Comment on "New Scaling of Child-Langmuir Law in the Quantum Regime"

TL;DR

This paper critiques a previous study on quantum Child-Langmuir law, highlighting errors in the numerical calculations due to improper boundary conditions and omission of exchange-correlation effects.

Contribution

It identifies and clarifies errors in prior work, emphasizing the importance of correct boundary conditions and exchange-correlation considerations in quantum nanogap modeling.

Findings

Previous calculations are incorrect due to boundary condition errors.

Exchange-correlation effects must be properly included in quantum models.

Correcting these errors impacts the understanding of maximum transmitted current.

Abstract

In their letter on the quantum Child-Langmuir law, Ang, Kwan and Lau (Phys. Rev. Lett. 91, 208303 (2003)) include exchange correlation effects within the Kohn-Sham density functional theory and explore numerically the maximum transmitted current in nanogaps. We show here that the calculations are in error as the exchange-correlation component of the chemical potential has been ignored while fixing the boundary conditions for the Hartree potential.