Incommensurate spin density wave as a signature of spin-orbit coupling and precursor of topological superconductivity

Center for Advanced Study in Theoretical Science,National Taiwan University, Taipei 10607, Taiwan(Dated: February 18, 2014)Close to half lling and in the limit of strong interactions the Hubbard model leads a spin Hamil-tonian. In its original isotropic form this is the Heisenberg model with antiferromagnetic coupling J.On a square lattice there is no frustration and the ground state is a classical antiferromagnet denotedby the commensurate order vector Q = (ˇ;ˇ). In this work we show that the inclusion of spin orbitcoupling (SOC) in the fermionic Hubbard model on a square lattice leads to an incommensuratespin density wave (ISDW) in the strong interactions limit at half lling. In this limit the Hubbardmodel leads to a non-diagonal and anisotropic spin Hamiltonian which exhibits the incommensuratespin order as its classical ground state. We note that an ISDW can be found in systems regardlessof spin orbit-coupling due to nesting and lattice distortion. These e ects, however, can usually berecognized by experimental probes.