## CMT154

##
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Edge States and Broken Symmetry Phases in Laterally Confined **^{3}He Films

**Author(s):**
Hao Wu and J. A. Sauls
- Address: Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
- Date: May 2, 2018
**Journal:**
Physical Review B (submitted)
[PDF]
**Abstract:**
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) 3He-A consists of branches of chiral edge
states. The negative energy states are related to the ground-state angular momentum,
L_{z}=(N/2)ℏ, for N/2 Cooper pairs. The power law suppression of the
angular momentum, L_{z}(T)=(N/2)ℏ [1-2/3 (πT/Δ)^{2}]
for 0 ≤ T ≪ 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} ≈ 16ξ_{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 → D_{c2}.
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}≈ 9ξ_{0}, in which
a single p-wave orbital state of Cooper pairs is aligned along the channel.

- Comment: 16 pages, 16 figures

**Eprint:**
[arXiv]