content_image/334580.jpg
<img src='content_image/334580.jpg'>

In the above discussions on the orbital magnetization of the 2D kagom´ e lattice, we have concentrated on the zero-temperature limit and omitted finite-temperature effect. Now let us briefly consider the more realistic cases in which the finite-temperature effect is included. Figure 8 plots the orbital magnetization at the field f =12 / 49 with different temperatures k$_{B}$T =0, 0 . 005, 0 . 01, and 0 . 02, respectively. From Fig. 8, one can find that the magnetic oscillations are suppressed by thermal broadening. 

## IV. SUMMARY 

In summary, we have theoretically investigated the orbital magnetization of a 2D kagom´ e lattice in a perpendicular magnetic field. Here, the orbital magnetization includes a con- ventional term and a Berry-phase term, which play different roles in metallic and insulating regions. As examples, we have carefully discussed the orbital magnetization and its two components at the fields f =1 / 4, 1 / 3, and 1 / 6, respectively. By varying the Fermi energy µ$_{0}$ , we have obtained the following results: (i) The conventional term and the Berry-phase term give the opposite contributions, with their magnitudes increasing (decreasing) with in- creasing (decreasing) the Fermi energy in metallic regions; (ii) The conventional term keeps unchanged in insulating regions; (iii) The slope of the Berry-phase term in insulating regions is proportional to the system’s Hall conductance. When the flux is applied near a commen- surate one (for example, 1 / 4), the magnetic dHvA oscillations develop a fractal structure, i.e., the orbital magnetization rapidly oscillates when the Fermi energy varies through the split subbands. The finite-temperature effect has also been shown to suppress the oscillating 

