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

TL;DR

This paper predicts the existence of Landau-Dirac points in topological nodal-line metals, where Landau levels conically disperse and touch, leading to observable anomalies in magnetoresistance and optical absorption.

Contribution

It identifies conditions for Landau-Dirac points in topological nodal-line metals, linking magnetic breakdown and symmetry to novel Landau level behavior.

Findings

Landau-Dirac points cause anomalous magnetoresistance peaks.

Optical absorption shows linear zero-frequency evolution.

CaP$_3$ exemplifies the theoretical predictions.

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 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 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.