Microwave Signature of the Emerging Abrikosov Lattice Above $H_{c2}$

Abstract

The emergence of the Abrikosov lattice in the normal phase of type-II superconducting films when the magnetic field approaches the critical field $H_{c2}$ from above was predicted in Ref.~\cite{GVV2011}. In the quantum fluctuation regime \cite{GL2001} it is characterized by the formation of relatively large (with sizes of order $\xi_{\mathrm{QF}} \sim \xi_{\mathrm{BCS}}\sqrt{H_{c2}/(H-H_{c2})}$) ``long lived'' (lifetime of order $\tau_{\mathrm{QF}} \sim \hbar \Delta^{-1} H_{c2}/(H-H_{c2})$) clusters of rotating fluctuation Cooper pairs - signatures of developing Abrikosov vortices. We demonstrate that these fluctuation-induced vortex clusters, previously considered unobservable due to their ultrafast dynamics and weak (only logarithmically singular) contribution to the dc-conductivity, can in fact be detected through their distinct electromagnetic signature. By analyzing the high-frequency electromagnetic response of these rotating fluctuation Cooper pairs above the second critical field in superconducting film, we predict a pronounced and measurable enhancement in the imaginary part of the ac-conductivity arising directly from quantum fluctuations. This enhancement is expected to occur at characteristic frequencies $\omega_{QF} \sim \hbar^{-1}\Delta(H-H_{c2})/H_{c2}$, which are well below the superconducting threshold at $2\hbar^{-1}\Delta $, where a similar increase in imaginary conductivity occurs in the superconducting phase. For niobium, a prototypical type II superconductor, $\omega_{QF}$ lies in the experimentally accessible microwave range, making the effect directly testable with modern microwave spectroscopy.