Analytical theory of enhanced Bose-Einstein condensation in thin films

Abstract

We present an analytically solvable theory of Bose-Einstein condensation 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 $T_c\sim L^{-1/2}$. 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. $C\sim T^2$, is predicted for nano-scale films, which implies a different $\lambda$ point behaviour with respect to bulk systems, while the condensate fraction is predicted to follow a $[1-(T/T_c{)}^2]$ law.

References in corpus (6)

• Bose-Einstein condensation of photons in an optical microcavity
• Evidence of high-temperature exciton condensation in 2D atomic double layers
• Observation of shell effects in superconducting nanoparticles of Sn
• Spatially Modulated Superfluid State in Two-Dimensional ${}^4$He Films
• Universal $L^{-3}$ finite-size effects in the viscoelasticity of confined amorphous systems
• Thermodynamics of Trapped Photon Gases at Dimensional Crossover from 2D to 1D

Cited by in corpus (8)

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• Low-Temperature Heat Transport under Phonon Confinement in Nanostructures
• Thickness-dependent conductivity of nanometric semiconductor thin films
• Quantum confinement theory of the heat capacity of thin films
• Quantum confinement theory of ultra-thin films: electronic, thermal and superconducting properties
• Topological Bardeen-Cooper-Schrieffer theory of superconducting quantum rings
• Phonon-confinement theory of thermal conductivity in ultrathin silicon films