We explore, with unprecedented single vortex resolution, the dissipation and motion of vortices in a superconducting ribbon under the influence of an external alternating magnetic field. This is achieved by combining the phase sensitive character of ac susceptibility, allowing us to distinguish between the inductive and dissipative responses, with the local power of scanning Hall probe microscopy. Whereas the induced reversible screening currents contribute only inductively, the vortices do leave a fingerprint in the out-of-phase component. The observed large phase-lag demonstrates the dissipation of vortices at time scales comparable to the period of the driving force (i.e., 13 ms The universal problem of energy dissipation embodies the irreversible conversion of work into heat in a dynamic system. This is fundamentally connected with the inequality present in the second law of thermodynamics, expressing a monotonic increase of the entropy or the fact that a perpetual motion machine of the second kind does not exist.1 The macroscopic quantum effect of superconductivity is the closest thing to the idiom of a perpetual motion machine. Indeed, due to the presence of an energy gap between the sea of condensed Cooper pairs and the fermionic quasiparticles, electrical current can circulate forever in a superconducting ring.2 However, when a type II superconductor is in the mixed state, the motion of vortices, perpendicular to supercurrents, results in a resistive voltage drop and the unique hallmark of dissipationless transport collapses.
3In general, whenever a dissipative system is subjected to a periodic excitation, e.g., a crystal to electromagnetic radiation or a driven damped harmonic oscillator, the periodic force will perform work to drive the system through subsequent dissipative cycles. The dissipative or frictional component of the system, related to a nonconservative force, will induce a phase shift between the response and the external drive. For example, the imaginary part of the relative permittivity is closely related to the absorption coefficient of a material 4 or a phase-lag appears in the motion of a damped harmonic oscillator. This close connection between dissipation of energy and the out-of-phase component of the system's response is used in spectroscopic measurements to gain information concerning the nature and efficiency of the dissipation processes and is in a one-to-one relationship with the system's equilibrium fluctuations through the fluctuation dissipation theorem.
5To investigate the dissipative nature of electrical transport, when a superconductor is in the mixed state, the integrated response of the superconductor under an external alternating magnetic field is recorded in measurements of the global ac susceptibility. 6 The action of the alternating magnetic field will result in a complex response arising from a collection of two contributors: the screening currents and the vortices.In the first approximation one can study only the linear response, which is completely determined by ...