Luigi Barletti

Quantum drift-diffusion modeling of spin transport in nanostructures

We consider a two-dimensional electron gas with a spin-orbit interaction of Bychkov and Rashba type. Starting from a microscopic model, represented by the von Neumann equation endowed with a suitable Bhatnagar–Gross–Krook collision term, we apply the Chapman–Enskog method to derive a quantum diffusive model. Such model is then semiclassically expanded up to second order, leading to nonlinear quantum corrections to the zero-order diffusive models of the literature.

Wigner-function approach to multiband transport in semiconductors

In this work we present a one-dimensional, multi-band model for electron transport in semiconductors that makes use of the Wigner-function formalism and that allows for energy bands of any shape. A simplified two-band model is then derived from the general equations, by using the parabolic band approximation.

Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle

The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.

Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period

Energy-conserving methods for the nonlinear Schrödinger equation

{epsilon}

Particle Dynamics in Graphene: Collimated Beam Limit

of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.

Multiband quantum transport models for semiconductor devices

Nonlinear charge transport in strongly coupled semiconductor super lattices is described by two-miniband Wigner-Poisson kinetic equations with BGK collision terms. The hyperbolic limit, in which the collision frequencies are of the same order as the Bloch frequencies due to the electric field, is investigated by means of the Chapman-Enskog perturbation technique, leading to nonlinear drift-diffusion equations for the two miniband populations. In the case of a lateral superlattice with spin-orbit interaction, the corresponding drift-diffusion equations are used to calculate spin-polarized currents and electron spin polarization.

Kinetic and Hydrodynamic Models for Multi-Band Quantum Transport in Crystals

In this paper, we further develop recent results in the numerical solution of Hamiltonian partial differential equations (PDEs) (Brugnano et al., 2015), by means of energy-conserving methods in the class of Line Integral Methods, in particular, the Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We shall use HBVMs for solving the nonlinear Schrodinger equation (NLSE), of interest in many applications. We show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional, confers more robustness on the numerical solution of such a problem.