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 $(p_x+i{p}_y{)}^{\nu }$ depends on the winding number $\nu$ in a striking manner. The ground state value for the $\nu =1$ case is $L_z=\hslash N/2$ as expected by counting the Cooper pairs, while a dramatic cancellation takes place for $\nu >1$. 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 $L_z=\hslash N/2$ is robust for $\nu =1$ under all studied circumstances. We study how angular momentum depends on the gap size $\Delta /E_F$ and obtain the result $L_z=\frac{\hslash \nu }{2}N(1-\frac{\mu }{E_F})$ for $\nu =2,3$. Thus, the gap-dependence of $L_z$ for $\nu <4$ enters at most through the chemical potential while $\nu \ge 4$ is qualitatively different. In addition, we generalize the spectral asymmetry arguments to \emph{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.

11 pages, 12 figures

References in corpus (10)

• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Role of the Majorana Fermion and the Edge Mode in Chiral Superfluidity near a p-Wave Feshbach Resonance
• Vanishing edge currents in non-$p$-wave topological chiral superconductors
• Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids
• Non-topological nature of the edge current in a chiral p-wave superconductor
• Current inversion at the edges of a chiral $\mathbf{p}$-wave superconductor
• Chern mosaic - topology of chiral superconductivity on ferromagnetic adatom lattices
• Orbital momentum of chiral superfluids and spectral asymmetry of edge states
• Bulk angular momentum and Hall viscosity in chiral superconductors
• Orbital angular momentum in a nonchiral topological superconductor

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• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Non-thermodynamic nature of the orbital angular momentum in neutral fermionic superfluids
• Floquet vortex states induced by light carrying the orbital angular momentum
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Interband interference effects at the edge of a multiband chiral p-wave superconductor
• Directly Detecting the Edge Current in a $p_x+i{p}_y$ Topological Superfluid
• Topological Superfluids
• Orbital angular momentum in a topological superconductor with Chern number higher than $1$
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Vortices in Two-Dimensional Chiral Superfluids