Abstract
We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced in the case of low hole doping. It seems that the spin-orbit coupling tends to form s+p-wave Cooper pairs, while the s+d-wave pairing is dominant when the spin-orbit coupling is absent.
Highlights
Antiferromagnetic (AFM) spin fluctuations can give rise to Cooper pairing
Due to the effect of spin-orbit coupling (SOC) on spin states, it is infered that SOC could affect the spin fluctuations and influence the orbital symmetry of Cooper pairs mediated by spin fluctuations
The magnetization is suppressed by the SOC, which agrees with the results obtained by mean-field approach (MFA)
Summary
We have studied the ground state of the two-dimensional Hubbard model with Rashba SOC on a square lattice. Both the results obtained by MFA and RPA show that the sublattice magnetization decreases with the increasing of SOC for a fixed Hubbard interaction. We are just aware of a numerical work studying the mechanism of p-wave Cooper pairs[46]. They state that the degeneracy of various p-wave states is split by the magnetic anisotropy. This paper indicates that the symmetry of Cooper pairs mediated by spin-fluctuations is still a hot topic
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