Quantum oscillations as a probe of interaction effects in Weyl semimetals in a magnetic field

The Weyl semimetal surface is modeled by applying the Bogolyubov boundary conditions, in which the quasiparticles have an infinite Dirac mass outside the semimetal. For a Weyl semimetal shaped as a slab of finite thickness, we derive an exact spectral equation for the quasiparticle states and obtain the spectrum of the bulk as well as surface Fermi arc modes. We also show that, in the presence of the magnetic field, the separation between Weyl nodes in momentum space and the length of the Fermi arcs in the reciprocal space are affected by the interactions. As a result, we find that the period of oscillations of the density of states related to closed magnetic orbits involving Fermi arcs has a nontrivial dependence on the orientation of the magnetic field projection in the plane of the semimetal surface. We conclude that the momentum-space separation between Weyl nodes and its modification due the interaction effects in the magnetic field can be measured in the experimental studies of quantum oscillations.

Figure 1

The model setup and the choice of the laboratory reference frame used in the current study (left panel) and a schematic representation of the closed quasiparticle orbits in a magnetic field involving the Fermi arcs (right panel).

Figure 2

The numerical results for the period of the density of state oscillations as a function of angle $\phi$ (left panel) and angle $\theta$ (right panel) for several fixed values of the other angle. The results with and without interaction effects are shown by thick and thin lines, respectively.

Figure 3

The density of states for bulk modes alone (left panel), the quasiparticle modes involving surface arc states (middle panel), and the superposition of both types of modes (right panel). The results are for the quasiparticle width parameter $\Gamma =0.2\text{meV}$.