Stability Limits of the Meissner State and the Mechanism of Spontaneous Vortex Nucleation in Superconductors

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Abstract
The limits of metastable existence of the superconducting Meissner state in a magnetic field are found by examining the second variation δ2Ω of the Ginzburg-Landau free energy. No assumptions about boundary conditions are made, and all possible fluctuations are examined. First, confining the fluctuations to one dimension, we show that δ2Ω is positive definite exactly up to that field Hs2 (first calculated by Ginzburg) at which the Meissner state ceases to exist as a Ginzburg-Landau solution. At Hs2, the normal state penetrates spontaneously. Then we take into account arbitrary fluctuations and show that for superconductors with κ≳0.5 another instability occurs at a lower field Hs1, leading to a new metastable modification of the Meissner state. This new state possesses small vortices with fluxoid quantum zero along the boundary, and is metastable up to a field Hs3, which is probably of the order of Hs2(Hs3=Hs2=Hc for κ≫1). At Hs3, the normal state penetrates. Then, in a type-II superconductor with Hs3 smaller than the upper critical field Hc2, spontaneous nucleation of Abrikosov vortices will take place in the normal region without violating fluxoid quantization. This should be the correct mechanism for vortex nucleation in ideal superheating experiments.