Phase of quantum oscillation in Weyl semimetals

We consider the semiclassical quantization condition for the energy of an electron in a magnetic field in the case when the electron orbit lies on a Fermi-surface pocket surrounding the Weyl point of a topological semimetal and analyze the constant $γ$ appearing in this condition. It is shown that this constant has the universal value, $γ=0$, independent of the tilt of the Weyl spectrum. Since the constant $γ$ for an extremal cross section of the Fermi surface determines the phase of quantum oscillations, this result explains why measurements of the phase permit one to find Weyl points in crystals even though the extremal cross section of the pocket does not pass through this point, and the appropriate Berry phase of the orbit differs from $π$.

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