Semiclassical quantization condition for magnetic energy levels of electrons in metals with band-contact lines

Abstract

We refine the well-known quantization condition for magnetic energy levels of a semiclassical electron. The refined condition results in the energy shift of the levels when in k space the closed electron orbit links to the band-contact line (i.e., surrounds it). This effect is closely analogous to that of Aharonov-Bohm provided the band-contact line plays the role of the infinitely thin "solenoid" with the fixed "magnetic flux". The predicted shift must manifest itself in oscillation phenomena.