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Quantum topological Hall effect and noncoplanar antiferromagnetism in K$_{0.5}$RhO$_2$

Quantum anomalous Hall (QAH) phase is a two-dimensional bulk ferromagnetic insulator with a nonzero Chern number in presence of spin-orbit coupling (SOC) but absence of applied magnetic fields. Associated metallic chiral edge states host dissipationless current transport in electronic devices. This intriguing QAH phase has recently been observed in magnetic impurity-doped topological insulators, {\it albeit}, at extremely low temperatures. Based on first-principles density functional calculations, here we predict that layered rhodium oxide K$_{0.5}$RhO$_2$ in noncoplanar chiral antiferromagnetic state is an unconventional three-dimensional QAH insulator with a large band gap and a Neel temperature of a few tens Kelvins. Furthermore, this unconventional QAH phase is revealed to be the exotic quantum topological Hall effect caused by nonzero scalar spin chirality due to the topological spin structure in the system and without the need of net magnetization and SOC.