Boundary Control of Surface States and Quantum Oscillations in Weyl Semimetals

We investigate topological surface and interface states in minimal two and four node continuum models of Weyl semimetal slabs. Enforcing particle current conservation at the surface yields a one parameter family of self-adjoint boundary conditions which fully determine the dispersion of the Fermi-arc states. By extending this formalism from the half-space to a finite slab geometry, we compute the spectrum of the bound states and demonstrate how their connectivity between opposite surfaces depends on the boundary conditions as well as slab thickness. Building on this, we analyze the semiclassical motion of electrons under an applied magnetic field and construct quantization conditions for closed orbits formed by the Fermi arcs connected by the chiral bulk states (Weyl orbits). In the four-node model, changing boundary conditions leads to discontinuous changes in the area of the allowed orbits, which is reflected in quantum oscillation frequencies. We discuss the role of magnetic breakdown in such models. Our results provide a framework for controlling interface Fermi arcs and magnetic quantum oscillations by boundary physics.