Time dependent London approach, dissipation due to out-of-core normal excitations by moving vortices

The dissipative currents due to normal excitations are included in the London description. The resulting time dependent London equations are solved for a moving vortex and a moving vortex lattice. It is shown that the field distribution of a moving vortex looses it cylindrical symmetry, it experiences contraction which is stronger in the direction of the motion, than in the direction normal to the velocity $\bm v$. The London contribution of normal currents to dissipation is small relative to the Bardeen-Stephen core dissipation at small velocities, but approaches the latter at high velocities, where this contribution is no longer proportional to $v^2$. To minimize the London contribution to dissipation, the vortex lattice orients as to have one of the unit cell vectors along the velocity, the effect seen in experiments and predicted within the time-dependent Ginzburg-Landau theory.Comment: 6 pages, 5 figure

Reply to Comment by E. Babaev and M. Silaev, arXiv:1105.3756

The criticism of Babaev and Silaev notwithstanding, we conclude that our analysis is correct. We have found in our papers on two-band superconductors close to Tc, where the Ginzburg-Landau (GL) theory applies, that these materials are characterized by a single order parameter, governed by a single correlation length. In the GL domain, the order parameters of individual bands are proportional to each other. This happens due to the unavoidable inter-band Josephson coupling. Consequently, in the regime where the GL theory applies, these systems are either type-I or type-II superconductors with no room for so called "1.5-type" superconductivity. This conclusion does not mean that at lower temperatures, outside of the GL domain, the inter-vortex interaction cannot have interesting properties, however, the latter cannot be addressed with the standard GL formalism.Comment: 2 page

Homes scaling and BCS

It is argued on the basis of the BCS theory that the zero-$T$ penetration depth satisfies $\lambda^{-2}(0)\propto\sigma T_c$ ($\sigma$ is the normal state dc conductivity) not only in the extreme dirty limit $\xi_0/\ell \gg 1$, but in a broad range of scattering parameters down to $\xi_0/\ell \sim 1$ ($\xi_0$ is the zero-$T$ BCS coherence length and $\ell$ is the mean-free path). Hence, the scaling $\lambda^{-2}(0)\propto\sigma T_c$, suggested as a new universal property of superconductors,\cite{Homes} finds a natural explanation within the BCS theory.Comment: 2 pages, 2 figure