Whether there is the intrinsic Hall effect in a multi-band superconductor?

The interplay of the microscopic models and the symmetry considerations in application to the superconducting state of putative chiral superconductor Sr2RuO4 are presented. There is demonstrated that chiral two-band superconducting ordering recently proposed as candidate for the superconducting state in this material and having the long-expected property such as the intrinsic Hall effect does not exist as energetically disadvantageous in comparison with the states not supporting the Hall effect. Other chiral multi-band superconducting states with intraband pairing do not support an intrinsic Hall properties as well. The superconducting states with direct interband pairing could serve as the probable candidates for the Hall effect existence.