# Two spinorial drift-diffusion models for quantum electron transport in graphene

## TL;DR

This paper derives and analyzes two quantum drift-diffusion models for electron transport in graphene that incorporate spin effects, providing theoretical properties and numerical simulations to understand their behavior.

## Contribution

It introduces two new spinorial drift-diffusion models for graphene based on a spinorial Wigner equation, including their derivation, mathematical analysis, and numerical validation.

## Key findings

- Proved global existence of weak solutions for one model
- Established entropy-dissipation and decay properties
- Performed numerical simulations demonstrating model behavior

## Abstract

Two drift-diffusion models for the quantum transport of electrons in graphene, which account for the spin degree of freedom, are derived from a spinorial Wigner equation with relaxation-time or mass- and spin-conserving matrix collision operators using a Chapman-Enskog expansion around the thermal equilibrium. Explicit models are computed by assuming that both the semiclassical parameter and the scaled Fermi energy are sufficiently small. For one of the models, the global existence of weak solutions, entropy-dissipation properties, and the exponential long-time decay of the spin vector are proved. Finally, numerical simulations of a one-dimensional ballistic diode using both models are presented, showing the temporal behavior of the particle density and the components of the spin vector.