Surface and 3D Quantum Hall Effects from Engineering of Exceptional Points in Nodal-line Semimetals

We show that, under a strong magnetic field, a 3D nodal-line semimetal can be driven into a topological insulating phase with chiral currents flowing along the surface of the material. When the magnetic field is perpendicular to the nodal ring, the surface states of the semimetal are transmuted into Landau states which correspond to exceptional points, i.e. branch points in the spectrum of a non-Hermitian Hamiltonian which endow the band structure with a nontrivial topology. When the magnetic field is parallel to the nodal ring, we find that the bulk states are built from the pairing of surface-like evanescent waves, giving rise to a 3D quantum Hall effect with a flat zero-energy level of Landau states residing in parallel 2D slices of the 3D material. The transverse Hall conductivity is quantized in either case in units of e²/h, leading in the 3D Hall effect to a number of channels growing linearly with the section of the surface and opening the possibility to observe a macroscopic chiral current at the surface of the material.