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The topology between Bloch states in reciprocal space has attractedtremendous attention in recent years. The quantum geometry of the bandstructure is composed of quantum metric as real part and berry curvature asimaginary part. While the Berry curvature, the Berry curvature dipole and Berryconnection polarizability have been recently revealed by the first orderanomalous hall, second order and third order nonlinear Hall effectrespectively, the quantum metric induced second order nonlinear transverse andlongitudinal response in topological antiferromagnetic material MnBi2Te4 wasonly very recently reported. Here we demonstrate the similar third ordernonlinear transport properties in the topological antiferromagnetic CoNb3S6. Weobserved that the third order nonlinear longitudinal V3{\omega} xx increasesignificantly at the antiferromagnetic transition temperature TN ~ 29 K, whichwas probably induced by the quantum metric without time-reversal symmetry orinversion symmetry. Besides, temperature-dependent nonlinear behaviour wasobserved in the first order I-V curve below the Neel temperature TN, which wasnot reported in MnBi2Te4 and FeSn. Such nonlinear I-V behaviour hints for thepossible existence of Charge Density Wave (CDW) state, which has beendiscovered in its sister material FeNb3S6. Simultaneously, two plateaus in thethird order nonlinear longitudinal V3{\omega} xx~ I^{\omega} curve areobserved, which is also speculated to be related with the possible CDW state.However, the genuine mechanism for the first order nonlinear I-V and itsrelation with the third order nonlinear transport call for more experimentalinvestigations and theoretical interpretation. Our work provides a way toexplore third harmonic nonlinear transport and interaction with magnetic orderand CDW.

Third order nonlinear transport properties in topological chiral antiferromagnetic semimetal CoNb3S6