Orbital magnetization of the electron gas on a two-dimensional kagom´ e lattice under a perpendicular magnetic field Zhigang Wang, 1 Zi-Gang Yuan, 2, 3 Zhen-Guo Fu, 1, 2 Shu-Shen Li, 2 and Ping Zhang 1, 4, ∗ $^{1}$LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, People’s Republic of China $^{2}$State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P. O. Box 912, Beijing 100083, People’s Republic of China $^{3}$College of Science, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China $^{4}$Center for Applied Physics and Technology, Peking University, Beijing 100871, People’s Republic of China The orbital magnetization of the electron gas on a two-dimensional kagom´ e lattice under a per- pendicular magnetic field is theoretically investigated. The interplay between the lattice geometry and magnetic field induce nontrivial k -space Chern invariant in the magnetic Brillouin zone, which turns to result in profound effects on the magnetization properties. We show that the Berry-phase term in the magnetization gives a paramagnetic contribution, while the conventional term brought about by the magnetic response of the magnetic Bloch bands produces a diamagnetic contribution. As a result, the superposition of these two components gives rise to a delicate oscillatory struc- ture in the magnetization curve when varying the electron filling factor. The relationship between this oscillatory behavior and the Hofstadter energy spectrum is revealed by selectively discussing the magnetization and its two components at the commensurate fluxes of f =1 / 4, 1 / 3, and 1 / 6, respectively. In particular, we reveal as a typical example the fractal structure in the magnetic oscillations by tuning the commensurate flux around f =1 / 4. The finite-temperature effect on the magnetization is also discussed. PACS numbers: 73.20.At, 71.10.Ca, 72.15.Gd Abstract arXiv:1001.5330v1 [cond-mat.mes-hall] 29 Jan 2010 ∗ Author to whom correspondence should be addressed. Electronic address: zhang ping@iapcm.ac.cn 1