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Register a new userObservation of the Kohn anomaly near the K point of bilayer graphene
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The dispersion of electrons and phonons near the K point of bilayer graphene was investigated in a resonant Raman study using different laser excitation energies in the near infrared and visible range. The electronic structure was analyzed within the tight-binding approximation, and the Slonczewski-Weiss-McClure (SWM) parameters were obtained from the analysis of the dispersive behavior of the Raman features. A softening of the phonon branches was observed near the K point, and results evidence the Kohn anomaly and the importance of considering electron-phonon and electron-electron interactions to correctly describe the phonon dispersion in graphene systems.
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Kohn anomalies in three-dimensional metallic crystals are dips in the phonon dispersion that are caused by abrupt changes in the screening of the ion-cores by the surrounding electron-gas. These anomalies are also present at the high-symmetry points Gamma and K in the phonon dispersion of two-dimensional graphene, where the phonon wave-vector connects two points on the Fermi surface. The linear slope around the kinks in the highest optical branch is proportional to the electron-phonon coupling. Here, we present a combined theoretical and experimental study of the influence of the dielectric substrate on the vibrational properties of graphene. We show that screening by the dielectric substrate reduces the electron-phonon coupling at the high-symmetry point K and leads to an up-shift of the Raman 2D-line. This results in the observation of a Kohn anomaly that can be tuned by screening. The exact position of the 2D-line can thus be taken also as a signature for changes in the (electron-phonon limited) conductivity of graphene.
We show that the recently observed superconductivity in twisted bilayer graphene (TBG) can be explained as a consequence of the Kohn-Luttinger (KL) instability which leads to an effective attraction between electrons with originally repulsive interaction. Usually, the KL instability takes place at extremely low energy scales, but in TBG, a doubling and subsequent strong coupling of the van Hove singularities (vHS) in the electronic spectrum occurs as the magic angle is approached, leading to extended saddle points in the highest valence band (VB) with almost perfect nesting between states belonging to different valleys. The highly anisotropic screening induces an effective attraction in a $p$-wave channel with odd parity under the exchange of the two disjoined patches of the Fermi line. We also predict the appearance of a spin-density wave (SDW) instability, adjacent to the superconducting phase, and the opening of a gap in the electronic spectrum from the condensation of spins with wave vector corresponding to the nesting vector close to the vHS.
In neutral graphene, two prominent cusps known as Kohn anomalies are found in the phonon dispersion of the highest optical phonon at $q=Gamma$ (LO branch) and $q=K$ (TO branch), reflecting a significant electron-phonon coupling to undoped Dirac electrons. In this work, high-resolution electron energy loss spectroscopy is used to measure the phonon dispersion around the $Gamma$ point in quasi-freestanding graphene epitaxially grown on Pt(111). The Kohn anomaly for the LO phonon is observed at finite momentum $qsim2k_F$ from $Gamma$, with a shape in excellent agreement with the theory and consistent with known values of the EPC and the Fermi level. More strikingly, we also observe a Kohn anomaly at the same momentum for the out-of-plane optical phonon (ZO) branch. This observation is the first direct evidence of the coupling of the ZO mode with Dirac electrons, which is forbidden for freestanding graphene but becomes allowed in the presence of a substrate. Moreover, we estimate the EPC to be even greater than that of the LO mode, making graphene on Pt(111) an optimal system to explore the effects of this new coupling in the electronic properties.
We calculate the screening function in bilayer graphene (BLG) both in the intrinsic (undoped) and the extrinsic (doped) regime within random phase approximation, comparing our results with the corresponding single layer graphene (SLG) and the regular two dimensional electron gas (2DEG). We find that the Kohn anomaly is strongly enhanced in BLG. We also discuss the Friedel oscillation and the RKKY interaction, which are associated with the non-analytic behavior of the screening function at $q=2k_F$. We find that the Kohn anomaly, the Friedel oscillation, and the RKKY interaction are all qualitatively different in the BLG compared with the SLG and the 2DEG.
The interaction of electron-hole pairs with lattice vibrations exhibits a wealth of intriguing physical phenomena. The Kohn anomaly is a renowned example where electron-phonon coupling leads to non-analytic phonon dispersion at specific momentum nesting the Fermi surface. Here we report evidence of another type of phonon anomaly discovered by low temperature Raman spectroscopy in bilayer graphene where the charge density is modulated by the electric field effect. This anomaly, arising from charge-tunable modulations of particle-hole pairs that are resonantly coupled to lattice vibrations, is predicted to exhibit a logarithmic divergence in the long-wavelength optical-phonon energy. In a non-uniform bilayer of graphene, the logarithmic divergence is abated by charge density inhomogeneity leaving as a vestige an anomalous phonon softening. The observed softening marks the first confirmation of the phonon anomaly as a key signature of the resonant deformation-potential electron-phonon coupling. The high sensitivity of the phonon softening to charge density non-uniformity creates significant venues to explore the interplay between fundamental interactions and disorder in the atomic layers.
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