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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

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...
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...
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...
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: 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...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Anomalous Josephson current through a spin-orbit coupled quantum dot.

A Zazunov1, R Egger, T Jonckheere

  • 1Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany.

Physical Review Letters
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

Researchers identified key conditions for anomalous Josephson current in quantum dots, requiring spin-orbit coupling, a Zeeman field, and chiral conduction. These findings enable control over spontaneous time-reversal symmetry breaking in mesoscopic systems.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Mesoscopic systems

Background:

  • Quantum dots are crucial in mesoscopic physics.
  • Josephson currents are fundamental to superconductivity.
  • Time-reversal symmetry breaking is key to novel quantum phenomena.

Purpose of the Study:

  • Determine conditions for anomalous Josephson current in quantum dots.
  • Investigate spontaneous time-reversal symmetry breaking.
  • Provide analytical models for anomalous supercurrent.

Main Methods:

  • Developed a general model for a mesoscopic multilevel quantum dot.
  • Analyzed the interplay of spin-orbit coupling and Zeeman fields.
  • Identified necessary conditions for chiral conduction.

Main Results:

  • Finite spin-orbit coupling is essential.
  • A suitably oriented Zeeman field is required.
  • Chiral conductor properties of the quantum dot are necessary.
  • Analytical expressions for anomalous supercurrent were derived.

Conclusions:

  • Established the necessary conditions for anomalous Josephson current.
  • Demonstrated the link between quantum dot properties and symmetry breaking.
  • Provided a theoretical framework for designing quantum devices.