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We discuss the orbital angular momentum (OAM) and the edge mass current inneutral fermionic superfluids with broken time reversal symmetry. Recent meanfield studies imply that total OAM of a uniform superfluid depends on boundaryconditions and is not a thermodynamic quantity. We point out that this does notconflict with thermodynamics, because there is no intensive external fieldconjugate to OAM with which a uniform superfluid is stable in the thermodynamiclimit, in sharp contrast to the orbital magnetization in a non-superfluidsystem. We establish a simple physical picture for the sensitivity of OAM toboundaries by introducing the notion of "unpaired fermions" and "fermionicLandau criterion" within a mean field description. In order to go beyond themean field approximation, we perform a density matrix renormalization groupcalculation and conclude that the mean field understanding is essentiallycorrect.

Non-thermodynamic nature of the orbital angular momentum in neutral fermionic superfluids