Ground-state angular momentum, spectral asymmetry, and topology in chiral superfluids and superconductors

Abstract

Recently, it was discovered that the ground-state orbital angular momentum in two-dimensional chiral superfluids with pairing symmetry ${({p}_{x}+i{p}_{y})}^{\ensuremath{\nu}}$ depends on the winding number $\ensuremath{\nu}$ in a striking manner. The ground-state value for the $\ensuremath{\nu}=1$ case is ${L}_{z}=\ensuremath{\hbar}N/2$ as expected by counting the Cooper pairs, while a dramatic cancellation takes place for $\ensuremath{\nu}>1$. The origin of the cancellation is associated with the topological edge states that appear in a finite geometry and give rise to a spectral asymmetry. Here, we study the reduction of orbital angular momentum for different potential profiles and pairing strengths, showing that the result ${L}_{z}=\ensuremath{\hbar}N/2$ is robust for $\ensuremath{\nu}=1$ under all studied circumstances. We study how angular momentum depends on the gap size $\mathrm{\ensuremath{\Delta}}/{E}_{F}$ and obtain the result ${L}_{z}=\frac{\ensuremath{\hbar}\ensuremath{\nu}}{2}N(1\ensuremath{-}\frac{\ensuremath{\mu}}{{E}_{F}})$ for $\ensuremath{\nu}=2,3$. Thus, the gap dependence of ${L}_{z}$ for $\ensuremath{\nu}<4$ enters at most through the chemical potential while $\ensuremath{\nu}\ensuremath{\ge}4$ is qualitatively different. In addition, we generalize the spectral asymmetry arguments to total angular momentum in the ground state of triplet superfluids where due to a spin-orbit coupling ${L}_{z}$ is not a good quantum number. We find that the ground-state total angular momentum also behaves very differently depending on total angular momentum of the Cooper pairs.