358 research outputs found

### Spectrum of third sound cavity modes on superfluid $^3$He films

We report theoretical calculations of the spectrum of third sound modes for a
cylindrically symmetric film of superfluid $^3$He, and compare these results
with experimental data for the mode frequencies and amplitude spectrum of
surface waves of superfluid $^3$He films.Comment: 8 pages, 5 figures, LaTeX, submitted to JLT

### Edge States and Broken Symmetry Phases of Laterally Confined $^3$He Films

Broken symmetries in topological condensed matter systems have implications
for the spectrum of Fermionic excitations confined on surfaces or topological
defects. The Fermionic spectrum of confined (quasi-2D) $^3$He-A consists of
branches of chiral edge states. The negative energy states are related to the
ground-state angular momentum, $L_z = (N/2) \hbar$, for $N/2$ Cooper pairs. The
power law suppression of the angular momentum, $L_z(T) \simeq (N/2)\,\hbar\,[1
- \frac{2}{3}(\pi T/\Delta)^2 ]$ for $0 \le T \ll T_c$, in the fully gapped 2D
chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We
discuss the effects of wave function overlap, and hybridization between edge
states confined near opposing surfaces on the edge currents, ground-state
angular momentum and ground-state order parameter. Under strong lateral
confinement, the chiral A phase undergoes a sequence of phase transitions,
first to a pair density wave (PDW) phase with broken translational symmetry at
$D_{c2} \approx 16 \xi_0$. The PDW phase is described by a periodic array of
chiral domains with alternating chirality, separated by domain walls. The
period of PDW phase diverges as the confinement length $D\rightarrow D_{c_2}$.
The PDW phase breaks time-reversal symmetry, translation invariance, but is
invariant under the combination of time-reversal and translation by a one-half
period of the PDW. The mass current distribution of the PDW phase reflects this
combined symmetry, and orignates from the spectra of edge Fermions and the
chiral branches bound to the domain walls. Under sufficiently strong
confinement a second-order transition occurs to the non-chiral "polar phase" at
$D_{c1} \approx 9\xi_0$, in which a single p-wave orbital state of Cooper pairs
is aligned along the channel.Comment: 16 pages, 16 figure

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