  We demonstrate theoretically an atomic liquid phase that supports
topologically nontrivial electronic structure. A minimum two-orbital model of
liquid topological insulator in two dimensions is constructed within the
framework of tight-binding molecular dynamics. As temperature approaches zero,
our simulations show that the atoms crystallize into a triangular lattice with
nontrivial band topology at high densities. Thermal fluctuations at finite
temperatures melt the lattice, giving rise to a liquid state which inherits the
nontrivial topology from the crystalline phase. The electronic structure of the
resultant atomic liquid is characterized by a nonzero Bott index. Our work
broadens the notion of topological materials, and points to a new systematic
approach for searching topological phases in amorphous and liquid systems.
