The half-quantized Hall phase represents a unique metallic or semi-metallic state of matter characterized by a fractional quantum Hall conductance, precisely half of an integer ν multiple of e2/h. Here we demonstrate the existence of a \({\mathbb{Z}}/2\) topological invariant that sets the half-quantized Hall phase apart from two-dimensional ordinary metallic ferromagnets. The \({\mathbb{Z}}/2\) classification is determined by the line integral of the intrinsic anomalous Hall conductance, which is safeguarded by two distinct categories of local unitary and anti-unitary symmetries in proximity to the Fermi surface of electron states. We further validate the \({\mathbb{Z}}/2\) topological order in the context of the quantized Hall phase by examining semi-magnetic topological insulator Bi2Te3 and Bi2Se3 film for ν = 1 and topological crystalline insulator SnTe films for ν = 2 or 4. Our findings pave the way for future exploration and understanding of topological metals and their unique properties.
