## CMT145

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Superfluid phases of **^{3}He in nano-scale channels

**Author(s):**
Joshua J. Wiman and J. A. Sauls
- Address: Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
- Date: October 6, 2015
**Journal:**
Physical Review B 92, 144515 (2015)
[DOI]
**Abstract:**
Confinement of superfluid ^{3}He on length scales comparable to the radial size of the p-wave
Cooper pairs can greatly alter the phase diagram by stabilizing broken symmetry phases not observed
in bulk ^{3}He.
We consider superfluid ^{3}He confined within long cylindrical channels of radius 100 nm, and
report new
theoretical predictions for the equilibrium superfluid phases under strong confinement. The results are
based on the strong-coupling formulation of Ginzburg-Landau theory with precise numerical minimization
of the free energy functional to identify the equilibrium phases and their regions of stability. We
introduce an extension of the standard GL strong-coupling theory that accurately accounts for the phase
diagram at high pressures, including the tri-crital point and TAB(p) line defining the region of stability
for the bulk A-phase. We also introduce tuneable boundary conditions that allow us to explore boundary
scattering ranging from maximal to minimal pairbreaking, and report results for the phase diagram as a
function of pressure, temperature, and boundary conditions. Four stable phases are found: a polar phase
stable in the vicinity of T_{c}, a strongly anisotropic, cylindrical analog of the bulk B phase
stable at
sufficiently low temperatures, and two chiral A-like phases with distinctly different orbital symmetry,
one of which spontaneously breaks rotation symmetry about the axis of the cylindrical channel. The
relative stability of these phases depends sensitively on pressure and the degree of pairbreaking by
boundary scattering. The broken symmetries exhibited by these phases give rise to distinct signatures in
transverse NMR resonance spectroscopy. We present theoretical results for the transverse NMR frequency
shifts as functions of temperature, the r.f. pulse tipping angle and the static NMR field orientation.

- Comment:
13 pages, 15 figures

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