Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

被引:31
作者
Burmistrov, I. S. [1 ,2 ]
Gornyi, I. V. [1 ,3 ,4 ,5 ]
Kachorovskii, V. Yu. [1 ,3 ,4 ,5 ]
Katsnelson, M. I. [6 ]
Mirlin, A. D. [1 ,3 ,4 ,5 ,7 ]
机构
[1] LD Landau Inst Theoret Phys, Kosygina St 2, Moscow 119334, Russia
[2] Natl Res Univ, Higher Sch Econ, Lab Condensed Matter Phys, Moscow 101000, Russia
[3] Karlsruhe Inst Technol, Inst Nanotechnol, D-76021 Karlsruhe, Germany
[4] Karlsruhe Inst Technol, Inst Theorie Kondensierten Materie, D-76128 Karlsruhe, Germany
[5] AF Ioffe Phys Tech Inst, St Petersburg 194021, Russia
[6] Radboud Univ Nijmegen, Inst Mol & Mat, NL-6525 AJ Nijmegen, Netherlands
[7] Petersburg Nucl Phys Inst, St Petersburg 188300, Russia
基金
俄罗斯科学基金会;
关键词
POLYMERIZED MEMBRANES; CRUMPLING TRANSITION; PHASE; CRYSTALLINE; FLUCTUATIONS; TEMPERATURE; MECHANICS;
D O I
10.1103/PhysRevB.94.195430
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
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) << 1, which vanishes in the classical limit (h -> 0) and is equal to similar or equal to 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-0 proportional to exp(-2/g(0)). We also find that alpha(T) diverges in the classical limit: alpha(T) proportional to -ln(1/g(0)) for g(0) -> 0. For graphene parameters, we estimate the value of the thermal expansion coefficient as alpha(T) similar or equal to -0.23 eV(-1), which applies below the temperature T-uv similar to g(0)x(0) similar to 500K(where x(0) similar to 1 eV is the bending rigidity) down to T-0 similar to 10(-1)4 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 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 Gruneisen parameter.
引用
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页数:18
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