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Energy Bands in Solids

Energy Bands in Solids

Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states...

Band Theory

Band Theory

When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...

UV–Vis Spectroscopy: Molecular Electronic Transitions

UV–Vis Spectroscopy: Molecular Electronic Transitions

In Ultraviolet–Visible (UV–Vis) spectroscopy, the absorption of electromagnetic radiation is used to probe the electronic structure of molecules. This technique provides insights into molecular electronic transitions, particularly the movement of electrons between different molecular orbitals. Radiation is absorbed if the energy of the electromagnetic radiation passing through the molecule is precisely equal to the energy difference between the excited and ground states. During this...

Atomic Spectroscopy: Effects of Temperature

Atomic Spectroscopy: Effects of Temperature

Atomization, converting samples into gas-phase atoms and ions, is essential for atomic spectroscopy. The flame temperature required for atomization affects the efficiency of the atomic spectroscopic methods by increasing the atomization efficiency and the relative population of the excited and ground states.
At thermal equilibrium, the relative populations of excited and ground state atoms can be estimated using the Maxwell–Boltzmann distribution. For example, an increase in temperature...

Atomic Nuclei: Nuclear Spin State Overview

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

Atomic Nuclei: Nuclear Spin State Population Distribution

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

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Updated: Dec 26, 2025

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Topological bands for ultracold atoms.

N R Cooper¹, J Dalibard², I B Spielman³

¹T.C.M. Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.

Reviews of Modern Physics

|March 20, 2020

Summary

Experiments with cold atomic gases are achieving novel band structures with geometric and topological properties. This review covers methods, characterization, and potential many-body phases in these advanced systems.

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Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures

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Last Updated: Dec 26, 2025

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

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Published on: March 30, 2017

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

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Area of Science:

Condensed Matter Physics
Quantum Gases
Topological Matter

Background:

Recent advances in cold atomic gases enable the creation of exotic band structures.
Geometric and topological concepts are crucial for understanding Bloch bands.

Purpose of the Study:

To review experimental developments in realizing geometric and topological band structures in cold atomic gases.
To provide a conceptual framework for understanding underlying physical principles and experimental approaches.

Main Methods:

Summarizing key concepts of geometry and topology for Bloch bands.
Describing methods used to generate novel band structures in cold atoms.
Detailing physical observables for band structure characterization.

Main Results:

Focus on physical principles behind experimental approaches.
Discussion of how experimental implementations affect physical properties.
Exploration of interparticle interactions and emergent many-body phases.

Conclusions:

Experimental realization of complex band structures in cold atoms is advancing rapidly.
Future experiments may explore novel many-body phases arising from these engineered systems.