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 discuss the known experimental data on the phase of the de Haas -van Alphen oscillations in graphite. These data can be understood if one takes into account that four band-contact lines exist near the HKH edge of the Brillouin zone of graphite.

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We discuss the electron energy spectra and the Berry phases for graphene, a graphite bilayer, and bulk graphite allowing for a small spin-orbit interaction. If an electron orbit in the Brillouin zone surrounds several Dirac points (band-contact lines in graphite), one can find relative signs of the Berry phases generated by these points (lines) by taking into account this interaction.