Diabolical touching point in the magnetic energy levels of topological nodal-line metals

Abstract

For three-dimensional metals, Landau levels disperse as a function of the magnetic field and the momentum wavenumber parallel to the field. In this two-dimensional parameter space, it is shown that two conicallydispersing Landau levels can touch at a diabolical point -a Landau-Dirac point. The conditions giving rise to Landau-Dirac points are shown to be magnetic breakdown (field-induced quantum tunneling) and certain crystallographic spacetime symmetry. Both conditions are realizable in topological nodal-line metals, as we exemplify with CaP 3 . A Landau-Dirac point reveals itself in anomalous "batman"-like peaks in the magnetoresistance, as well as in the onset of optical absorption linearly evolving to zero frequency as a function of the field magnitude/orientation.