## CMT142

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

**Author(s):**
J. J. Wiman and J. A. Sauls
- Address: Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
- Date: July 27, 2013
**Journal:**
J. Low Temp. Phys. 175, 17-30 (2014)
[DOI]
**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**^{L+S}_{4h} point symmetry.

- Comment: 14 pages, 4 figures

**Eprint:**
[arXiv]
[PDF]