Magnetic Field Screening and Mirroring in Graphene

The orbital magnetism in spatially varying magnetic fields is studied in monolayer graphene within the effective-mass approximation. We find that, unlike the conventional two-dimensional electron system, graphene with a small Fermi wave number $k_F$ works as a magnetic shield where the field produced by a magnetic object placed above graphene is always screened by a constant factor on the other side of graphene. The object is repelled by a diamagnetic force from the graphene, as if there exists its mirror image with a reduced amplitude on the other side of graphene. The magnitude of the force is much greater than that of the conventional two-dimensional system. The effect disappears with the increase of $k_F$.

Figure 1

Magnetic susceptibility $\chi (\mathbf{q})$ in (a) graphene and (b) a conventional 2D system.

Figure 2

Electric current $j_{\theta }(r)$ on graphene induced by a magnetic charge $q_m$ at $z=d$.

Figure 3

Diamagnetic force per unit area of a semi-infinite magnet cylinder with radius $a$ as a function of the distance $d$ from the tip to (a) graphene and (b) a conventional 2D system.