Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors

Abstract

We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for κ = λ/ξ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-gap model for MgB2 suggests high anisotropy of the superheating field near zero temperature. On the other hand, within Ginzburg-Landau theory for a single gap, we see that the superheating field shows significant anisotropy only when the crystal anisotropy is large and the Ginzburg-Landau parameter κ is small. We then conclude that only small anisotropies in the superheating field are expected for typical unconventional superconductors near the critical temperature. Using a generalized form of Ginzburg Landau theory, we do a quantitative calculation for the anisotropic superheating field by mapping the problem to the isotropic case, and present a phase diagram in terms of anisotropy and κ, showing type I, type II, or mixed behavior (within GinzburgLandau theory), and regions where each asymptotic solution is expected. We estimate anisotropies for a number of different materials, and discuss the importance of these results for radio-frequency cavities for particle accelerators.

Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: stability theory, disorder, and laminates

“…We will return to these issues when we discuss the effects of anisotropy in Sec. (IV B), and discuss them further in the full publication [36].…”

“…[36]). The main idea is to compute the work necessary to push magnetic field onto the superconductor through an energy barrier set by the magnetic energy, and compare the result with the condensation energy.…”

“…Here we review Ref. [36], which investigates the effects of crystal anisotropy on the superheating field of superconductors, motivated partly by the opportunity of controlling surface orientation in order to achieve higher accelerating fields inside the cavity. Near the critical temperature, for the anisotropy axis c aligned with one of the Cartesian directions, the anisotropic formulation of Ginzburg-Landau theory [58][59][60][61] provides a clean approach to study the anisotropy of the superheating field.…”

“…6. Phase diagram of anisotropic superconductors in terms of mass anisotropy (γ = mc/ma) and GL (λa/ξa) parameters (from [36]). The superconductor is of type-I to the left of the blue line, of type-II to the right of the dark red line, and mixed in between (in the mixed phase, the SC is of type-I for c z and of type-II for c ⊥ z).…”

Analysis of Magnetic Vortex Dissipation in Sn-Segregated Boundaries in Nb$_3$Sn Superconducting RF Cavities

“…Inhomogeneous properties of superconductors have high impact on the performance of SRF cavities, affect- ing figures of merit such as the residual resistance due to trapped magnetic flux [33][34][35], and the superheating field [1,2,7,[36][37][38]. Grain boundaries well aligned with the surface magnetic field can become weak spots for the nucleation of superconducting vortices (see Fig.…”