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Thermodynamical Properties and Stability of Crystalline Membranes in the Quantum Regime

Published online by Cambridge University Press:  11 February 2015

B. Amorim
Affiliation:
Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, E28049 Madrid, Spain
R. Roldán
Affiliation:
Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, E28049 Madrid, Spain
E. Cappelluti
Affiliation:
Istituto dei Sistemi Complessi, CNR, U.O.S. Sapienza, v. dei Taurini 19, 00185 Roma, Italy
A. Fasolino
Affiliation:
Radboud University Nijmegen,Institute for Molecules and Materials, NL-6525AJ Nijmegen, The Netherlands
F. Guinea
Affiliation:
Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, E28049 Madrid, Spain
M. I. Katsnelson
Affiliation:
Radboud University Nijmegen,Institute for Molecules and Materials, NL-6525AJ Nijmegen, The Netherlands
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Abstract

We study the thermodynamical properties and lattice dynamics of two-dimensional crystalline membranes, such as graphene and related compounds, in zero temperature limit, where quantum effects are dominant. We find out that, just as in the high temperature classical limit, a fundamental role is played by the anharmonic coupling between in-plane and out-of plane lattice modes, which leads to a strong reconstruction of the dispersion relation of the out-of-plane mode. We identify a crossover temperature, T*, bellow which quantum effects are dominant. We estimate that for graphene T* ∼ 70 - 90 K. Inclusion of anharmonic effects makes the thermal expansion finite in the thermodynamic limit, and below T* it tends to zero as a power law as T→0 as required by the third law of thermodynamics. The specific heat also goes to zero as a power law as T→0, but with a exponent that differs from the one predicted by the harmonic theory.

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Articles
Copyright
Copyright © Materials Research Society 2015 

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References

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