Spin-mixing Effects In Many Body Systems

The unconventional superconductors and spinor Fermi gas attract much attention.The spin-orbit coupling(SOC)can induce the admixture of spin-up and spin-down and the spin-mixing interaction of the spinor Fermi gas can change the population balance.The effects of SOC on the unconventional superconductors and the spin-mixing effects of spinor Fermi gas are investigated in this thesis.Firstly,we study the two-dimensional square lattice with the SOC.We show that the antiferromagnetic order is suppressed by SOC.The magnetic susceptibility turns out to be anisotropic and energy spectrums of transverse spin fluctuations opens a gap in the presence of the SOC.The effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced.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 SOC is absent.Next,the interplay between SOC and p-wave potential on the superconducting order is studied.Our results show that SOC can induce s+p-wave pairing when the interaction between electrons is p-wave.The effect of SOC on the p-wave Cooper pairs is dependent on the strength of p-wave potential.If the pairing potential is small,both the s-wave and p-wave pairs are enhanced by the SOC.On the other hand,increasing SOC leads to increment of the s-wave pairs,but reduction of the p-wave one.Then,the effect of Rashba and Dresselhaus SOC on the superconductivity in the magnetic field is investigated.It is shown that both SOCs could induce the mixture of s+p-wave Cooper pairs and s-wave pairs is suppressed by the magnetic field.When the strengths of two SOC are the same,the strength of superconducting energy gap reach an extremum.we investigate the unconventional superconductivity in the external magnetic field.In the absence of SOC,the dependence of the upper critical field on the temperature is logarithmic.Last,the itinerate ferromagnetism for the spin-3/2 spinor Fermi gas is investigated.The results show that the spin-mixing effect might be bad for the ferromagnetic state.The population of the m= ±3/2 components is more than the m=± 1/2 components in the case of the ferromagnetic state.