Density Functional Theory and Tight-Binding Models

Description

This lecture covers the motivation behind modeling and simulating multilayer 2D materials, including graphene and transition metal dichalcogenides. It explores the multiscale approach, from first-principle calculations to tight-binding models, to predict electronic and optical properties. The Quantum Drude model and Kubo formula are discussed for understanding electrical conductivity in materials. The lecture also delves into the construction of reduced tight-binding models for multilayer 2D materials, emphasizing the importance of symmetries in obtaining accurate results. Mathematical results regarding Wannier functions and Gaussian-type orbitals are presented, along with practical computations of conductivity. The conclusion highlights the transition from first-principle calculations to mesoscopic/macroscopic models for homogeneous and disordered materials.

Official source

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Drude model

The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials (especially metals). Basically, Ohm's law was well established and stated that the current J and voltage V driving the current are related to the resistance R of the material. The inverse of the resistance is known as the conductance. When we consider a metal of unit length and unit cross sectional area, the conductance is known as the conductivity, which is the inverse of resistivity.

Graphene

Graphene (ˈgræfiːn) is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. The name is derived from "graphite" and the suffix -ene, reflecting the fact that the graphite allotrope of carbon contains numerous double bonds. Each atom in a graphene sheet is connected to its three nearest neighbors by σ-bonds and a delocalised π-bond, which contributes to a valence band that extends over the whole sheet.

Nanomaterials

Nanomaterials describe, in principle, materials of which a single unit is sized (in at least one dimension) between 1 and 100 nm (the usual definition of nanoscale). Nanomaterials research takes a materials science-based approach to nanotechnology, leveraging advances in materials metrology and synthesis which have been developed in support of microfabrication research. Materials with structure at the nanoscale often have unique optical, electronic, thermo-physical or mechanical properties.

Free electron model

In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.