example of such a phenomenon is the Josephson plasma resonance effect, which holds great technological promise, as evidenced by the high level of Japanese investment in this area.

A vortex system is a tunable, correlated system. The density of vortex lines in a superconductor depends on the applied magnetic field, so that by varying the external field, one can control the density of the “particles” in the system and hence also their interactions. Vortex separation is ~80 nm at 1 T, 14 nm at 10 T, 6 nm at 50 T, and 4 nm at 100 T. The radius of strong interaction between vortices is determined by λ, generally 200-400 nm for HTS materials. At distances exceeding this scale, interactions are screened and become exponentially weaker. Most experiments—as well as practical applications—are conducted in the range where the vortex spacing is much less than the London depth, which ensures retention of the tunable property of these strongly correlated systems. Additionally, the degree of vortex disorder can often be changed by altering its density using magnetic field strength as the controlling variable. Thus, by adjusting both the temperature and the magnetic field one can scan the entire range of possible interactions.

In general, the quantum mechanics of particles in N dimensions is equivalent to the statistical mechanics of elastic lines in an N + 1 dimensional space. Thus the physics of vortex systems in a bulk sample can be mapped onto the quantum mechanics of a two-dimensional system of repulsively interacting bosons. In particular, a vortex lattice can correspond to a two-dimensional Wigner crystal, while a vortex liquid maps onto a two-dimensional superfluid. As tunable systems, vortex states in high magnetic fields offer a unique possibility for study of the fundamental localization problem in strongly correlated systems.

One of the most important questions being investigated today is how the mixed superconducting state depends on the collective properties of the vortices when a transport current is applied. Hydrodynamic interactions of the applied current with the circular currents of the vortices cause the vortices to migrate (via the so-called Magnus force), and energy is dissipated. Thus, in the presence of vortices, a superconductor cannot carry a current without energy loss unless the vortices are pinned in place. Since the first field penetration at Hc1 occurs at ~0.01 T, even weak currents generate vortices in superconducting devices.

A closely related topic is the behavior of very small superconductor samples in relatively high magnetic fields (a few tesla). For instance, transport properties of superconducting point contacts, which will be an issue in most of the next generation of superconducting devices, is an increasingly important research topic. At the tip of such a contact, superconductivity disappears, and charge transport occurs exclusively via Andreev states. Extensive theoretical research is being carried out on this kind of nanoscale superconductivity, and corresponding experimental investigations are needed. Another important topic concerns superconductor



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