# Driven flow with exclusion and spin-dependent transport in graphenelike structures

## TL;DR

This paper models spin-dependent electronic transport in honeycomb structures using a generalized exclusion process, analyzing how double site occupancy affects current and polarization, with implications for doped graphenelike materials.

## Contribution

It introduces a simplified stochastic model for spin-dependent transport in honeycomb lattices, incorporating double occupancy effects and analyzing their impact through mean field theory and simulations.

## Key findings

- Double occupancy significantly affects transport at high injection rates.
- Effects of double occupancy are minimal at low injection or high ejection rates.
- Results suggest relevance to experiments on doped graphenelike structures.

## Abstract

We present a simplified description for spin-dependent electronic transport in honeycomb-lattice structures with spin-orbit interactions, using generalizations of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. Mean field theory and numerical simulations are used to study currents, density profiles and current polarization in quasi- one dimensional systems with open boundaries, and externally-imposed particle injection ($\alpha$) and ejection ($\beta$) rates. We investigate the influence of allowing for double site occupancy, according to Pauli's exclusion principle, on the behavior of the quantities of interest. We find that double occupancy shows strong signatures for specific combinations of rates, namely high $\alpha$ and low $\beta$, but otherwise its effects are quantitatively suppressed. Comments are made on the possible relevance of the present results to experiments on suitably doped graphenelike structures.