Analytical theory of enhanced Bose–Einstein condensation in thin films

Abstract

We present an analytically solvable theory of Bose–Einstein condensation (BEC) in thin film geometries. Analytical closed-form expressions for the critical temperature are obtained in both the low-to-moderate confinement regime (where the film thickness L is in the order of microns) as well as in the strong confinement regime where the thickness is in the order of few nanometers or lower. The possibility of high-temperature BEC is predicted in the strong confinement limit, with a square-root divergence of the critical temperature T c ∼ L −1/2. For cold Bose gases, this implies an enhancement up to two orders of magnitude in T c for films on the nanometer scale. Analytical predictions are also obtained for the heat capacity and the condensate fraction. A new law for the heat capacity of the condensate, i.e. C ∼ T 2, is predicted for nano-scale films, which implies a different λ-point behavior with respect to bulk systems, while the condensate fraction is predicted to follow a [ 1 − ( T / T c ) 2 ] law.

Extended analytical BCS theory of superconductivity in thin films

“…[15,17] for phonons/elastic waves and bosons, respectively, and the result for phonons is summarized in Fig. 2 of [15]. For the example of phonons, as discussed in Ref.…”

“…In this work, following the ideas from Refs. [15][16][17][18], we consider a system confined in the z-direction, as shown in Fig. 1, and unconfined in the x and y directions; the following discussion is hence directly relevant to the study of the physics of thin films.…”

“…This was done in Refs. [15,17] for phonons/elastic waves and bosons, respectively, and the result for phonons is summarized in Fig. 2 of [15].…”