Bose-Einstein condensation in multilayers

TL;DR

This paper investigates how layered structures affect Bose-Einstein condensation temperature, revealing a minimum at a specific layer separation and showing how interlayer interactions influence critical temperature and specific heat features.

Contribution

It introduces a model for non-interacting bosons in layered structures, analyzing the effects of layer separation and penetrability on BEC temperature and thermodynamic properties.

Findings

Critical temperature has a minimum at a specific layer separation.

Reducing layer separation increases the critical temperature.

Additional specific heat features appear due to layering effects.

Abstract

The critical BEC temperature $T_{c}$ of a non interacting boson gas in a layered structure like those of cuprate superconductors is shown to have a minimum $T_{c,m}$, at a characteristic separation between planes $a_{m}$. It is shown that for $a<a_{m}$, $T_{c}$ increases monotonically back up to the ideal Bose gas $T_{0}$ suggesting that a reduction in the separation between planes, as happens when one increases the pressure in a cuprate, leads to an increase in the critical temperature. For finite plane separation and penetrability the specific heat as a function of temperature shows two novel crests connected by a ridge in addition to the well-known BEC peak at $T_{c}$ associated with the 3D behavior of the gas. For completely impenetrable planes the model reduces to many disconnected infinite slabs for which just one hump survives becoming a peak only when the slab widths are infinite.