Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids

We study the orbital angular momentum (OAM) $L_z$ in two dimensional chiral $(p_x+ip_y)^{\nu}$-wave superfluids (SF) of $N$ fermions on a disc at zero temperature, in terms of spectral asymmetry and spectral flow. It is shown that $L_z=\nu N/2$ for any integer $\nu$, in the BEC regime. In contrast, in the BCS limit, while the OAM is $L_z=N/2$ for the $p+ip$-wave SF, for chiral SF with $\nu\geq2$, the OAM is remarkably suppressed as $L_z=N\times O(\Delta_0/\varepsilon_F)\ll N$, where $\Delta_0$ is the gap amplitude and $\varepsilon_F$ is the Fermi energy. We demonstrate that the difference between the $p+ip$-wave SF and the other chiral SFs in the BCS regimes originates from the nature of edge modes and related depairing effects.