Abstract
In most Weyl semimetal (WSMs), the Weyl nodes with opposite chiralities usually have the same type of band dispersions (either type-I or type-II), whereas realistic candidate materials hosting different types of Weyl nodes have not been identified to date. Here we report for the first time that, a ternary compound HfCuP, is an excellent WSM with the coexistence of type-I and type-II Weyl nodes. Our results show that, HfCuP totally contains six pairs of type-I and six pairs of type-II Weyl nodes in the Brillouin zone, all locating at the H-K path. These Weyl nodes situate slightly below the Fermi level, and do not coexist with other extraneous bands. The nontrivial band structure in HfCuP produces clear Fermi arc surface states in the (1 0 0) surface projection. Moreover, we find the Weyl nodes in HfCuP can be effectively tuned by strain engineering. These characteristics make HfCuP a potential candidate material to investigate the novel properties of type-I and type-II Weyl fermions, as well as the potential entanglements between them.