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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...
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...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
Valence Bond Theory02:45

Valence Bond Theory

Overview of Valence Bond Theory

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Excitonic condensation under spin-orbit coupling and BEC-BCS crossover.

T Hakioğlu1, Mehmet Sahin

  • 1Department of Physics and National Nanotechnology Research Center, Bilkent University, 06800 Ankara, Turkey.

Physical Review Letters
|May 16, 2007
PubMed
Summary

Weak spin-orbit coupling in quantum wells affects electron-hole condensates. This coupling breaks symmetry, leading to a complex order parameter dependent on condensate density, offering new detection methods.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Optics
  • Materials Science

Background:

  • Electron-hole pair condensation forms excitonic states in quantum wells.
  • Spin-orbit coupling (SOC) influences electronic properties, but its effect on excitonic condensates is less explored.
  • Understanding symmetry breaking is crucial for characterizing condensed phases.

Purpose of the Study:

  • To investigate the impact of weak spin-orbit coupling (SOC) on excitonic condensates at zero temperature.
  • To analyze how SOC affects the order parameter symmetry and properties of the condensate.
  • To propose experimental signatures for detecting excitonic condensates influenced by SOC.

Main Methods:

  • Theoretical study of electron-hole pair condensation in coupled quantum wells.
  • Application of perturbative spin-orbit coupling under realistic conditions.
  • Analysis of the order parameter's symmetry and parity, and static spin susceptibility.

Main Results:

  • Absence of fermion exchange symmetry leads to a condensate spin with no definite parity.
  • Excitonic SOC breaks rotational symmetry, resulting in a complex order parameter.
  • The order parameter's phase pattern becomes density-dependent, a novel manifestation.
  • Finite off-diagonal components in static spin susceptibility are predicted.

Conclusions:

  • Perturbative SOC significantly alters the nature of excitonic condensates in quantum wells.
  • The density-dependent phase pattern of the order parameter is a key consequence of excitonic SOC.
  • Observed changes in spin susceptibility offer a potential experimental pathway to confirm excitonic condensates.