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

@article{Wang2020DiabolicalTP,
  title={Diabolical touching point in the magnetic energy levels of topological nodal-line metals},
  author={Chong Wang and Zhongyi Zhang and Liqin Zhou and Hongming Weng and Chen Fang and A. Alexandradinata},
  journal={Physical Review B},
  year={2020}
}
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 conically-dispersing 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… 
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Two-dimensional Dirac-line semimetals resistant to strong spin-orbit coupling.

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