[Paper Review] Frustrated superconductivity and sextetting order

Zhiming Pan, Lu Chen+2 more|arXiv (Cornell University)|Sep 27, 2022

Physics of Superconductivity and Magnetism4 citations

TL;DR

This paper proposes a mechanism for sextetting order in superconductors arising from phase frustration in a pair-density-wave (PDW) state with a vortex-antivortex honeycomb lattice. By mapping the superconducting phase coherence to a three-coloring model, the system exhibits macroscopic degeneracy and extensive entropy, stabilizing a charge-6e sextetting order above the superconducting transition temperature $T_c$, with $1/3$-fractional vortices as fundamental topological defects that explain fractional flux oscillations in CsV₃Sb₅.

ABSTRACT

The superconducting state typically favors a uniform spatial distribution akin to ferromagnetism. Nevertheless, the pair-density-wave state exhibits sign changes in the pairing order, leading to potential frustrations in phase coherence.We propose a mechanism to the sextetting order stemming from the frustrations in the phase coherence of a pair-density-wave state, whose spatial modulation manifests a vortex-antivortex honeycomb lattice. The classical ground state configurations are mapped to Baxter's three-coloring model, revealing a macroscopic degeneracy accompanied by extensive entropy. The phase coherence problem intertwines the U(1) phases and the vorticity variables. While the resultant color and phase fluctuations suppress the pair-density-wave order, they maintain the sextetting order above the superconducting transition temperature ($T_{ ext{c}}$). The $1/3$-fractional vortex emerges as the fundamental topological defect in the sextetting order. This novel mechanism of frustrated superconductivity provides an alternative explanation for the experimental observed fractional oscillations in CsV$_3$Sb$_5$.

Motivation & Objective

• To explain the experimental observation of $hc/6e$ quantum oscillations in CsV₃Sb₅ above $T_c$.
• To identify a mechanism for charge-6e sextetting order arising from phase frustration in a PDW state.
• To establish a connection between the three-coloring model and superconducting phase coherence in vortex-antivortex lattices.
• To demonstrate that sextetting order persists above $T_c$ due to extensive entropy from degenerate color configurations.
• To show that $1/3$-fractional vortices emerge as topological defects in the sextetting state.

Proposed method

• Map the PDW state's phase coherence problem to the classical three-coloring model on a honeycomb lattice, enforcing the constraint that three bonds at each vertex have distinct colors.
• Identify the U(1) phase variables and discrete vorticity variables as the fundamental degrees of freedom in the frustrated system.
• Use Monte Carlo simulations to explore the phase diagram and analyze the competition between Cooper pairing and sextetting order.
• Derive the low-energy effective theory coupling phase fluctuations to vorticity, showing suppression of PDW order but stabilization of sextetting order.
• Analyze the local density of states (LDOS) patterns to distinguish $3Q$ and $6Q$ PDW states via wavevector peaks at $\pm(\mathbf{Q}_i - \mathbf{Q}_j)$ and $\pm 2\mathbf{Q}_i$.
• Generalize the three-coloring model to a four-coloring model on a diamond lattice to explore potential charge-8e states in three dimensions.

Experimental results

Research questions

• RQ1 How can phase frustration in a PDW state lead to a stable sextetting (charge-6e) order above $T_c$?
• RQ2 What is the role of macroscopic degeneracy and extensive entropy in stabilizing the sextetting order?
• RQ3 How do $1/3$-fractional vortices emerge as topological defects in the sextetting state?
• RQ4 Can the three-coloring model accurately describe the phase coherence and topological structure of the PDW vortex-antivortex lattice?
• RQ5 What experimental signatures, such as LDOS patterns or flux oscillations, distinguish the $3Q$ and $6Q$ PDW states?

Key findings

• The classical ground state of the frustrated PDW system maps to the three-coloring model on a honeycomb lattice, exhibiting macroscopic degeneracy and extensive entropy of $0.38k_B$ per hexagon.
• Above $T_c$, the sextetting (charge-6e) order persists due to the entropy of color configurations, outcompeting the conventional Cooper pairing (charge-2e) order.
• The $1/3$-fractional vortex emerges as the fundamental topological defect, with its core pinned in mesoscopic rings, leading to $hc/6e$ flux oscillations.
• Monte Carlo simulations confirm the phase diagram where sextetting order dominates above $T_c$ before full disorder sets in.
• The LDOS pattern for the $6Q$ state shows additional peaks at $\pm 2\mathbf{Q}_i$, distinguishing it from the $3Q$ state and providing a detectable signature.
• The model generalizes to a four-coloring model on a diamond lattice, suggesting a possible route to charge-8e states in three-dimensional systems.