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 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.

• Received 24 November 1997

DOI:https://doi.org/10.1103/PhysRevLett.82.2147