  We identify an unusual mechanism for quantum oscillations in nodal
semimetals, driven by a single pair of Landau levels periodically closing their
gap at the Fermi energy as a magnetic field is varied. These `zero Landau
level' quantum oscillations (ZQOs) appear in the nodal limit where the
zero-field Fermi volume vanishes, and have distinctive periodicity and
temperature dependence. We link the Landau spectrum of a two-dimensional (2D)
nodal semimetal to the Rabi model, and show by exact solution that across the
entire Landau fan, pairs of opposite-parity Landau levels are intertwined in a
`serpentine' manner. We propose 2D surfaces of topological crystalline
insulators as natural settings for ZQOs, and comment on implications for
anomaly physics in 3D nodal semimetals.
