The analysis of the electronic properties of strained or lattice deformed graphene combines ideas from classical condensed matter physics, soft matter, and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent theoretical and exp
erimental work shows the influence of strains in many properties of graphene not considered before, such as electronic transport, spin-orbit coupling, the formation of Moire patterns, optics, ... There is also significant evidence of anharmonic effects, which can modify the structural properties of graphene. These phenomena are not restricted to graphene, and they are being intensively studied in other two dimensional materials, such as the metallic dichalcogenides. We review here recent developments related to the role of strains in the structural and electronic properties of graphene and other two dimensional compounds.
In this note, we reply to the comment made by E.I.Kats and V.V.Lebedev [arXiv:1407.4298] on our recent work Thermodynamics of quantum crystalline membranes [Phys. Rev. B 89, 224307 (2014)]. Kats and Lebedev question the validity of the calculation pr
esented in our work, in particular on the use of a Debye momentum as a ultra-violet regulator for the theory. We address and counter argue the criticisms made by Kats and Lebedev to our work.
We investigate the thermodynamic properties and the lattice stability of two-dimensional crystalline membranes, such as graphene and related compounds, in the low temperature quantum regime $Trightarrow0$. A key role is played by the anharmonic coupl
ing between in-plane and out-of plane lattice modes that, in the quantum limit, has very different consequences than in the classical regime. The role of retardation, namely of the frequency dependence, in the effective anharmonic interactions turns out to be crucial in the quantum regime. We identify a crossover temperature, $T^{*}$, between classical and quantum regimes, which is $sim 70 - 90$ K for graphene. Below $T^{*}$, the heat capacity and thermal expansion coefficient decrease as power laws with decreasing temperature, tending to zero for $Trightarrow0$ as required by the third law of thermodynamics.
