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K3.03 - Thermodynamical Properties and Stability of Crystalline Membranes in the Quantum Regime 
December 1, 2014   2:00pm - 2:30pm

The very existence of isolated graphene is a challenge to the Mermin-Wagner theorem that forbid long-range (lattice) ordering in truly two-dimensional (2D) systems, which should be unstable against lattice fluctuations leading to crumpling, folding etc. In real materials, however, the anharmonic coupling between the in-plane lattice mode and the out-of-plane flexural modes was shown, in the high-temperature classical regime, to stabilize the system [1-4]. The generalization of these results in the low temperature quantum regime leads however to unphysical results signalizing that new physics is involved.

In this contribution we present a microscopic theory to investigate the thermodynamical properties of graphene, modeled as a crystalline membranes, in the zero/low-temperature regime. Using Quantum Field Theory, we generalize the self-consistent screening approximation (SCSA) approach [5] at the quantum level. A key role is played by the retarded nature of the anharmonic coupling between in-plane and out-of-plane lattice modes that, in the quantum limit, turns to have crucial different consequences than in the classical regime.

We identify a crossover temperature T* between classical and quantum regimes, which is T* ~ 70-79 K for graphene [6]. Below T* the heat capacity and thermal expansion coefficients results to decrease as power laws with decreasing temperature, vanishing at T=0, reconciling the SCSA theory with the third law of thermodynamics [6].

[1] A. Fasolino, J. Los, and M.I. Katsnelson, Nat. Mater. 6, 858 (2007).
[2] D. Nelson and L. Peliti, J. Phys. 48, 1085 (1987).
[3] P. Le Doussal and L. Radzihovsky, Phys. Rev. Lett. 69, 1209 (1992).
[4] D. Gazit, Phys. Rev. E 80, 041117 (2009).
[5] K. V. Zakharchenko, R. Roldan, A. Fasolino, and M.I. Katsnelson, Phys. Rev. B82, 125435 (2010).
[6] B. Amorim, R. Roldan, E. Cappelluti, A. Fasolino, F. Guinea, and M.I. Katsnelson, arXiv:1403.2637 (2014).

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