Brillouin zone

About: Brillouin zone is a research topic. Over the lifetime, 13849 publications have been published within this topic receiving 383077 citations.

Quasicrystalline 30° twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling.

Abstract: The interlayer coupling can be used to engineer the electronic structure of van der Waals heterostructures (superlattices) to obtain properties that are not possible in a single material. So far research in heterostructures has been focused on commensurate superlattices with a long-ranged Moire period. Incommensurate heterostructures with rotational symmetry but not translational symmetry (in analogy to quasicrystals) are not only rare in nature, but also the interlayer interaction has often been assumed to be negligible due to the lack of phase coherence. Here we report the successful growth of quasicrystalline 30° twisted bilayer graphene (30°-tBLG), which is stabilized by the Pt(111) substrate, and reveal its electronic structure. The 30°-tBLG is confirmed by low energy electron diffraction and the intervalley double-resonance Raman mode at 1383 cm-1 Moreover, the emergence of mirrored Dirac cones inside the Brillouin zone of each graphene layer and a gap opening at the zone boundary suggest that these two graphene layers are coupled via a generalized Umklapp scattering mechanism-that is, scattering of a Dirac cone in one graphene layer by the reciprocal lattice vector of the other graphene layer. Our work highlights the important role of interlayer coupling in incommensurate quasicrystalline superlattices, thereby extending band structure engineering to incommensurate superstructures.

Ab initio study of the optical absorption and wave-vector-dependent dielectric response of graphite

Abstract: We performed ab initio calculations of the optical absorption spectrum and the wave-vector-dependent dielectric and energy-loss functions of graphite in the framework of the random-phase approximation. In the absorption spectrum, the most prominent peaks were analyzed in terms of interband transitions from specific regions of the Brillouin zone. The inclusion of the crystal local-field effects (LFE) in the response had an important influence on the absorption spectrum for light polarization parallel to the c axis. The calculated electron energy-loss spectra, even without LFE, were in very good agreement with existing momentumdependent energy-loss experiments concerning the peak positions of the two valence-electron plasmons. Important aspects of the line shape and anisotropy of the energy-loss function at large momentum transfer q were also well described: the splitting of the total sp +sd plasmon and the appearance of peaks originating from interband transitions. Finally, the role of the interlayer interaction was studied, in particular with regard to its effect on the absorption spectrum for light polarization parallel to c, and to the position of the higher-frequency p +s plasmon.

Electron' drift velocity and diffusivity in germanium

Abstract: Experimental results for electron drift velocity and diffusivity in germanium, obtained with the time-of-flight technique in hyperpure material, are presented for temperatures between 8 and 240 K and fields between 1 and ${10}^{4}$ V/cm oriented along $〈111〉$ and $〈100〉$ directions. An anisotropy of the drift velocity and of the diffusion coefficient is found with the electric field applied along $〈111〉$ and $〈100〉$ directions, the latter due to the intervalley diffusion. The effect of the electron-electron interaction in the anisotropy properties has also been investigated. Theoretical Monte Carlo calculations have been performed with a model which includes lower, $〈111〉$, nonparabolic bands as well as upper bands at the center of the Brillouin zone and along the $〈100〉$ directions. Acoustic scattering with proper energy relaxation, optical scattering, and intervalley scattering between equivalent and nonequivalent valleys has been taken into account. Besides drift velocities and diffusion coefficients, other quantities such as mean electron energy, electron distribution function, and valley repopulation have been obtained from the Monte Carlo simulation.

Photoemission studies of intrinsic surface states on Si(100)

Abstract: We have determined the energy vs. k∥ dispersion of intrinsic surface states on Si(100) (2×1) by means of angle‐resolved photoemission with synchrotron radiation. For k∥=0, there is a very pronounced surface state 0.7 eV below EF(i.e.,∠0.4 eV below the top of the valence band) which disperses downwards with increasing k∥. At J′ on the boundary of the surface Brillouin zone, we find two states with binding energies of 0.7 and 1.2 eV with respect to EF. A number of geometrical models and their corresponding theoretical surface state bands have recently been published for Si(100) (2×1). Our results disagree qualitatively with all surface state dispersions calculated up to date, i.e., the ideal surface, the vacancy model, the pairing model, and the zig‐zag‐chain model. Namely, we observed semiconducting surface state bands with a low state density at EF while all models calculated to date yield metallic surface states with a large state density at EF.

Phonons in Twisted Bilayer Graphene

Abstract: We theoretically investigate phonon dispersion in AA-stacked, AB-stacked, and twisted bilayer graphene with various rotation angles. The calculations are performed using the Born--von Karman model for the intralayer atomic interactions and the Lennard-Jones potential for the interlayer interactions. It is found that the stacking order affects the out-of-plane acoustic phonon modes the most. The difference in the phonon densities of states in the twisted bilayer graphene and in AA- or AB-stacked bilayer graphene appears in the phonon frequency range 90--110 cm${}^{\ensuremath{-}1}$. Twisting bilayer graphene leads to the emergence of different phonon branches---termed hybrid folded phonons---which originate from the mixing of phonon modes from different high-symmetry directions in the Brillouin zone. The frequencies of the hybrid folded phonons depend strongly on the rotation angle and can be used for noncontact identification of the twist angles in graphene samples. The obtained results and the tabulated frequencies of phonons in twisted bilayer graphene are important for the interpretation of experimental Raman data and in determining the thermal conductivity of these material systems.