MAGNETIZATION OF GRAPHENE TUBULES

Magnetization (M) comes from both the persistent currents and the spin polarization. The spin-B interaction is important in a graphene tubule, because it makes the one-dimensional subband with the divergent density of states capable of crossing the Fermi level (E(F)=0 eV). It causes cusps in magnetization and power divergencies in differential susceptibility (chi(M)), and destroys the periodicity (period phi(0)=hc/e) of the physical properties. The special structures shown in M and chi(M) are found to be insensitive to the chirality. The power divergencies in chi(M) are replaced by the peak structures at low temperature (T). The order of chi(M) is 10(-4)-10(-5); therefore, the peak structures are measurable at T less than or equal to 1K. The temperature effect in reducing magnetization is relatively obvious for a larger semiconducting tubule. Moreover, the anomalous temperature effect due to the spin-B interaction exists in all the metallic tubules at the relatively low T For the doped graphene tubule, M and chi(M) exhibit more special structures, since both the electronic structure and the finite Fermi level vary with phi simultaneously. The magnetic response is enhanced by the doping, and it is relatively strong for a larger tubule. The magnetism at the small flux is possibly altered from paramagnetism (diamagnetism) to diamagnetism (paramagnetism) by varying the free-carrier density.