It is shown that in crystals the semiclassical quantization condition for energy levels of electrons in the magnetic field depends on Berry's phase. When the electron orbit links to the band-contact line of the metal (i.e., surrounds it), Berry's phase is nonzero and the quantization condition differs from that commonly used. This result is closely analogous to the Aharonov-Bohm's effect provided the bandcontact line plays the role of the infinitely thin "solenoid" with the fixed "magnetic flux." The predicted effect must manifest itself in oscillation phenomena for a number of metals. [S0031-9007(99)08623-8]

We show that an ac external magnetic field can generate a dc voltage in type-II superconductors carrying a constant transport current. This rectifying effect occurs even at low temperatures where flux creep may be disregarded and even for arbitrarily small applied current. The dc signal appears when the magnitude of the applied ac field exceeds a threshold value which depends on the shape of the superconductor and on the applied current. Experiments on this subject are discussed.

Quantized magnetic vortices driven by electric current determine key electromagnetic properties of superconductors. While the dynamic behavior of slow vortices has been thoroughly investigated, the physics of ultrafast vortices under strong currents remains largely unexplored. Here, we use a nanoscale scanning superconducting quantum interference device to image vortices penetrating into a superconducting Pb film at rates of tens of GHz and moving with velocities of up to tens of km/s, which are not only much larger than the speed of sound but also exceed the pair-breaking speed limit of superconducting condensate. These experiments reveal formation of mesoscopic vortex channels which undergo cascades of bifurcations as the current and magnetic field increase. Our numerical simulations predict metamorphosis of fast Abrikosov vortices into mixed Abrikosov-Josephson vortices at even higher velocities. This work offers an insight into the fundamental physics of dynamic vortex states of superconductors at high current densities, crucial for many applications.

We show that for a thin superconducting strip placed in a transverse dc magnetic field--the typical geometry of experiments with high-T(c) superconductors--the application of a weak ac magnetic field perpendicular to the dc field generates a dc voltage in the strip. This voltage leads to the decay of the critical currents circulating in the strip, and eventually the equilibrium state of the superconductor is established. This relaxation is not due to thermally activated flux creep but to the "walking" motion of vortices in the two-dimensional critical state of the strip with in-plane ac field. Our theory explains the shaking effect that was used for detecting phase transitions of the vortex lattice in superconductors.