Disorder-dependent slopes of the upper critical field in nodal and nodeless superconductors

Abstract

We study the slopes of the upper critical field ${\partial }_T{H}_{c2}{|}_{T_c}\equiv \partial H_{{}_{c2}}/\partial T$ at $T_c$ in anisotropic superconductors with transport (non-magnetic) scattering employing the Ginzburg-Landau theory, developed for this situation by S. Pokrovsky and V. Pokrovsky, Phys. Rev. B 54, 13275 (1996). We found unexpected behavior of the slopes for a $d-$wave superconductor and in a more general case of materials with line nodes in the order parameter. Specifically, the presence of line nodes causes ${\partial }_T{H}_{c2}{|}_{T_c}$ to decrease with increasing non-magnetic scattering parameter $P$, unlike the nodeless case where the slope increases. In a pure $d-$wave case, the slope $\partial H_{c2}{|}_{T_c}$ changes from decreasing to increasing when scattering parameter approaches $P\approx 0.91P_{\mathrm{crit}}$, where $P_{\mathrm{crit}}\approx 0.2807$ at which $T_c\to 0$ that implies the the existence of a gapless state in $d-$wave superconductors with transport scattering in the interval, $0.91P_{\mathrm{crit}}<P<P_{\mathrm{crit}}$. Furthermore, we have considered the mixed $s+d$ order parameter that has 4 nodes on a cylindrical Fermi surface when a $d-$part is dominant, or no nodes at all when an $s-$phase is the major one. We find that presence of nodes causes the slope ${\partial }_T{H}_{c2}{|}_{T_c},$ to decrease initially with increasing $P$, whereas in the nodeless state, ${\partial }_T{H}_{c2}{|}_{T_c}$ monotonically increases. Therefore, fairly straightforward experiments make it possible to decide whether or not the order parameter of a superconductor has nodes by measuring the disorder-dependence of the slope of $H_{c2}$ at $T_c$.

References in corpus (4)

• A Sharp Peak of the Zero-Temperature Penetration Depth at Optimal Composition in BaFe2(As1-xPx)2
• Enhanced upper critical field in Co-doped Ba122 superconductors by lattice defect tuning
• Magnetic penetration-depth measurements of a suppressed superfluid density of superconducting Ca${}_{0.5}$Na${}_{0.5}$Fe${}_2$As${}_2$ single crystals by proton irradiation
• Superconducting properties of (Ba-K)Fe2As2 single crystals disordered with fast neutron irradiation

Cited by in corpus (3)

• Theory of potential impurity scattering in pressurized superconducting La${}_3$Ni${}_2$O${}_7$
• Anisotropic multiband superconductivity in 2M-WS${}_2$ probed by controlled disorder
• Slope of the upper critical field at $T_c$ in two-band superconductors with non-magnetic disorder: $s_{++}$ superconductivity in ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$