Atomistic Band-Structure Computation for Investigating Coulomb Dephasing and Impurity Scattering Rates of Electrons in Graphene

In this paper, by introducing a generalized quantum-kinetic model which is coupled self-consistently with Maxwell and Boltzmann transport equations, we elucidate the significance of using input from first-principles band-structure computations for an accurate description of ultra-fast dephasing and scattering dynamics of electrons in graphene. In particular, we start with the tight-binding model (TBM) for calculating band structures of solid covalent crystals based on localized Wannier orbital functions, where the employed hopping integrals in TBM have been parameterized for various covalent bonds. After that, the general TBM formalism has been applied to graphene to obtain both band structures and wave functions of electrons beyond the regime of effective low-energy theory. As a specific example, these calculated eigenvalues and eigen vectors have been further utilized to compute the Bloch-function form factors and intrinsic Coulomb diagonal-dephasing rates for induced optical coherence of electron-hole pairs in spectral and polarization functions, as well as the energy-relaxation time from extrinsic impurity scattering of electrons for non-equilibrium occupation in band transport.

Elucidation of ion motion in quadrupole mass spectrometer by Bloch function

In the optimization of the quadrupole mass spectrometer (QP-MS), the understanding of ion motion in terms of the phase space (the combined representation of the trajectory coordinate and momentum) is useful. The phase space representation gives an “ensemble” behavior of ions inside the filter. Even though each ion trajectory does not have the RF periodicity of the applied field, the phase space evolution does. It is only when appropriate ensemble ions are considered together that a proper QP filter characterization is possible. We here report a new framework for the phase space calculation of the QP-MS. The Mathieu–Hill equation is first solved for “complex eigen-trajectory” that has pseudo RF periodicity (the Bloch function). It is then shown that the acceptance phase space can be derived from the Bloch function without a need to calculate each ion trajectory. The ensemble behavior of ions can be estimated from a single Bloch function by expressing the trajectory phase space point by the complex amplitude (coefficient) of the Bloch function. The application of the Bloch function method to the auxiliary (pre-rod) field reveals that the ion injection efficiency may significantly be improved by optimizing the number of RF periods the ions spend in the pre-rod section.

Decomposition of the Laplacian and pluriharmonic Bloch functions

We decompose the invariant Laplacian of the deleted unit complex ball by two directional Laplacians, tangential one and radial one. We give a characterization of pluriharmonic Bloch function in terms of the growth of these Laplacians.

Distance of a Bloch Function to the Little Bloch Space

Motivated by a formula of P. Jones that gives the distance of a Bloch function to BMOA, the space of bounded mean oscillations, we obtain several formulas for the distance of a Bloch function to the little Bloch space, β0. Immediate consequences are equivalent expressions for functions in β0. We also give several examples of distances of specific functions to β0. We comment on connections between distance to β0 and the essential norm of some composition operators on the Bloch space, β. Finally we show that the distance formulas in β have Bloch type spaces analogues.