Unusual electronic properties of clean and disordered zigzag graphene nanoribbons

TL;DR

This paper investigates the unique electronic properties of zigzag graphene nanoribbons, revealing anomalous transport behaviors and localization phenomena at zero energy, especially under disorder respecting chiral symmetry.

Contribution

It provides a detailed analytical and numerical study of zero-energy states, uncovering novel power-law dispersions, divergence of density of states, and unusual localization properties in clean and disordered ribbons.

Findings

Power-law dispersion of energy bands near zero energy

Divergence of density of states at zero energy

Conductance decays as exp(-C_Nw√L) in disordered ribbons

Abstract

We revisit the problem of electron transport in clean and disordered zigzag graphene nanoribbons, and expose numerous hitherto unknown peculiar properties of these systems at zero energy, where both sublattices decouple because of chiral symmetry. For clean ribbons, we give a quantitative description of the unusual power-law dispersion of the central energy bands and of its main consequences, including the strong divergence of the density of states near zero energy, and the vanishing of the transverse localization length of the corresponding edge states. In the presence of off-diagonal disorder, which respects the lattice chiral symmetry, all zero-energy localization properties are found to be anomalous. Recasting the problem in terms of coupled Brownian motions enables us to derive numerous asymptotic results by analytical means. In particular the typical conductance $g_N$ of a disordered sample of width $N$ and length $L$ is shown to decay as $\exp(-C_Nw\sqrt{L})$, for arbitrary values of the disorder strength $w$, while the relative variance of $\ln g_N$ approaches a non-trivial constant $K_N$. The dependence of the constants $C_N$ and $K_N$ on the ribbon width $N$ is predicted. From the mere viewpoint of the transfer-matrix formalism, zigzag ribbons provide a case study with many unusual features. The transfer matrix describing propagation through one unit cell of a clean ribbon is not diagonalizable at zero energy. In the disordered case, we encounter non-trivial random matrix products such that all Lyapunov exponents vanish identically.