The behavior of the order parameter in pure, type I superconductors in the presence of high-frequency fields is discussed. It is shown that in second order in the field the order parameter is disturbed at considerably larger distances from the surface than the penetration depth and the coherence length.
- It is well known that a static magnetic field is completely excluded from the interior of a massive superconductor. The field penetrates only to a depth 6 -10 -5 cm, and the order parameter A(r, t) is disturbed only in the thin layer of width ~0-max (~r(T), 6), 1 where ((T) is the temperaturedependent coherence length. Usually ((T) does not exceed 10 -4 era, and for pure superconductors is far smaller than the electron mean free path l-10 -1 era. However, in the presence of a high-frequency field one can anticipate that the disturbance of the order parameter spreads to a distance d >> ((T), d << 1 from the surface. Such an effect may occur due to electron warmup in the skin and slow relaxation at a distance greater than ~r(T). In this paper we consider this effect in pure, type I superconductors and show that in the second order in the hf field the time-averaged order parameter ~(r, t) increase at a distance d >> ((T) from the surface for T ~ 0. The rise of A(r, t) in the presence of an hf field was studied earlier by Eliashberg. 2 He considered dirty superconducting films. There the warmup of quasiparticles was responsible for the rise of A(r, t) and the energy relaxation time was the important parameter. In the case considered below the warmup is collisionless and the change of A(r, t) is instead the result of the modification of the wave function and the spectrum of quasiparticles by the field.
Basically the quasiparticles with energy e = A, A+w (h = 1)play the main role, where to is the field frequency and A is the equilibrium order 545