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•The investigation of the dissipationless momentum transport in topological superconductors with broken time reversal symmetry is done.•The calculations should be done in the low-momentum limit and is valid for all frequencies.•The dissipationless momentum transport has a resonance feature which arises from “the intrinsic mechanism” and appears even at finite temperatures.•There are three types of terms that only two types of them contributes to the chirality region.
The Hall viscosity known as the anti-symmetric part of the viscosity fourth-rank tensor. Such dissipationless response which appears for systems with broken time reversal symmetry. We calculate this non-dissipative quantity for a chiral two-orbital superconductor placed in a viscoelastic magnetic field using the linear response theory and apply our calculations to the putative multiband chiral superconductor Sr2RuO4. The chirality origin of a multiband superconductor arises from the interorbital coupling of the superconducting state. This feature leads to the robustness of the Hall viscosity against temperature and impurity effects. We study the temperature effect on the Hall viscosity at the one-loop approximation.