Tc for non s-wave pairing superconductors correlated with coherence length and effective mass

Abstract

For unconventional heavy Fermion superconductors, typified by UBe_13, the superconducting transition temperatures Tc are shown to correlate with a characteristic energy hbar^2 /(m* xi^2), m* being the effective mass and xi the coherence length. For four of the six materials for which Tc, m* and xi are available, kB Tc ~ 20 hbar^2 / (m* xi^2). One heavy Fermion material, UPd_2Al_3, reveals a tendency for the above linear behaviour to saturate at substantially larger hbar^2 / (m* xi^2) than for UBe_13. The sixth material considered, URu_2Si_2, falls between UBe_13 and UPd_2Al_3. To embrace d-wave pairing in cuprates, a log-log plot reveals that kB Tc ~ hbar^2 / (m* xi^2), but more materials for which m* and xi are measured will be required to substantiate the correlation in these high-Tc substances.