Magnetization of graphene tubules

摘要: Magnetization (M) comes from both the persistent currents and spin polarization. The spin-B interaction is important in a graphene tubule, because it makes one-dimensional subband with divergent density of states capable crossing Fermi level (${\mathit{E}}_{\mathit{F}}$=0 eV). It causes cusps magnetization power divergencies differential susceptibility (${\mathrm{\ensuremath{\chi}}}_{\mathit{M}}$), destroys periodicity (period ${\mathrm{\ensuremath{\varphi}}}_{0}$=hc/e) physical properties. special structures shown M ${\mathrm{\ensuremath{\chi}}}_{\mathit{M}}$ are found to be insensitive chirality. replaced by peak at low temperature (T). order ${10}^{\mathrm{\ensuremath{-}}4}$\char21{}${10}^{\mathrm{\ensuremath{-}}5}$; therefore, measurable T\ensuremath{\le}1 K. effect reducing relatively obvious for larger semiconducting tubule. Moreover, anomalous due exists all metallic tubules T. For doped exhibit more structures, since electronic structure finite vary \ensuremath{\varphi} simultaneously. magnetic response enhanced doping, strong magnetism small flux possibly altered paramagnetism (diamagnetism) diamagnetism (paramagnetism) varying free-carrier density.