Topological Amorphous Metals*

A Weyl semimetal, a crystalline material with translational symmetry, possesses pairs of Weyl points in momentum space band structures and its topology is characterized by the first Chern number defined over a closed surface in momentum space. Here, we study amorphous systems with completely random sites and find that, through constructing and exploring a concrete model Hamiltonian, such a system can host an exotic phase of topological amorphous metal in three dimensions. In contrast to the traditional Weyl semimetals, topological amorphous metals break translational symmetry, and thus cannot be characterized by the first Chern number defined based on the momentum space band structures. Instead, their topological properties will manifest in the Bott index and the Hall conductivity as well as the surface states. Moreover, by studying the energy band and quantum transport properties, we find that topological amorphous metals exhibit a diffusive metal behavior. Our results open a door for exploring topological gapless phenomena in amorphous systems.