Surface-induced vortex core restructuring in a spin-triplet superfluid

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Surface-induced vortex core restructuring in a spin-triplet superfluid".

Mira: Here's the gist of the paper. Surface-induced vortex core restructuring in a spin-triplet superfluid shows that vortex structure at the surface can be distinct from that in bulk, originating from the interaction of spin and orbital degrees of freedom with a surface Vortex Structure in Bulk In zero magnetic field, two superfluid phases of 3He exist in bulk: the A phase at higher pressures and temperatures and the B phase in the rest of the pressure-temperature phase diagram The order parameter in the B phase is given by A = ∆Be iϕR, where ∆B is the amplitude and R a rotation matrix that describes the relative orientation of the spin and orbital spaces Around a quantized vortex in 3He-B, the phase ϕ winds by 2π, which is associated with a superfluid mass flow The bulk amplitude is recovered at a radius of several Ginzburg-Landau coherence lengths ξ In a multicomponent system the cost of condensation energy from the suppression of the bulk order parameter in the vortex core can be compensated by the appearance of other non-rotating components that fill the core and form superfluid phases distinct from bulk In 3He-B there are two such non-singular vortex structures which are realized in experiments The A-phase-core vortex is axially symmetric Its core is dominated by the A-phase order parameter A = ∆Adˆ(mˆ + inˆ) (2), where dˆdescribes the spin direction of the Cooper pairs and mˆ and nˆ define the direction of the orbital angular momentum ˆl = mˆ × nˆ The double-core vortex has a more complicated order parameter due to broken axial symmetry The core is split into two subcores connected by a planar phase wall In order to join the superfluid phase in the core to the B phase outside in an energetically optimal way, there is bending of the order parameter on approach to the vortex This means that R in Eq.

Kai: (1) deviates from its bulk value R(ϑ0) in a region known as a soft core The size of the soft core is controlled by the spin-orbit interaction and is about 10 µm, much larger than the coherence length ξ In the bulk vortex αb = 0 due to translational symmetry along z and we want to minimize the bending, that is θb and βb Vortices at the Surface The surface provides two important effects for the structure of the vortex core.

Mira: First, the surface breaks translation symmetry along the vortex.

Kai: Second, quasiparticle scattering at the surface distorts the order parameter near the boundary The calculations reveal a dramatic change in the vortex core structure near the boundary Two types of behavior are found depending on the relative orientation of the vortex soft core p and the inwards pointing surface normal wˆ At a left-handed end, the A-phase core expands and forms a ”funnel” shape at the boundary This structure appears independently of the boundary conditions, temperature and pressure in all our simulations At a right-handed end, the A-phase core contracts, while the double core is stable The extent of the funnel at the left-handed end increases with surface specularity, being the largest for a fully specular surface Such a surface favors the Aphase funnel so much that at an originally right-handed end we observe a spontaneous reversal of the soft-core orientation, resulting in a vortex with two left-handed ends Two vortex segments with opposite softcore orientations are joined via a singular defect (the ”ovortex”

31: ) Origin of the Surface Effect The observed vortex restructuring is found to originate from the interaction of the spin and orbital degrees of freedom of the order parameter in presence of a surface We explain our observations on the basis of the gradient energy for the spintriplet p-wave pairing fgrad = K1∇iA∗µj∇iAµj + K2∇iA∗µi∇jAµj + K3∇iA∗µj∇jAµi (3), where the coefficients K1, K2 and K3 are of the same order

32: Triplet-specific physics originates from the K2 and K3 terms These terms connect spatial coordinates (gradient indices) to the orbital directions (second index of the A matrix) A well-known consequence of this is an induced anisotropy of the order parameter near the surface where, in particular, the A phase with ˆl along the surface normal becomes energetically favored over the B phase Surface-induced suppression leading to the gradient of the order parameter along the surface normal (z direction) allows the reduction of the energy of the system by forming an appropriate gradient in the direction along the surface (x, y) owing to the terms mixing linear gradients in Eq.

Title and authors: Kai: So, to recap where we are, this paper is about how a vortex core changes its shape when it's near a surface in a spin-triplet superfluid, and the authors point out that the structure can be totally different from what you see deep inside the bulk.

Mira: They explain that this restructuring is driven by the interaction between spin-orbit coupling in triplet pairing and the symmetry breaking caused by being at a surface. That's where things get interesting for me as we think about these complex order parameters.

Lev: From an error correction standpoint, if you're building hardware, this means your models for vortex dynamics near surfaces are going to be way more complex than just looking at the bulk behavior.

Kai: Yeah, and the paper shows that this effect is asymmetric depending on whether you look at a left-handed or right-handed end of the vortex relative to the surface normal.

Mira: That asymmetry is driven by how spin currents around the vortex interact with those topological surface spin currents in 3He-B, which shifts the energy balance and changes the core size <ref:2604.12682#pg1>.

The paper's summary: Kai: The paper summarizes finding that there are two main behaviors depending on whether you're looking at a left-handed or right-handed end of the vortex near a surface.

Mira: At a left-handed end, the A-phase core actually expands and forms what they call a "funnel" shape right at the boundary.

Lev: That funnel structure is something we have to model carefully on real hardware because it depends on the specific boundary conditions like maximum pairbreaking or specular ones.

Kai: And at a right-handed end, things contract, but they show that the double core structure can remain stable there.

Mira: But the most striking part is that at a left-handed end, as you increase surface specularity, the size of that funnel increases dramatically to its largest extent for a fully specular surface.

The paper's improvements: Kai: One of the main improvements suggested is that they show how this funnel structure can spontaneously lead to a reversal of the soft core orientation at an originally right-handed end.

Mira: That spontaneous reversal results in a vortex with two left-handed ends connected by what they call a singular defect, which is like an "ovortex."

Lev: From an experimental standpoint, detecting these defects would be tricky because they are pushed away from the boundary into the bulk until the surface funnel gradient becomes negligible.

Kai: The paper also shows that in restricted geometries, like thin slabs of superfluid 3He with thicknesses around seven hundred nanometers or one thousand five hundred nanometers, this surface effect becomes especially important.

Conclusion: Mira: So, to wrap up the "Surface-induced vortex core restructuring in a spin-triplet superfluid," the main implication is that what we see near a surface might not reflect the bulk structure at all.

Kai: And it shows that this effect comes from combining spin-orbit interaction with symmetry breaking at the surface, which means our bulk models are incomplete without accounting for these boundary conditions.

Lev: If you're building hardware, you need to consider that these surface-limited vortex core observations in a triplet candidate system may not reflect the bulk structure, so your assumptions about error rates need to be checked against this new boundary physics.

Kai: So we see that the funnel shape at the left-handed end and the double core stability at the right-handed end are key features dictated by those surface interactions.

Mira: It really highlights how important it is to look closely at these details when interpreting vortex measurements in solid state systems, ensuring our conclusions aren't based only on potentially misleading surface observations.

Lev: We need to keep this boundary physics in mind as we design the next generation of error-correction protocols for these complex superfluids.