Tunnelling theory of Weyl semimetals in proximity to a metallic band

We study the effects of tunnelling on the band structure and Fermi arc of a time-reversal broken Weyl semimetal (WSM). When coupled to a non-magnetic parabolic band, the WSM's chiral arc state lowers in energy and forms, together with a previously extended state, a noticeable spin-dependent asymmetry in the interface spectrum in the vicinity of the Weyl nodes. We study these effects with a lattice model which we solve numerically on a finite sample and analytically through using an ansatz on an infinite sample. Our ansatz agrees very well with the numerical simulation as it accurately describes the behaviour of the chiral state, from its energy asymmetry to the spin canting at the interface. We find that the tunnelling effectively increases the Fermi arc length, allowing for the presence of interface states beyond the bare Weyl nodes. These additional states may carry current along the interface and their contribution can be detected in the conductance. Across the interface, the spin-independent conductance reproduces the results of an electron tunnelling experiment to reveal the WSM's density of states. Besides conductivity, the effect of tunnelling between the WSM and the metallic band can be seen in quantum oscillations experiments which we briefly comment about.