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We propose a feasible experimental scheme to realize a three-dimensionalchiral topological insulator with cold fermionic atoms in an optical lattice,which is characterized by an integer topological invariant distinct from theconventional $Z_2$ topological insulators and has a remarkable macroscopiczero-energy flat band. To probe its property, we show that its characteristicsurface states---the Dirac cones---can be probed through time-of-flight imagingor Bragg spectroscopy and the flat band can be detected via measurement of theatomic density profile in a weak global trap. The realization of this noveltopological phase with a flat band in an optical lattice will provide a uniqueexperimental platform to study the interplay between interaction and topologyand open new avenues for application of topological states.

Probe of Three-Dimensional Chiral Topological Insulators in an Optical Lattice