Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids

TL;DR

This paper investigates the orbital angular momentum in two-dimensional chiral superfluids, revealing a universal value in the BEC regime and a suppressed value in the BCS regime for higher angular momentum states, linked to edge modes.

Contribution

It provides a detailed analysis of spectral asymmetry and flow, showing how edge modes influence OAM in different superfluid regimes, especially for higher angular momentum states.

Findings

In the BEC regime, L_z = νN/2 for all integer ν.

In the BCS limit, L_z is suppressed for ν ≥ 2, much less than N.

Edge modes and depairing effects explain the differences in OAM behavior.

Abstract

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.