Persistent current in triangle silicene rings with spin-orbit interaction

The energy spectrum and magnetic response of triangle silicene rings (TSRs) are investigated within the tight-binding model. It is shown that the flux-dependent energy spectrum is divided into bands, with three levels per band, owing to the three-fold rotational symmetry structure of TSRs. The zigzag TSRs are metallic, exhibiting either diamagnetic or paramagnetic response depending on the size of inner ring radius. Armchair TSRs are semiconducting, exhibiting diamagnetic response. Taking into account the intrinsic spin-orbit interaction, the magnetic-field-driven spin-up electrons flow anticlockwise around the TSRs and the spin-down electrons flow clockwise around the TSRs. Additionally, paramagnetism-diamagnetism or diamagnetism-paramagnetism transitions are observed with the increase of exchange field. The results may be very helpful for the design and application of TSR-based nanodevices.