On the temperature dependence of the London penetration depth in a superconductor

In the framework of the electron-phonon theory of superconductivity 1], it is shown that the magnetic field penetration depth _L increases like a certain power of temperature atTT _c due to the low-lying excitations in the phonon spectrum. For the acoustic phonons with the density of states ² the penetration depth increases T ⁵. The origin of such a high power ofT is the same as that in the case of resistivity of the normal metal: the phonon corrections to the electromagnetic vertex should be taken into account, and major terms (T ³) cancel, the surviving ones having a higher power ofT. The possibility of linear and quadratic terms in _L(T) is discussed in a model of electrons interacting with two-level centers 2].