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Related Concept Videos

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...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization
Hybridization of Atomic Orbitals I03:24

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
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Cooper-pair injection into quantum spin Hall insulators.

Koji Sato1, Daniel Loss, Yaroslav Tserkovnyak

  • 1Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA.

Physical Review Letters
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

We explored Cooper pair tunneling into topological insulator edges. This reveals quantum entanglement and fractionalized charge pulses, impacting edge state transport.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Materials science

Background:

  • Topological insulators possess unique edge states with spin-momentum locking.
  • Superconductors exhibit Cooper pairs, which are bound electron pairs responsible for superconductivity.

Purpose of the Study:

  • To theoretically investigate Cooper pair tunneling from a superconductor into the helical edge states of a 2D topological insulator.
  • To understand the resulting quantum phenomena, including current cross-correlations and charge fractionalization.

Main Methods:

  • Theoretical modeling of Cooper pair tunneling.
  • Analysis of quantum entanglement processes.
  • Investigation of Luttinger liquid correlations.

Main Results:

  • Observed positive current cross-correlations along the edges due to Cooper pair tunneling.
  • Demonstrated Cooper pair partitioning into helical edge liquids, leading to spin-dependent electron transport.
  • Showcased fractionalization of injected electrons into counterpropagating charge pulses.

Conclusions:

  • Cooper pair tunneling into topological insulator edge states is a viable mechanism for generating exotic quantum phenomena.
  • The interplay of superconductivity and topological properties leads to novel charge transport behaviors.
  • This research provides insights into the fundamental physics of quantum entanglement and fractionalization in condensed matter systems.