Manifestation of Berry's phase in metal physics

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 band-contact line prays 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.