Effective Land\'{e} factors for an electrostatically defined quantum point contact in silicene

The transconductance and effective Land'{e} $g^{\ast }$ factors for a quantum point contact defined in silicene by the electric field of a split gate is investigated. The strong spin-orbit coupling in buckled silicene reduces the $g^{\ast }$ factor for in-plane magnetic field from the nominal value 2 to around 1.2 for the first- to 0.45 for the third conduction subband. However, for perpendicular magnetic field we observe an enhancement of $g^{\ast }$ factors for the first subband to 5.8 in nanoribbon with zigzag and to 2.5 with armchair edge. The main contribution to the Zeeman splitting comes from the intrinsic spin-orbit coupling defined by the Kane-Mele form of interaction.