Comment on Half metallicity along the edge of zigzag boron nitride nanoribbons (Phys. Rev. B 78, 205415 (2008)

TL;DR

This paper critiques a previous claim of half-metallicity in zigzag boron nitride nanoribbons, clarifying that the electronic structure does not support such a property due to fundamental quantum principles.

Contribution

It provides a detailed correction to earlier work by explaining why the observed band crossing does not imply half-metallicity, based on quantum mechanical principles.

Findings

The previous claim of half-metallicity is incorrect.

Band crossing at the Fermi level is forbidden by Pauli exclusion principle.

ZBNNR-BH exhibits insulating and conducting behavior for different spins, but not half-metallicity.

Abstract

We would like to comment that the prediction of Half-mtallicity in only B edge H-passivated zigzag boron nitride nanoribbons (ZBNNR-BH), by Zheng et al.1, is not correct as their interpretation is erroneous. Since it is well known that for a material, to be a half-metal, as a primary condition one type of spin channels or bands (either spin up or spin down) are conducting and the opposite ones are insulating. In commented article 1, ZBNNR-BH shows insulating behavior for spin up bands (Eg=4.5 eV) whereas conducting nature for spin down electrons. They claim1 through the electronic band structure of 8-ZBNNR-BH [as shown in figure 2 (b)]1, that spin down - Alpha (conduction band minimum - CBM) and Beta (valence band maximum - VBM) bands are crossing each other at the Fermi level (green dotted line) and thus the ribbons are conducting for spin down electrons. But this crossing of two same spin bands is impossible because according to well-known Paulis exclusion principle- Two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously.In the case of electrons, it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers (n, l, ml and ms). Thus for two electrons residing in the same orbital (same energy level e.g. above stated crossing point 1), n, l, and ml are the same, so ms must be different and the electrons must have opposite spins.