Renormalization Group Flows for Superfluid 3He under Confinement

• Author / Creator

  Attar, Adil A

• We theoretically investigate the effect of fluctuations in the order parameter on the
  phase transition of 3He under nanoscale confinement of one spatial dimension realized
  in recent experiments. We derive a new quasi two-dimensional free energy that relies
  on a 3×2 complex matrix instead of the 3×3 complex matrix order parameter found
  in the three-dimensional system. We minimize the quasi two-dimensional free energy
  and present two energetically degenerate phases that are predicted: the A-phase and
  the planar phase.
  Beyond the mean-field approximation, we calculate the RG flow in the three-dimensional, two-dimensional, and quasi two-dimensional limits. We derive the perturbative flow equations for all quartic coupling constants with non-trivial kinetic
  factor. We find that the B-phase is energetically favoured in the three-dimensional
  system in agreement with experiment. In contrast, in the quasi two-dimensional
  limit, weak-coupling perturbative renormalization group predicts the planar phase to
  be energetically favoured. However, strong-coupling corrections favour the A-phase
  observed in experiment.
  We derived FRG flow equations for the 3D, 2D and quasi-2D cases with non-trivial
  kinetic factor. In the quasi-2D limit, we found that the A-phase was favoured over
  the planar phase for certain levels of confinement. These confinement scales were
  also confirmed to have a prominent Fermi liquid to A-phase transition in experiment.
  Due to the unstable fixed point, we find that under confinement there is a fluctuation-induced first-order transition to the A-phase.

• Subjects / Keywords

  • Physics
  • Condensed Matter
  • Superfluid Helium

• Graduation date

  Spring 2024

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-5ks0-ty05

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.