Discovering Dirac materials with quad-helicoid surface states

    Surface states of Dirac materials consist of two opposite helicoid surfaces, which cross each other along a line in the Brillouin zone and will hybridize with each other even against symmetry-allowed perturbations [1]. However, recent studies show that Dirac points with nonzero Z2 monopole charge can host gapless surface states under certain conditions [1-3], and such Dirac points can even have topologically protected quad-helicoid surface states which have never been explored in electronic and phononic systems. 

    In this talk, we will show all the possible momenta and space groups that may obtain the Dirac points with quad-helicoid surface states by three conditions summarized in our work. Those conditions are universal for systems with/without spin-orbit coupling, e.g., electronic systems, phononic systems, and photonic systems. We also offer two material candidates to show the topological property of Dirac points carrying quad-helicoid surface states in the spinless electronic band structure and phonon band structure, respectively. Topological phase transition from Z2 Dirac points to Weyl dipoles by breaking certain symmetries will also be discussed.