Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
Abstract
We explore thermodynamics of a quantum membrane, with a particular application to suspended graphene membrane and with a particular focus on the thermal expansion coefficient. We show that an interplay between quantum and classical anharmonicitycontrolled fluctuations leads to unusual elastic properties of the membrane. The effect of quantum fluctuations is governed by the dimensionless coupling constant, g_{0}≪1 , which vanishes in the classical limit (ℏ →0 ) and is equal to ≃0.05 for graphene. We demonstrate that the thermal expansion coefficient α_{T} of the membrane is negative and remains nearly constant down to extremely low temperatures, T_{0}∝exp(2 /g_{0}) . We also find that α_{T} diverges in the classical limit: α_{T}∝ln(1 /g_{0}) for g_{0}→0 . For graphene parameters, we estimate the value of the thermal expansion coefficient as α_{T}≃0.23 eV^{1} , which applies below the temperature T_{uv}∼g_{0}ϰ_{0}∼500 K (where ϰ_{0}∼1 eV is the bending rigidity) down to T_{0}∼10^{14} K. For T <T_{0} , the thermal expansion coefficient slowly (logarithmically) approaches zero with decreasing temperature. This behavior is surprising since typically the thermal expansion coefficient goes to zero as a powerlaw function. We discuss possible experimental consequences of this anomaly. We also evaluate classical and quantum contributions to the specific heat of the membrane and investigate the behavior of the Grüneisen parameter.
 Publication:

Physical Review B
 Pub Date:
 November 2016
 DOI:
 10.1103/PhysRevB.94.195430
 arXiv:
 arXiv:1609.00924
 Bibcode:
 2016PhRvB..94s5430B
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 20 pages, 5 figures