Connected by voids: Interactions and screening in sparse matter

Using theory and computations, we study structural and electronic properties of nanoscale systems where regions of low density are important for response and function. Materials with such properties are called sparse matter. Examples include assemblies of organic molecules and layered structures like graphite. Binding in molecular crystals and physisorption onto surfaces is studied using density-functional theory (DFT) with a van der Waals density functional (vdW-DF) account of exchange-orrelation. We examine binding properties of molecular crystals of high symmetry (hexamine, dodeacahedrane, cubane, C60, graphite) as they allow straightforward analysis of binding nature. We find that vdW-DF describes a non-local attraction that is significantly enhanced at shorter separations compared to the 1/r6 form common in pair-potential descriptions. The binding of adenine, benzene, and C60 on graphene are studied. Several properties of the non-local vdW-DF correlation is elucidated, like sensitivity to geometry, length-scales, and role of exchange companion. Adsorption of H2 and benzene on Cu(111) is studied. We find that benzene affects the surface state and that the corrugation is small enough to allow it to react to surface-state mediated (SSM) interactions. In all cases, the results of vdW-DF calculations compare well to experimental observations.Noble metal surfaces like Cu(111) harbor a metallic Shockley surface state that supports two-dimensional electron gas (2DEG). This surface state is believed to play a crucial role in the self-assembly of molecules. Using DFT, we study this surfacestate and how an external field and physisorbed molecules influence its properties. To aid our study, we developed a method to enhance slab-based calculations of surfacestates. We also investigate the self-assembly of benzene on Cu(111), where we include a simple analytical expression for the SSM interaction in addition to the direct van der Waals interactions. The resulting binding curves have two separate minima that coincide with the periodicity of the measured overlayer phases.Finally, we draw a link to AlN/GaN heterostructures. In analogy to sparse matter, they exhibit wide regions of low conduction electron density. Associated with these depletion regions are inversion layers supporting 2DEGs. This charge redistribution arise from internal fields originating in intrinsic polarization. These structures are studied using a custom-built Schr\uf6dinger-Poisson solver. A systematic design strategy to remove the internal fields in the leads is developed to aid the design of devices based on transport perpendicular to the interfaces