o, E, k) can be extracted from high-quality ARPES data. Regarding graphene, we have shown previously 27 that a 2 F(o, E, k) contains an isotropic contribution in both high-symmetry directions of two peaks for the graphene-derived optical phonons from G and K points while an extra low-energy peak appears in KM direction only.…”

“…1 we show the dopant and carbon core level spectra probed in normal emission and grazing emission as it is displayed in the inset. This method allows to determine the carbon/metal stoichiometry and the location of the dopant atom (inside the Au/graphene interface or on top of graphene) via the relative photoemission intensities for normal and grazing emission 27 . From the ratios shown in Fig.…”

“…To that end we employ the ARPES technique to evaluate the electronic band structure and to extract the Eliashberg functions 26,27 of graphene doped with Cs, K, Na, Rb, Li and Ca. The results clearly show an emerging low-energy peak whose position depends on the dopant atom, indicating coupling to a dopant-derived vibration.…”

Efficient gating of epitaxial boron nitride monolayers by substrate functionalization

“…These methods allow us to study the interface structure of the dopant/hBN system, i.e., whether the dopant preferably is above or under hBN, and to probe the unoccupied states, respectively. The crucial point in this approach is that hBN is on a Au substrate that readily ionizes the deposited alkali atoms, which is somewhat similar for doped graphene on metal substrates, where ARPES and density functional theory (DFT) have shown that a part of the electron charge is transferred to the metal [8,24]. The present case is different from the graphene case, in the sense that graphene accepts a large fraction of the alkali atom's charge while hBN does not.…”

“…The lack of electronic states at or close to the Fermi level also limits the chemical activity of hBN. In contrast to carbon materials, where ionic [8], covalent [9], and substitutional [10] doping have been successfully carried out, the interaction of potassium with bulk hBN does not result in charge transfer to the electronic states of hBN [11] owing to the large energy band gap. This insulating and chemically inert behavior is exploited in novel 2D devices which use hBN as a substrate for graphene in order to attain high electronic mobilities.…”