Acoustic plasmons in extrinsic free-standing graphene

An acoustic plasmon is predicted to occur, in addition to the conventional two-dimensional (2D) plasmon, as the collective motion of a system of two types of electronic carriers coexisting in the same 2D band of extrinsic (doped or gated) graphene. The origin of this novel mode stems from the anisotropy present in the graphene band structure near the Dirac points K and K'. This anisotropy allows for the coexistence of carriers moving with two distinct Fermi velocities along the Gamma K and Gamma K' directions, which leads to two modes of collective oscillation: one mode in which the two types of carriers oscillate in phase with one another (this is the conventional 2D graphene plasmon, which at long wavelengths (q -> 0) has the same dispersion, q(1/2), as the conventional 2D plasmon of a 2D free electron gas), and the other mode found here corresponds to a low-frequency acoustic oscillation (whose energy exhibits at long-wavelengths a linear dependence on the 2D wavenumber q) in which the two types of carriers oscillate out of phase. This prediction represents a realization of acoustic

Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)