Upper Critical Field in a Spin-Charge Separated Superconductor

It is demonstrated that the spatial decay of the pair propagator in a Luttinger liquid with spin charge separation contains a logarithmic correction relative to the free fermi gas result in a finite interval between the spin and charge thermal lengths. It is argued that similar effects can be expected in higher dimensional systems with spin charge separation and that the temperature dependence of the upper critical field $H_{c2}$ curve is a probe of this effect.