Orbital magnetic susceptibility of finite-sized graphene

TL;DR

This paper investigates how finite size and temperature affect the orbital magnetic susceptibility of graphene ribbons, revealing oscillations, edge currents, and enhanced magnetic screening in multilayer graphene.

Contribution

It provides a detailed analysis of finite-size effects on graphene's orbital magnetism and connects these findings to multilayer graphene magnetic screening.

Findings

Susceptibility oscillates between diamagnetism and paramagnetism with Fermi energy.

Edge currents supporting diamagnetism are temperature-dependent and localized.

Low-temperature multilayer graphene shows strong magnetic field screening.

Abstract

We study the orbital magnetism of graphene ribbon in the effective-mass approximation, to figure out the finite-size effect on the singular susceptibility known in the bulk limit. We find that the susceptibility at T = 0 oscillates between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the subband structure formed by quantum confinement. In increasing T, the oscillation rapidly disappears once the thermal broadening energy exceeds the subband spacing, and the susceptibility approaches the bulk limit i.e., a thermally broadened diamagnetic peak centered at zero energy point. The electric current supporting the diamagnetism is found to flow near the edge with a depth which proportional to reciprocal of T, with v being the band velocity, while at T = 0 the current distribution spreads entirely in the sample reflecting the absence of the characteristic wavelength in graphene. The result is applied to estimate the three-dimensional random-stacked multilayer graphene, where we show that the external magnetic field is significantly screened inside the sample in low temperatures, in a much stronger manner than in graphite.