Semiclassical energy levels of electrons in metals with band degeneracy lines

We show that in calculating the semiclassical energy levels of electrons in metals located in a magnetic field, one must determine whether or not the corresponding electron paths in the space of wave vectors k are attached to a band degeneracy line. Calculations in the two possible cases, i.e., with and without such attachment, differ by \e\(h) over bar/2m*c, where e is th e electron charge and m* is the cyclotron mass of the electron. This shift in the energy levels is of a topological nature, and its existence depends neither on the specific form of the electron dispersion relation epsilon(k) near the electron path nor on the shape or size of this path. The reason f or this shift lies in the fact that the electron orbit is attached to the b and degeneracy line, which is the line of singular points of the Bloch wave functions. In many respects this effect is similar to the Aharonov-Bohm ef fect if the band degeneracy line is considered an infinitely thin "solenoid ." This shift in energy levels should become apparent in studies of oscilla tion phenomena in metals. We give examples of metals in which the condition s for observing the shift is probably the most favorable. (C) 1998 American Institute of Physics. [S1063-7761(98)01510-8].