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Related Concept Videos

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: 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,...
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: 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: 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...
Atomic Nuclei: Nuclear Spin01:08

Atomic Nuclei: Nuclear Spin

All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to...

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Josephson current in carbon nanotubes with spin-orbit interaction.

Jong Soo Lim1, Rosa López, Ramón Aguado

  • 1Departament de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.

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Curvature-induced spin-orbit coupling drives a 0-π transition in Josephson currents through carbon nanotube quantum dots. This transition is tunable with magnetic fields and shows distinct phases depending on electron interactions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dots
  • Spintronics

Background:

  • Josephson currents are crucial for superconducting devices.
  • Spin-orbit coupling influences electron behavior in nanostructures.
  • Carbon nanotube quantum dots offer tunable electronic properties.

Purpose of the Study:

  • To investigate the effect of curvature-induced spin-orbit coupling on Josephson currents.
  • To explore the 0-π transition in carbon nanotube quantum dots.
  • To map the phase diagram considering various interaction regimes.

Main Methods:

  • Theoretical calculations of Josephson current.
  • Analysis of spin-orbit coupling effects.
  • Investigation of Coulomb blockade, cotunneling, and Kondo regimes.

Main Results:

  • Demonstrated curvature-induced spin-orbit coupling causes a 0-π Josephson current transition.
  • Identified magnetic field tunability of the transition in the noninteracting regime.
  • Revealed a rich phase diagram with analytical boundaries due to interplay of charging and spin-orbit effects.
  • Observed the 0 phase dominance in the Kondo regime.

Conclusions:

  • Curvature-induced spin-orbit coupling is a key factor in controlling Josephson currents in carbon nanotube quantum dots.
  • The findings provide a theoretical framework relevant to experimental advances in nanotube transport.