Title: Giant microwave absorption in the vortex lattice in $s$-wave superconductors

Abstract: In this article we study microwave absorption in superconductors in the presence of a vortex lattice. We show that in addition to the conventional absorption mechanism associated with the vortex core motion, there is another mechanism of microwave absorption, which is caused by the time-dependence of the quasiparticle density of states outside the vortex cores. This mechanism exists even in the absence of vortex motion and provides the dominant contribution to microwave absorption in a broad interval of physical parameters. At low frequencies, the dissipative part of the microwave conductivity $\sigma(\omega)$ is proportional to the inelastic relaxation time, $\tau_{\mathrm{in}}$, which is typically much larger than the elastic relaxation time, $\tau_{\mathrm{el}}$. At high frequencies $\sigma(\omega)$ is proportional to the quasiparticle diffusion time across the inter-vortex distance, $\tau_{\mathrm D}$, which is still larger than $\tau_{\mathrm{el}}$.