DMPK Equation for Transmission Eigenvalues in Metallic Carbon Nanotubes

TL;DR

This paper derives a DMPK equation for metallic carbon nanotubes with multiple channels, analyzing conductance behavior and the effects of magnetic fields on transport properties in long systems.

Contribution

It introduces a DMPK equation tailored for metallic carbon nanotubes with multiple channels and explores their conductance decay and transition under magnetic fields.

Findings

Long system length leads to a fixed point with one perfect channel.

Presence of a perfect channel reduces the conductance decay length.

Magnetic field induces a transition to the unitary class, eliminating the perfect channel.

Abstract

The Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission eigenvalues is derived for metallic carbon nanotubes with several conducting channels when the potential range of scatterers is larger than the lattice constant. With increasing system length L, the system approaches a fixed point, where only one channel is perfectly conducting and other channels are completely closed. The asymptotic behavior of the conductance in the long-L regime is investigated on the basis of the DMPK equation. It is shown that the length scale for the exponential decay of the typical conductance is reduced due to the presence of the perfectly conducting channel. If a magnetic field is applied, the system falls into the unitary class. It is pointed out that this transition is characterized by the disappearance of the perfectly conducting channel and the increase in decay length for the typical conductance.