The orbital magnetization of the electron gas on a two-dimensional kagome' lattice under a perpendicular magnetic field is theoretically investigated.The interplay between the lattice geometry and magnetic field induces 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 structure 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.
Self-assembly and growth of manganese phthalocyanine （MnPc） molecules on an Au（111） surface is investigated by means of low-temperature scanning tunneling microscopy. At the initial stage, MnPc molecules preferentially occupy the step edges and elbow sites on the Au（111） surface, then they are separately adsorbed on the face-centered cubic and hexagonal closely packed regions due to a long-range repulsive molecule-molecule interaction. After the formation of a closely packed monolayer, molecular islands with second and third layers are observed.
The de Haas van Alphen （dHvA） oscillations of electronic magnetization m a monotayer grapnene with structuteinduced spin orbit interaction （SOI） are studied. The results show that the dHvA oscillating centre in this system deviates from the well known （zero） value in a conventional two-dimensional electron gas. The inclusion of S0I will change the well-defined sawtooth pattern of magnetic quantum oscillations and result in a beating pattern. In addition, the SOI effects ola Hall conductance and magnetic susceptibility are also discussed.
