## 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_{c1} < 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_{c2} < T_{c1} 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}^{L+S} point symmetry.

Original language | English (US) |
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Pages (from-to) | 17-30 |

Number of pages | 14 |

Journal | Journal of Low Temperature Physics |

Volume | 175 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 2014 |

### Funding

Acknowledgements This research is supported by the National Science Foundation (Grant DMR-1106315). We thank David Ferguson for many discussions and critique during the course of this work.

## Keywords

- Confined quantum liquids
- Phase transitions

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- General Materials Science
- Condensed Matter Physics

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