The oscillation of the single Abrikosov’s vortex in hard superconductors type II
V.F. Rusakov1, V.V. Chabanenko2, A. Nabiałek3, and О.М. Chumak2,3
1Donetsk National University, 21 Str. 600-richchia, Vinnytsia 21021, Ukraine
2O.O. Galkin Donetsk Institute for Physics and Engineering NAS of Ukraine, Kyiv 03680, Ukraine
3Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, Warsaw 02-668, Poland
Received August 3, 2016
During the last decade registration and manipulation of single vortex lines in bulk superconductors have been investigated with the aid of experimental techniques. Electrodynamical response of pinned vortices in high frequency range allows studying some of their characteristic. In the submitted survey the analysis of the problem of contemporary status of the single Abrikosov vortex oscillation in type II superconductors has been performed. The solutions of the free and forced oscillations of the single elastic vortex line have been analyzed considering different affecting on movement forces: pinning, elasticity, viscosity and Lorenz force. Also vortex inert properties due to the different mechanisms of massiveness have been taken into account. The nature and magnitude of the vortex effective mass caused by some of them are discussed in the paper. The roles of every force and inert in the free oscillation spectrum have been detailed investigated. In De Gennes and Matricon mode (about megahertz) with parabolic dispersion dependence and considering the pinning force an activation threshold appears. The account of the effective vortex mass in the equation of motion leads to the occurrence of high-frequency mode (about terahertz) in the oscillation spectrum which also has an activation character. Estimations of the characteristic frequencies for these modes have been given for two widespread superconductors (NbTi and anisotropic YBaCuO material). The paper also presents the features of the resonant behavior of elastic massive vortex line arising under the influence of the external driving uniform damped into the sample depth harmonic force taking into account all the forces mentioned above. The frequency and temperature dependences of the energy absorption by the vortex line have been analyzed. Maximum absorption in the low-frequency mode corresponds to the threshold frequency, in the high-frequency mode one corresponds to the cyclotron frequency of the vortex. At the end the single vortices manipulation experiments and vortex dynamics simulation have been considered.