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Related Concept Videos

Ionic Crystal Structures02:42

Ionic Crystal Structures

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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
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Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

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Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
87
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

49.7K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
49.7K
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

31.8K
Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Chirality at Nitrogen, Phosphorus, and Sulfur02:30

Chirality at Nitrogen, Phosphorus, and Sulfur

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Chirality is most prevalent in carbon-based tetrahedral compounds, but this important facet of molecular symmetry extends to sp3-hybridized nitrogen, phosphorus and sulfur centers, including trivalent molecules with lone pairs. Here, the lone pair behaves as a functional group in addition to the other three substituents to form an analogous tetrahedral center that can be chiral.
A consequence of chirality is the need for enantiomeric resolution. While this is theoretically possible for all...
7.5K
Radicals: Electronic Structure and Geometry01:07

Radicals: Electronic Structure and Geometry

5.4K
This lesson delves into the geometry of a radical, which is influenced by the electronic structure of the molecule. The principle is similar to that of a lone pair, where the unpaired electron influences the geometry at the radical center.
Accordingly, the structure of a trivalent radical lies between the geometries of carbocations and carbanions. An sp2-hybridized carbocation is trigonal planar, while an sp3-hybridized carbanion is trigonal pyramidal. Here, the difference in geometry is...
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Angle-resolved Photoemission Spectroscopy At Ultra-low Temperatures
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Large Chern Number and Edge Currents in Sr2RuO4.

Thomas Scaffidi1, Steven H Simon1

  • 1Rudolf Peierls Centre for Theoretical Physics, Oxford OX1 3NP, United Kingdom.

Physical Review Letters
|September 5, 2015
PubMed
Summary

The most favored chiral superconducting order parameter in Sr2RuO4 has a Chern number of |C|=7. This finding may resolve the conflict between time-reversal symmetry breaking and the absence of edge currents in Sr2RuO4.

Area of Science:

  • Condensed Matter Physics
  • Superconductivity Research
  • Materials Science

Background:

  • Strontium ruthenate (Sr2RuO4) is a candidate material for chiral superconductivity.
  • Experimental observations in Sr2RuO4 show time-reversal symmetry breaking but lack of observed edge currents.
  • Existing theoretical models often assume a simpler superconducting order parameter.

Purpose of the Study:

  • To identify the most favored chiral superconducting order parameter in Sr2RuO4.
  • To investigate the implications of different order parameters on observable properties like edge currents.
  • To reconcile theoretical predictions with experimental findings in Sr2RuO4.

Main Methods:

  • Weak-coupling microscopic calculation.
  • Analysis of superconducting order parameter components.

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  • Determination of Chern numbers associated with the order parameters.
  • Investigation of symmetry constraints imposed by the tetragonal point group.

    • Main Results:

    • The most favored chiral superconducting order parameter in Sr2RuO4 possesses a Chern number of |C|=7.
    • Two dominant order parameter components, sin(3k(x))+isin(3k(y)) and sin(k(x))cos(k(y))+isin(k(y))cos(k(x)), are identified.
    • These components belong to the E(u) irreducible representation, consistent with tetragonal symmetry.
    • The calculated Chern number of -7 is permissible under the material's symmetry constraints.

    Conclusions:

    • A chiral superconducting order parameter with |C|=7 provides a potential explanation for experimental observations in Sr2RuO4.
    • The vanishing or strong reduction of edge currents for |C|>1 superconductors in continuum and lattice limits, respectively, aligns with experimental data.
    • This theoretical finding offers a resolution to the discrepancy between observed time-reversal symmetry breaking and the absence of edge currents in Sr2RuO4.