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 experimental work shows the influence of strains in many properties of graphene not considered before, such as electronic transport, spin-orbit coupling, the formation of Moir\'e 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.Comment: 75 pages, 15 figures, review articl

We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-André model and the models of Sriram Ganeshan, J. H. Pixley, and S. Das Sarma [ Phys. Rev. Lett. 114, 146601 (2015)] and J. Biddle and S. Das Sarma [ Phys. Rev. Lett. 104, 070601 (2010)]. The analytical treatment follows from recognizing these models as a novel type of fixed points of the renormalization group procedure recently proposed in Phys. Rev. B 108, L100201 (2023) for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and nontrivial mobility edges in an undriven system without the need for the unbounded potentials required by previous proposals.

Out of plane vibrations are suppressed in graphene layers placed on a substrate. These vibrations, in suspended samples, are relevant for the understanding of properties such as the electrical resistivity, the thermal expansion coefficient, and others. We use a general framework to study the properties of the out of plane mode in graphene on different substrates, taking into account the dynamics of the substrate. We discuss broadening of this mode and how it hybridizes with the substrate Rayleigh mode, comparing our model with experimental observations. We use the model to estimate the substrate induced changes in the thermal expansion coefficient and in the temperature dependence of the electrical resistivity.

We investigate the spontaneous emission rate of a two-level quantum emitter near a graphene-coated substrate under the influence of an external magnetic field or strain induced pseudomagnetic field. We demonstrate that the application of the magnetic field can substantially increase or decrease the decay rate. We show that a suppression as large as $99\%$ in the Purcell factor is achieved even for moderate magnetic fields. The emitter's lifetime is a discontinuous function of $\left|\mathbf{B}\right|$, which is a direct consequence of the occurrence of discrete Landau levels in graphene. We demonstrate that, in the near-field regime, the magnetic field enables an unprecedented control of the decay pathways into which the photon/polariton can be emitted. Our findings strongly suggest that a magnetic field could act as an efficient agent for on-demand, active control of light-matter interactions in graphene at the quantum level.

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 $T\to 0$. A key role is played by the anharmonic coupling between in-plane and out-of-plane lattice modes that, in the quantum limit, has very different consequences from those in the classical regime. The role of retardation, namely of frequency dependence, in the effective anharmonic interactions turns out to be crucial in the quantum regime. We identify a crossover temperature, $T^{*}$, between the 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 $T\to 0$ as required by the third law of thermodynamics.