Pair-breaking as the fundamental limit to persistent-current stabilization in fermionic superfluids

TL;DR

The paper investigates the stability of persistent currents in fermionic superfluids within the weakly coupled BCS regime in a ring geometry, focusing on how impurities affect dissipation and topological stability. The authors employ time-dependent superfluid local density approximation (TD-SLDA) to simulate dynamics at $a_s k_F = -1$, imprint a phase winding $w_0$, and vary impurity size $s$ and density $N_d$, monitoring $E_{flow}$ and $E_{cond}$ to diagnose dissipation and pair breaking. They find that pair breaking imposes a fundamental limit on current stability through a threshold $w_ ext{pb}$; below this threshold impurities can enhance stability but dissipation persists via pair breaking, while above it vortices nucleate and drive topological relaxation. Impurity size and spacing strongly modulate vortex mobility and pinning, yielding regimes of collective pinning and hopping, yet pinned vortices do not guarantee dissipationless flow due to ongoing pair breaking. The study identifies pair breaking as the intrinsic limit to persistent-current stability in fermionic superfluids, with implications for ultracold Fermi gases and neutron-star matter and highlighting a clear distinction from bosonic (BEC) systems.

Abstract

We study the stability of persistent currents in fermionic superfluids with impurities within the BCS regime by using time-dependent density functional theory. Unlike in Bose-Einstein condensates, we find that current stabilization by impurities is intrinsically limited by the pair-breaking threshold. Below the threshold, impurities enhance winding number stability, but pair-breaking continues to drive dissipation of the flow. Above this critical velocity, superflow destabilizes, emitting vortices. Impurities then govern vortex mobility and pinning, exhibiting regimes of collective pinning and hopping. Moreover, pinned vortices do not guarantee dissipationless flow due to ongoing pair-breaking. Our results identify pair breaking as the fundamental mechanism that sets the ultimate limit of persistent-current stability in fermionic superfluids, providing insights relevant to ultracold Fermi gases and neutron-star matter.

Figures (3)

• Figure 1: (a) Magnitude of the pairing field $|\Delta(x,y)|$ for $w_0 = 7$ in the absence of impurities ($N_d = 0$) and with $N_d = 6$ impurities, shown at $t\varepsilon_F \approx 400$. The impurity size is $s_2=0.67\xi$. The imposed flow direction and vortex positions are indicated by the swirling arrows. (b) Flow–energy decay rate $A/\tau$ for the impurity size $s_1 = 1.33\xi$ as a function of the winding number $w_0$ and the number of impurities $N_d$. The grey markers separate the unstable regime, where the winding number decays, from the stable regime, where $w(t)$ remains constant. The dashed black line marks the pair-breaking threshold $w_\mathrm{pb}$ for this configuration.
• Figure 2: Dissipation mechanisms of persistent currents in the presence of impurities. (a) Flow–energy decay rate $A/\tau$ obtained from exponential fits for impurity sizes $s = 1.33\xi$ (main panel) and $s = 0.67\xi$ (inset). (b) Time evolution of the winding number $w(t)$ for $s = 1.33\xi$. (c) Per-particle flow–energy change $\delta E_\mathrm{flow}/N$ between initial and final states. (d) Condensation–energy change $\delta E_\mathrm{cond}$ highlighting pair-breaking effects. Panels (c) and (d) show that the impurity size primarily governs variations in the flow and condensation energies, rather than the topological properties of the order parameter, which in turn are encoded in $w(t)$.
• Figure 3: (a,b) Radial and angular vortex mobilities as functions of the number of impurities $N_d$ for two impurity sizes, at $w_0 = 7$. (c) Two-dimensional vortex trajectories for $w_0 = 7$ for different numbers of impurities and their sizes.