# Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

@article{Barletti2018QuantumTC, title={Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials}, author={Luigi Barletti and Claudia Negulescu}, journal={Journal of Statistical Physics}, year={2018}, volume={171}, pages={696-726} }

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport…

## One Citation

Mathematical modelling of charge transport in graphene heterojunctions

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A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region),…

## References

SHOWING 1-10 OF 29 REFERENCES

Hybrid Classical-Quantum Models for Charge Transport in Graphene with Sharp Potentials

- Physics
- 2015

ABSTRACT We give a concise account on the derivation of hybrid quantum-classical models for stationary electron transport in graphene, in presence of sharp potential steps or barriers. A quantum…

A coupled Schrödinger drift-diffusion model for quantum semiconductor device simulations

- Physics
- 2002

In this paper, we derive a coupled Schrodinger drift-diffusion self-consistent stationary model for quantum semiconductor device simulations. The device is decomposed into a quantum zone (where…

A Hybrid Kinetic-Quantum Model for Stationary Electron Transport

- Physics
- 1998

Interface conditions between a classical transport model described by the Boltzmann equation and a quantum model described by a set of Schrödinger equations are presented in the one-dimensional…

Macroscopic models for semiconductor heterostructures

- Physics
- 1998

The semiconductor Boltzmann equation is considered within a material with a space-dependent band characteristic. Its fluid limit under strong elastic collisions leads to the so-called spherical…

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

- Physics
- 2014

This chapter is devoted to the derivation of k⋅p multi-band quantum transport models, in both the pure-state and mixed-state cases. The first part of the chapter deals with pure-states. Transport…

Charge transport and mobility in monolayer graphene

- Physics
- 2016

For electron devices that make use of innovative materials, a basic step in the development of models and simulation computer aided design (CAD) tools is the determination of the mobility curves for…

Chiral tunnelling and the Klein paradox in graphene

- Physics
- 2006

The so-called Klein paradox—unimpeded penetration of relativistic particles through high and wide potential barriers—is one of the most exotic and counterintuitive consequences of quantum…

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

- Physics
- 2013

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…

Quantum interference and Klein tunnelling in graphene heterojunctions

- Physics
- 2009

The observation of oscillations in the conductance characteristics of narrow graphene p–n-junctions confirms their ability to collimate ballistic carriers. Moreover, the phase of these oscillations…

Particle Dynamics in Graphene: Collimated Beam Limit

- Physics, Mathematics
- 2014

We investigate the particle dynamics in a two-dimensional structure containing two different populations of particles. We consider the semiclassical high temperature limit of the particle gas. The…