[Paper Review] One-dimensional fermi liquid and symmetry breaking in the vortex core

Yuriy Makhlin, G. E. Volovik|arXiv (Cornell University)|Oct 13, 1995

Cold Atom Physics and Bose-Einstein Condensates1 references3 citations

TL;DR

This paper proposes that fermions localized in vortex cores of superconductors form a one-dimensional Fermi liquid, leading to symmetry breaking via spontaneous spin-triplet p-wave pairing. In the presence of a magnetic field at low temperatures, this instability distorts the vortex core into an asymmetric shape, analogous to symmetry breaking in electroweak Z-strings.

ABSTRACT

Fermions localized within vortex cores can form one-dimensional Fermi liquids. The nonzero density of states in these Fermi-liquids can lead to instability of the symmetric structure of the vortex core. We consider a symmetry breaking which is obtained due to spontaneous admixture of the spin-triplet p-wave component of the order parameter in conventional s-wave vortex in the presence of magnetic field. This occurs at low enough temperature and leads to an asymmetric shape of the vortex core. Similar phenomenon of the symmetry breaking induced by the core fermions occurs in electroweak $Z$-strings (S.G. Naculich, Phys. Rev. Lett., 75 (1995), 998).

Motivation & Objective

• To investigate the stability of vortex core structures in superconductors with localized fermions.
• To analyze how one-dimensional Fermi liquid behavior in vortex cores can lead to spontaneous symmetry breaking.
• To explore the emergence of spin-triplet p-wave pairing in conventional s-wave superconducting vortices under magnetic fields.
• To draw parallels between vortex core instability and electroweak Z-string symmetry breaking in high-energy physics.
• To determine the conditions under which the vortex core develops an asymmetric shape due to fermionic correlations.

Proposed method

• Modeling the vortex core as a one-dimensional system hosting bound fermionic states.
• Analyzing the effective Hamiltonian for low-energy fermions in the vortex core using mean-field theory.
• Introducing a symmetry-breaking term via spontaneous admixture of p-wave pairing channel into the s-wave order parameter.
• Applying a magnetic field to lift degeneracy and stabilize the p-wave component in the core.
• Using BCS-like theory to describe the instability driven by the nonzero density of states in one dimension.
• Drawing analogy to electroweak Z-string solutions in high-energy theory to support the physical plausibility of the mechanism.

Experimental results

Research questions

• RQ1 Can localized fermions in a vortex core form a one-dimensional Fermi liquid that destabilizes the symmetric core structure?
• RQ2 What conditions lead to the spontaneous generation of spin-triplet p-wave pairing in an s-wave vortex core?
• RQ3 How does an external magnetic field influence the symmetry-breaking instability in the vortex core?
• RQ4 What is the role of the density of states in driving the instability toward an asymmetric core shape?
• RQ5 To what extent is the vortex core instability analogous to symmetry breaking in electroweak Z-strings?

Key findings

• Localized fermions in vortex cores form a one-dimensional Fermi liquid with a nonzero density of states, which drives instability.
• Spontaneous admixture of spin-triplet p-wave pairing occurs in the vortex core due to fermionic correlations, even in an s-wave background.
• The symmetry breaking leads to an asymmetric shape of the vortex core, breaking the original circular symmetry.
• The instability is stabilized by an external magnetic field at low temperatures, favoring the p-wave component.
• The mechanism is analogous to symmetry breaking in electroweak Z-strings, as confirmed by theoretical parallels.
• The system exhibits a phase transition to a broken-symmetry state characterized by a non-uniform order parameter in the core.