Superfluid phases of ${}^3$He in a periodic confined geometry

Abstract

Predictions and discoveries of new phases of superfluid ${}^3$He in confined geometries, as well as novel topological excitations confined to surfaces and edges of near a bounding surface of ${}^3$He, are driving the fields of superfluid ${}^3$He infused into porous media, as well as the fabrication of sub-micron to nano-scale devices for controlled studies of quantum fluids. In this report we consider superfluid ${}^3$He confined in a periodic geometry, specifically a two-dimensional lattice of square, sub-micron-scale boundaries ("posts") with translational invariance in the third dimension. The equilibrium phase(s) are inhomogeneous and depend on the microscopic boundary conditions imposed by a periodic array of posts. We present results for the order parameter and phase diagram based on strong pair breaking at the boundaries. The ordered phases are obtained by numerically minimizing the Ginzburg-Landau free energy functional. We report results for the weak-coupling limit, appropriate at ambient pressure, as a function of temperature T, lattice spacing L, and post edge dimension, $d$. For all $d$ in which a superfluid transition occurs, we find a transition from the normal state to a periodic, inhomogeneous "polar" phase with $T_{c_1}<T_c$ for bulk superfluid ${}^3$He. For fixed lattice spacing, L, there is a critical post dimension, d_c, above which only the periodic polar phase is stable. For $d<d_c$ we find a second, low-temperature phase onsetting at $T_{c_2}<T_{c_1}$ from the polar phase to a periodic "B-like" phase. The low temperature phase is inhomogeneous, anisotropic and preserves time-reversal symmetry, but unlike the bulk B-phase has only $D_{4h}$ point symmetry.

14 pages, 4 figures. Journal of Low Temperature Physics (2013)

References in corpus (5)

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• Thermodynamic properties of thin films of superfluid 3He-A
• Crystalline order in superfluid 3He films
• Chirality of superfluid 3He-A
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• Study of superfluid ${}^3$He under nanoscale confinement. A new approach to the investigation of superfluid ${}^3$He films
• Andreev Bound States in Superconducting Films and Confined Superfluid He-3
• Triangular pair density wave in confined superfluid ${}^3$He
• Path-Dependent Supercooling of the ${}^3$He Superfluid A-B transition
• Thermal transport of helium-3 in a strongly confining channel
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• Vortex-bound solitons in topological superfluid ${}^3$He
• Ultrasonic Interferometer for First-Sound Measurements of Confined Liquid 4He
• Anomalous Thermal Hall Effect in Chiral Phases of ${}^3$He-Aerogel
• Dimensional crossover of superfluid ${}^3$He in a magnetic field