Phonons and electrons in 2d materials and layered structures

Abstract

This thesis is focused on the theoretical study of the mechanical and electronic properties of two-dimensional (2D) crystals, such as graphene, and of layered materials based on them, with emphasizes on both fundamental physics and on potential applications. We start on the study of mechanical properties of free 2D crystals, moving then to mechanical and electronic transport properties of 2D crystals, in particular graphene, supported by a substrate. Then we move to layered structures formed by 2D crystals, studying the phenomena of Coulomb drag and electronic vertical tunneling transport. This thesis is split into two main parts. In the first one we study the mechanical properties of 2D crystals, or crystalline membranes. We start by studying the effect of anharmonicities and quantum fluctuations to the dispersion relation of the lattice vibrations, in particular of out-of-plane vibrations, and how these affect the thermodynamics properties of thermal expansion and specific heat. The we consider 2D crystals supported by a substrate. We study the spectral properties of the out-of-plane vibrations of the 2D crystal, when these are coupled to the lattice degrees of freedom of the substrate. We also study how the thermal expansion of the 2D crystal cannot be considered as an intrinsic property, but instead, becomes dependent on the substrate that supports it. In the second part of this thesis, we focus on electronic transport phenomena in 2D crystals and layered structures. We pay special attention to graphene and graphene based structures. We start by studying the limits imposed by electronic scattering by lattice vibrations to the resistivity of graphene. In particular, we study the role of scattering by in-plane and out-of-plane vibrations both in suspend and supported graphene samples, comparing the relative importance of the two in both cases. Next we move to electronic transport phenomena in layered structures. We study the phenomena of Coulomb drag between two parallel arbitrary metallic layers. Then we specialize to the case of drag between two graphene layers and study the effect of polar substrate phonons to drag. We finally study the phenomena of vertical tunneling transport in van der Waals structures, specializing graphene–hexagonal boron nitride–graphene vertical structures. We study how lattice misalignment between the graphene layers and simultaneous energy and momentum conservation in the tunneling process leads to the occurrence of negative differential conductance in these devices. We then show that, by controlling the relative alignment between the graphene layers and the boron nitride slab, processes involving the transference of momentum by the boron nitride crystal can lead to the occurrence of multiple negative differential conductance regions in the I-V characteristics of the device. The effect of scattering by optical phonons of the structure is also analyzed and we show that it opens up new inelastic tunneling channels, which manifest themselves as sharp features in the low temperature I-V characteristics of the device.