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Volumn 78, Issue 22, 2008, Pages

Temperature dependence of the superheating field for superconductors in the high-κ London limit

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EID: 57749083353     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.224509     Document Type: Article
Times cited : (84)

References (41)
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    • Here the vector potential is the original noninvariant one without the phase gradient contribution discussed after Eq. 10.
    • Here the vector potential is the original noninvariant one without the phase gradient contribution discussed after Eq. 10.
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    • This approximation breaks down if the order parameter changes by an amount of order Δ0 (i.e., order 1 in our notation) over a length scale comparable to ξ0 (=1/ κ0 in our units), so that | ∇Δ | ∼ k0. This is the case, for example, near a vortex core at low temperatures (but not at sufficiently high temperatures, since the change in Δ is approximately limited by Δ (T) ≤ Δ0 over a length scale of order ξ (T) ≥ ξ0) or for nonuniform applied fields with large variations over the same length scale (i.e., such that ξ0 | ∇H | /H∼1).
    • This approximation breaks down if the order parameter changes by an amount of order Δ0 (i.e., order 1 in our notation) over a length scale comparable to ξ0 (=1/ κ0 in our units), so that | ∇Δ | ∼ k0. This is the case, for example, near a vortex core at low temperatures (but not at sufficiently high temperatures, since the change in Δ is approximately limited by Δ (T) ≤ Δ0 over a length scale of order ξ (T) ≥ ξ0) or for nonuniform applied fields with large variations over the same length scale (i.e., such that ξ0 | ∇H | /H∼1).
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    • This can be justified by treating x as a time coordinate, A and Δ as generalized coordinates, and Ω as an action; then Eq. 44 corresponds to the energy conservation law.
    • This can be justified by treating x as a time coordinate, A and Δ as generalized coordinates, and Ω as an action; then Eq. 44 corresponds to the energy conservation law.
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    • We note that Eq. 52 is valid when A0 > Δs0 (i.e., λ<1); if A0 < Δs0, then the right-hand side of Eq. 43 is simply 1/3 and the equality is not satisfied.
    • We note that Eq. 52 is valid when A0 > Δs0 (i.e., λ<1); if A0 < Δs0, then the right-hand side of Eq. 43 is simply 1/3 and the equality is not satisfied.
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