Ordered phases in a bilayer system of dipolar fermions

TL;DR

This paper investigates phase transitions in a bilayer of dipolar fermions, revealing conditions under which stripe or Wigner crystal phases emerge due to interlayer interactions, using density-functional theory.

Contribution

It demonstrates how interlayer interactions induce inhomogeneous phases and maps the conditions favoring stripe or Wigner crystal formations in dipolar fermion bilayers.

Findings

Instability to a one-dimensional stripe phase precedes Wigner crystal formation.

Tuning layer separation can switch the favored phase between stripe and crystal.

Other crystalline symmetries are energetically unfavorable compared to the studied phases.

Abstract

The liquid-to-ordered phase transition in a bilayer system of fermions is studied within the context of a recently proposed density-functional theory [Phys. Rev. A {\bf 92}, 023614 (2015)]. In each two-dimensional layer, the fermions interact via a repulsive, isotropic dipolar interaction. The presence of a second layer introduces an attractive {\em interlayer} interaction, thereby allowing for inhomogeneous density phases which would otherwise be energetically unfavourable. For any fixed layer separation, we find an instability to a commensurate one-dimensional stripe phase in each layer, which always precedes the formation of a triangular Wigner crystal. However, at a certain {\em fixed} coupling, tuning the separation can lead to the system favoring a commensurate triangular Wigner crystal, or one-dimensional stripe phase, completely bypassing the Fermi liquid state. While other crystalline symmetries, with energies lower than the liquid phase can be found, they are never allowed to form owing to their high energetic cost relative to the triangular Wigner crystal and stripe phase.