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Register a new userDecay and Frequency Shift of Inter and Intravalley Phonons in Graphene -Dirac Cone Migration-
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By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D$$ Raman bands with changes in doping ($mu$) and light excitation energy ($E_L$). Comparing the self-energy with the observed $mu$ dependence of the 2D bandwidth, we estimate the wavevector $q$ of the constituent intervalley phonon at $hbar vqsimeq E_L/1.6$ ($v$ is electrons Fermi velocity) and conclude that the self-energy makes a major contribution (60%) to the dispersive behavior of the D and 2D bands. The estimation of $q$ is based on an image of shifted Dirac cones in which the resonance decay of a phonon satisfying $q > omega/v$ ($omega$ is the phonon frequency) into an electron-hole pair is suppressed when $mu < (vq-omega)/2$. We highlight the fact that the decay of an intervalley (and intravalley longitudinal optical) phonon with $q=omega/v$ is strongly suppressed by electron-phonon coupling at an arbitrary $mu$. This feature is in contrast to the divergent behavior of an intravalley transverse optical phonon, which bears a close similarity to the polarization function relevant to plasmons.
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We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states (EES) that appear at the AB-BA interfaces. The CEP form an hexagonal network with an unique energy scale $epsilon_p=frac{e^2}{epsilon_0epsilon t_0}$ with $t_0$ the moire lattice constant and $epsilon$ the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i) a diverging density of states at zero energy, and (ii) the presence of a plasmonic Dirac cone at $hbaromegasimepsilon_p/2$ with sound velocity $v_D=0.0075c$, which is formed by zigzag and armchair current oscillations. A network model reveals that the antisymmetry of the plasmon bands implies that CEP scatter at the hexagon vertices maximally in the deflected chiral outgoing directions, with a current ratio of 4/9 into each of the deflected directions and 1/9 into the forward one. We show that scanning near-field microscopy should be able to observe the predicted plasmonic Dirac cone and its broken symmetry phases.
By means of first-principles calculations and modeling analysis, we have predicted that the traditional 2D-graphene hosts the topological phononic Weyl-like points (PWs) and phononic nodal line (PNL) in its phonon spectrum. The phonon dispersion of graphene hosts three type-I PWs (both PW1 and PW2 at the BZ corners emph{K} and emph{K}, and PW3 locating along the $Gamma$-emph{K} line), one type-II PW4 locating along the $Gamma$-emph{M} line, and one PNL surrounding the centered $Gamma$ point in the $q_{x,y}$ plane. The calculations further reveal that Berry curvatures are vanishingly zero throughout the whole BZ, except for the positions of these four pairs of Weyl-like phonons, at which the non-zero singular Berry curvatures appear with the Berry phase of $pi$ or -$pi$, confirming its topological non-trivial nature. The topologically protected non-trivial phononic edge states have been also evidenced along both the zigzag-edged and armchair-edged boundaries. These results would pave the ways for further studies of topological phononic properties of graphene, such as phononic destructive interference with a suppression of backscattering and intrinsic phononic quantum Hall-like effects.
$require{mediawiki-texvc}$ A theoretical study is presented on the in-plane conductance of graphene that is partially sandwiched by Ni(111) slabs with a finite size and atom-scale width of $approx12.08 AA$. In the sandwiched part, the gapped Dirac cone of graphene can be controlled via pseudospin by changing the magnetic alignment of the Ni(111) slabs. When the magnetic moments of the upper and lower Ni(111) slabs have antiparallel and parallel configurations, the bandgap at the Dirac cone is open and closed, respectively. The transmission probability calculation for the in-plane conductance of the system indicated that the antiparallel configuration would result in nearly zero conductance of $E-E_F=0.2$ eV. In the parallel configuration, the transmission probability calculation indicated that the system would have a profile similar to that of pristine graphene. A comparison of the transmission probabilities of the antiparallel and parallel configurations indicated that a high magnetoresistance of $1450%$ could be achieved. An ultimate magnetoresistance can be expected if the Ni(111) slab widths are increased to the nanometer scale.
The opening of a gap in single-layer graphene is often ascribed to the breaking of the equivalence between the two carbon sublattices. We show by angle-resolved photoemission spectroscopy that Ir- and Na-modified graphene grown on the Ir(111) surface presents a very large unconventional gap that can be described in terms of a phenomenological massless Dirac model. We discuss the consequences and differences of this model in comparison of the standard massive gap model, and we investigate the conditions under which such anomalous gap can arise from a spontaneous symmetry breaking.
We study the nuclear magnetic relaxation rate and Knight shift in the presence of the orbital and quadrupole interactions for three-dimensional Dirac electron systems (e.g., bismuth-antimony alloys). By using recent results of the dynamic magnetic susceptibility and permittivity, we obtain rigorous results of the relaxation rates $(1/T_1)_{rm orb}$ and $(1/T_1)_{rm Q}$, which are due to the orbital and quadrupole interactions, respectively, and show that $(1/T_1)_{rm Q}$ gives a negligible contribution compared with $(1/T_1)_{rm orb}$. It is found that $(1/T_1)_{rm orb}$ exhibits anomalous dependences on temperature $T$ and chemical potential $mu$. When $mu$ is inside the band gap, $(1/T_1)_{rm orb} sim T ^3 log (2 T/omega_0)$ for temperatures above the band gap, where $omega_0$ is the nuclear Larmor frequency. When $mu$ lies in the conduction or valence bands, $(1/T_1)_{rm orb} propto T k_{rm F}^2 log (2 |v_{rm F}| k_{rm F}/omega_0)$ for low temperatures, where $k_{rm F}$ and $v_{rm F}$ are the Fermi momentum and Fermi velocity, respectively. The Knight shift $K_{rm orb}$ due to the orbital interaction also shows anomalous dependences on $T$ and $mu$. It is shown that $K_{rm orb}$ is negative and its magnitude significantly increases with decreasing temperature when $mu$ is located in the band gap. Because the anomalous dependences in $K_{rm orb}$ is caused by the interband particle-hole excitations across the small band gap while $left( 1/T_1 right)_{rm orb}$ is governed by the intraband excitations, the Korringa relation does not hold in the Dirac electron systems.
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