Triple-core structure of the double-core vortex in superfluid $^3$He-B

Abstract

The order parameter of superfluid $^3$He involves nine complex components, and the multicomponent structure allows quantized vortices in superfluid $^3$He to have complicated cores. One of the vortices found in the B phase is the double-core vortex, which has been often described as a pair of two half-quantum vortices (HQVs) connected by a domain wall. Our numerical calculations of the core structure suggest an alternative representation of the vortex as a combination of three vortices, one in each component of the spin-triplet superfluid. Based on the results we present a qualitative analytical model for the triple-core structure of the double-core vortex. Additionally we numerically calculate the structure of a double-core vortex stretched between pinning sites, and show that the HQV picture becomes more applicable when separation between subcores becomes large.

Figures (2)

• Figure 1: A double-core vortex with the two half-cores aligned along the $y$ axis. The data is taken from a numerical calculation at $p = 20$ bar and $T = 0.80T_{\rm{c}}$. Distances are given in units of the temperature and pressure dependent Ginzburg-Landau coherence length $\xi\approx 30\text{ nm}$. (Left) The spatial profile of the order parameter in the angular momentum basis in the region $x,y\in [-10\xi, 10\xi]$. The amplitudes are shown for all nine components and the phase for the three components with phase winding in the bulk. The three distinct subcores are clearly visible in the $C_{-+}$, $C_{00}$, and $C_{+-}$ components. (Right) The same order parameter amplitudes on the $y$ axis. The half-cores are located at $y = \pm 3.5\xi$.
• Figure 2: The order parameter along the $y$ axis for a stretched double-core vortex calculated at $p = 20\text{ bar}$ and $T = 0.80T_{\rm{c}}$. The lines represent the components as labeled in Figure \ref{['fig:doublecorecomponents']}. The pinning sites are cylindrical obstacles with a diameter of $\xi$, marked by the grey regions. The state shown in panel (a) corresponds to $7\xi$ distance between cores, which is the equilibrium distance found in the bulk. Panels (b), (c) and (d) correspond to spacings of $15\xi$, $25\xi$ and $40\xi$, respectively.