"In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands)."
The study of the arrangement of the electronic energy levels of electrons in solids.
Single-electron and many-body Hamiltonians: Describing the quantum mechanical behavior of electrons in solids.
Bloch theorem and periodic potentials: Identifying the periodic nature of the lattice potential and its impact on electron behavior.
Electronic band structure: Understanding the distribution of electron energies in the material.
Density of states and Fermi level: Describing the number of available states at a given energy level and the level at which the electrons are distributed in the system.
Brillouin zones and reciprocal lattice: Identifying the symmetry and periodicity of the crystal lattice in reciprocal space.
Effects of symmetry and dimensionality: Exploring the impact of symmetry and dimensionality on the electronic properties of materials.
Tight-binding approximation: A method of describing the electronic wavefunction using localized atomic orbitals.
Band gaps and conductivity: Describing the relationship between the band structure and the electrical conductivity of the material.
Magnetic properties: Understanding the impact of magnetic fields on electronic properties and the behavior of magnetic materials.
Topological insulators: Identifying exotic electronic states in materials with interesting topological properties.
Superconductivity: Understanding the complex quantum mechanical behavior of electrons in superconductive materials.
Monte Carlo simulations: A method of modeling and predicting the behavior of complex systems, including the electronic behavior of materials.
Tight-Binding Theory: This theory uses a localized basis set to describe the electronic structure of a crystal. It is particularly useful for predicting the electronic properties of materials that have a strong covalent bonding.
Molecular Orbital Theory: This theory uses molecular orbitals to describe the electronic structure of a crystal. It is particularly useful for predicting the electronic properties of materials that have a weak covalent bonding.
Band Structure theory: This theory describes the electronic structure of a crystal in terms of the allowed energy bands or zones. It is useful for predicting the electronic properties of materials with strong ionic bonding.
Density Functional Theory (DFT): This is a quantum mechanical theory that uses the electron density to describe the electronic structure of a crystal. It is widely used for predicting the electronic properties of materials, especially metal and semiconductors.
Kronig-Penney Model: It is a theoretical model used to analyze the electronic structure of a one-dimensional periodic potential. It is particularly useful for predicting the properties of semiconductors and metals.
Hubbard Model: This model is based on the concept of strongly correlated electron systems, in which the behavior of electrons in the crystal is directly related to the interactions between them.
Extended Hueckel Theory: This model analyzes the electronic structure of a molecule or crystal in terms of the atomic orbitals forming the molecule. It is particularly useful for predicting the electronic properties of organic compounds.
"Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules."
"Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption."
"Band theory forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.)."
"...as well as the ranges of energy that they may not have (called band gaps or forbidden bands)."
"The electronic band structure... describes the range of energy levels that electrons may have within it..."
"Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules."
"Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption."
"Band theory forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.)."
"Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity..."
"Band theory has been successfully used to explain many physical properties of solids, such as... optical absorption..."
"Band theory forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.)."
"...ranges of energy that they may not have (called band gaps or forbidden bands)."
"...ranges of energy that they may not have (called band gaps or forbidden bands)."
"Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron..."
"Band theory has been successfully used to explain many physical properties of solids..."
"Band theory forms the foundation of the understanding of all solid-state devices..."
"...ranges of energy that they may not have (called band gaps or forbidden bands)."
"Band theory forms the foundation of the understanding of all solid-state devices..."
"The electronic band structure... describes the range of energy levels that electrons may have within it..."