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Graphene Plasmonics
Published in Qiaoliang Bao, Hui Ying Hoh, Yupeng Zhang, Graphene Photonics, Optoelectronics, and Plasmonics, 2017
Qingyang Xu, Yao Lu, Jian Yuan, Yupeng Zhang, Qiaoliang Bao
In EELS experiments, acoustic-like quasi-linear dispersions of plasmons are found in the long-wavelength limit, which is a strange quantum behavior in graphene. As early as in 1959, Kohn had predicted that ∂ ω(q)/ ∂ q|q = 2kF = ∞ for the phonon wave mode in ordinary 2D metals due to the strong electronphonon interactions, which was called Kohn anomaly [40]. By Raman spectroscopy Kohn anomalies are also found in graphene with a breakdown ofthe Born-Oppenheimer approximation. Therefore, the phonons interacting with electron might be responsible for the quasi-linear dispersion. Because of the chirality in graphene, Tse et al. found four distinct Kohn anomalies, which are different from the metals [41]. After that, researchers achieved the breakthrough from graphene on polar substrates. Within the angle-resolved EELS, a strong plasmon- phonon coupling was found in epitaxial graphene on SiC $ {\text{SiC}} $ (0001) [42]. As interpreted, surface state charges on the SiC are transferred into empty π* states in the graphene sheet, and surface optical phonon modes in SiC $ {\text{SiC}} $ cause the π* and electrons in graphene oscillating. Moreover a transition from plasmon-like to phonon-like dispersion is obtained with increasing graphene layers, where the discontinuous dispersions of ω± modes are exhibited, as shown in Fig. 7.2. Both modes are strongly damped when they enter into the SPE regions. Combined with EELS data and numerical calculations, a gap in dispersion relation is found between the two modes, where ω+ modes converge to the LO phonon dispersion line and ω- modes converge to the TO phonon dispersion line [43], as shown in Fig. 7.2b. The strong coupling with a gap can also be obtained in theory by considering the nonperturbative Coulomb coupling between electronic excitations and phonons [44], as shown in Figs. 7.2c-f. The coupling in single-layer graphene is strong at all densities; however it is strong only at high densities for bilayer graphene, which agree with the ω± EELS results in Ref. [42]. Consequently substrates indeed impact the plasmon-phonon coupling seriously [45].
Impact of Electron-Phonon Interaction on Thermal Transport: A Review
Published in Nanoscale and Microscale Thermophysical Engineering, 2021
Yujie Quan, Shengying Yue, Bolin Liao
In principle, any states in a solid can be accurately determined by solving the Schrödinger equation involving all interactions between electrons and atomic nuclei. However, this full quantum mechanical treatment is infeasible for most condensed matter systems due to the complicated forms of interactions and a large number of involved atomic and electronic coordinates. To simplify this problem, in 1927, Born and Oppenheimer proposed that the electrons and atomic nuclei can be treated as separate quantum mechanical systems [24], the so-called Born-Oppenheimer approximation (BOA), given the fact that electrons are much lighter than atomic nuclei and that they move rapidly enough to adjust instantaneously to the much slower vibrations of the nuclei. Under BOA, the interaction term originating from the electrostatic potential generated by ionic vibrations, whose quantum description is the phonons, is dropped from the electronic Schrödinger equation. Although BOA has achieved great success in giving a reliable estimate of the total electronic energy given any atomic configurations, the dropped term, known as the EPI, is responsible for a broad range of phenomena. For example, the electrical resistance in metals at high temperatures is mainly attributed to the scattering of electrons by phonons; the attractive interaction between two electrons that form a Cooper pair, which is the origin of superconductivity, is mediated by phonons. Besides, the coupling between two electrons on the Fermi surface connected by a nesting wave vector and a phonon with a matching momentum leads to an abrupt change in the screening of lattice vibrations, which is manifested in the distortion of phonon dispersions, known as the Kohn anomaly [25].