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Related Concept Videos

Band Theory02:35

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,...
Energy Bands in Solids01:01

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 that no two...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The orientation of the...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

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Related Experiment Video

Updated: May 31, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

Moire bands in twisted double-layer graphene.

Rafi Bistritzer1, Allan H MacDonald

  • 1Department of Physics, University of Texas, Austin, TX 78712, USA.

Proceedings of the National Academy of Sciences of the United States of America
|July 7, 2011
PubMed
Summary
This summary is machine-generated.

Twisted bilayer graphene exhibits unique electronic properties at specific "magic angles." These angles lead to flat moiré Bloch bands, enhancing conductivity and density of states in the moiré pattern.

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Last Updated: May 31, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
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Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
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Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding

Published on: September 23, 2018

Area of Science:

  • Condensed Matter Physics
  • Materials Science

Background:

  • Moiré patterns arise from overlaying periodic structures with a twist.
  • Understanding the electronic structure of twisted bilayer graphene is crucial for novel electronic applications.

Purpose of the Study:

  • Investigate the electronic band structure of twisted bilayer graphene.
  • Analyze the impact of twist angle on electronic properties and identify "magic angles."

Main Methods:

  • Utilized the continuum Dirac model for twisted bilayer graphene.
  • Analyzed moiré pattern periodicity and its effect on electronic bands.
  • Examined the Dirac velocity and its dependence on the twist angle.

Main Results:

  • Moiré pattern periodicity creates moiré Bloch bands.
  • Reduced twist angles increase interlayer coupling and cause Dirac velocity to approach zero.
  • At specific magic angles, Dirac velocity vanishes, leading to flat bands.

Conclusions:

  • Magic angles in twisted bilayer graphene result in significantly enhanced Dirac-point density-of-states and counterflow conductivity.
  • These findings highlight the potential for novel electronic devices based on moiré superlattices.