Fermi arcs of topological surface states and Lifshitz transitions in multi-Weyl semimetals

Abstract Utilizing a continuum model, this study systematically investigates the Fermi arcs of topological surface states in three-dimensional multi-Weyl semimetals. We analyzed the energy spectra and wave functions for bulk quadratic and cubic-Weyl semimetals, each with a single Weyl point. The Fermi arcs of the topological surface states in these multi-Weyl semimetals were derived analytically. Those results reveal a direct proportionality between the number of arcs emanating from a Weyl point and its winding number. Furthermore, we elucidate the topological Lifshitz transition of Fermi arcs, which depends on boundary condition parameters, and pinpoint the critical points associated with the Lifshitz transition in these semimetals. These findings highlight the evolution of Fermi arcs of topological surface states in multi-Weyl semimetals, potentially opening new avenues for modulating transport properties of topological quantum materials. Our study provides a robust analytic framework for understanding the behavior of Fermi arcs in multi-Weyl semimetals, offering valuable insights for developing topological quantum devices.