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23 April 2024 |
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Article overview
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Quantum elasticity of graphene: Thermal expansion coefficient and specific heat | | I.S. Burmistrov
; I.V. Gornyi
; V.Yu. Kachorovskii
; M.I. Katsnelson
; A.D. Mirlin
; | | Date: |
4 Sep 2016 | | 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 anharmonicity-controlled fluctuations leads to unusual elastic
properties of the membrane. The effect of quantum fluctuations is governed by
the dimensionless coupling constant, $g_0 ll 1$, which vanishes in the
classical limit ($hbar o 0$) and is equal to $simeq 0.05$ for graphene. We
demonstrate that the thermal expansion coefficient $alpha_T$ of the membrane
is negative and remains nearly constant down to extremely low temperatures,
$T_0propto exp (-2/g_0)$. We also find that $alpha_T$ diverges in the
classical limit: $alpha_T propto - ln(1/g_0)$ for $g_0 o 0$. For graphene
parameters, we estimate the value of the thermal expansion coefficient as
$alpha_T simeq - 0.23 {
m eV}^{-1}$, which applies below the temperature
$T_{
m uv} sim g_0 varkappa_0 sim 500$ K (where $varkappa_0 sim 1$ eV is
the bending rigidity) down to $T_0 sim 10^{-14}$ K. For $T<T_0$, the thermal
expansion coefficient slowly (logarithmically) approaches zero with decreasing
temperature. Being in agreement with the third law of thermodynamics, this
behavior is nevertheless surprising since typically the thermal expansion
coefficient goes to zero as a power-law 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 Gr"uneisen parameter. | | Source: | arXiv, 1609.0924 | | Services: | Forum | Review | PDF | Favorites | |
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