Bose-Einstein Condensation and quasicrystals

TL;DR

This paper investigates the conditions under which Bose-Einstein condensates and supersolids can exist in quasicrystal potentials, showing that most quasicrystals prevent condensate formation in low dimensions, but long-range interactions can enable supersolids.

Contribution

It demonstrates that typical quasicrystal potentials inhibit Bose-Einstein condensation in low dimensions, while long-range interactions can still produce supersolids.

Findings

Most quasicrystal potentials do not support BEC in D≤2.

Supersolids are not possible in quasicrystals at D≤2 with local potentials.

Long-range interactions can enable supersolids in low dimensions.

Abstract

We consider interacting Bose particles in an external local potential. It is shown that large class of external quasicrystal potentials cannot sustain any type of Bose-Einstein condensates. Accordingly, at spatial dimensions $D\leq 2$ in such quasicrystal potentials a supersolid is not possible via Bose-Einstein condensates at finite temperatures. The latter also hold true for the two-dimensional Fibonacci tiling. However, supersolids do arise at $D\leq 2$ via Bose-Einstein condensates from infinitely long-range, nonlocal interparticle potentials.