Triangular pair density wave in confined superfluid ${}^3$He

Abstract

Recent advances in experiment and theory suggest that superfluid ${}^3$He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wavevectors, of possibly square or hexagonal symmetry. In this Letter, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau's theory of the liquid-solid transition. A soft-mode instability at finite wavevector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wavevectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice.

main text: 6 pages, 4 figures; supplemental material: 17 pages, 1 figure, 9 animated plots (see ancillary files). v2: published version

References in corpus (9)

• Classification of topological insulators and superconductors in three spatial dimensions
• Thermodynamic properties of thin films of superfluid 3He-A
• Crystalline order in superfluid 3He films
• Nodal $d+id$ pairing and topological phases on the triangular lattice: unconventional superconducting state of Na${}_x$CoO${}_2\cdot y$H${}_2$O
• Strong Coupling Corrections to the Ginzburg-Landau Theory of Superfluid ^{3}He
• Hard domain walls in superfluid 3He-B
• Surface Majorana fermions and bulk collective modes in superfluid 3He-B
• Domain Walls in Superfluid 3He-B
• Bosonic Surface States and Acoustic Spectroscopy of Confined Superfluid ${}^3$He-B

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• Anomalous dispersion of shear waves in dipolar supersolids
• Superfluid phase transition of nanoscale-confined helium-3
• Dimensional crossover of superfluid ${}^3$He in a magnetic field
• Spin-triplet pair density wave superconductors
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors