Superfluid phase transition of nanoscale-confined helium-3
- URL: http://arxiv.org/abs/2307.08808v1
- Date: Mon, 17 Jul 2023 19:45:54 GMT
- Title: Superfluid phase transition of nanoscale-confined helium-3
- Authors: Canon Sun, Adil Attar, Igor Boettcher
- Abstract summary: We investigate the superfluid phase transition of helium-3 under nanoscale confinement.
The quasi two-dimensional superfluid is described by a reduced 3x2 complex matrix.
We show that mean-field theory predicts precisely two energetically degenerate superfluid orders to emerge at the transition.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We theoretically investigate the superfluid phase transition of helium-3
under nanoscale confinement of one spatial dimension realized in recent
experiments. Instead of the 3x3 complex matrix order parameter found in the
three-dimensional system, the quasi two-dimensional superfluid is described by
a reduced 3x2 complex matrix. It features a nodal quasiparticle spectrum,
regardless of the value of the order parameter. The origin of the 3x2 order
parameter is first illustrated via the two-particle Cooper problem, where
Cooper pairs in the $p_x$ and $p_y$ orbitals are shown to have a lower bound
state energy than those in $p_z$ orbitals, hinting at their energetically
favorable role at the phase transition. We then compute the Landau free energy
under confinement within the mean-field approximation and show that the
critical temperature for condensation of the 3x2 order parameter is larger than
for other competing phases. Through exact minimization of the mean-field free
energy, we show that mean-field theory predicts precisely two energetically
degenerate superfluid orders to emerge at the transition that are not related
by symmetry: the A-phase and the planar phase. Beyond the mean-field
approximation, we show that strong-coupling corrections favor the A-phase
observed in experiment, whereas weak-coupling perturbative renormalization
group predicts the planar phase to be stable.
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