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

Abstract

For unconventional heavy fermion superconductors, typified by ${\mathrm{UBe}}_{13},$ the superconducting transition temperatures ${T}_{c}$ are shown to correlate with a characteristic energy ${\ensuremath{\Elzxh}}^{2}{/(m}^{*}{\ensuremath{\xi}}^{2}{),m}^{*}$ being the effective mass, and $\ensuremath{\xi}$ the coherence length. For four of the six materials for which ${T}_{c},$ ${m}^{*},$ and $\ensuremath{\xi}$ are available, ${k}_{B}{T}_{c}\ensuremath{\sim}20{\ensuremath{\Elzxh}}^{2}{/(m}^{*}{\ensuremath{\xi}}^{2}).$ One heavy fermion material, ${\mathrm{UPd}}_{2}{\mathrm{Al}}_{3},$ reveals a tendency for the above linear behavior to saturate at substantially larger ${\ensuremath{\Elzxh}}^{2}{/(m}^{*}{\ensuremath{\xi}}^{2})$ than for ${\mathrm{UBe}}_{13}.$ The sixth material considered, ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2},$ falls between ${\mathrm{UBe}}_{13}$ and ${\mathrm{UPd}}_{2}{\mathrm{Al}}_{3}.$ To embrace d-wave pairing in cuprates, a $\mathrm{log}\ensuremath{-}\mathrm{log}$ plot reveals that ${k}_{\mathrm{B}}{T}_{c}\ensuremath{\sim}{\ensuremath{\Elzxh}}^{2}{/(m}^{*}{\ensuremath{\xi}}^{2}),$ but more materials for which ${m}^{*}$ and $\ensuremath{\xi}$ are measured will be required to substantiate the correlation in these high-${T}_{c}$ substances.