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Trends in Lattice Energy: Ion Size and Charge02:54

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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Atomic Nuclei: Nuclear Relaxation Processes01:23

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Spin–Spin Coupling: One-Bond Coupling01:17

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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,...
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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.
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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...
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Spin–Spin Coupling Constant: Overview01:08

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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.
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Interaction-driven Chern insulating phases in the lattice with Rashba spin-orbit coupling.

Shi-Qing Lin1, Hui Tan1, Pei-Hao Fu1,2

  • 1School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China.

Iscience
|August 31, 2023
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Summary

This study explores topological phases in a minimal model, revealing new high-Chern-number and valley-polarized Chern insulators. These findings highlight potential for advanced topology electronics and valleytronics applications.

Keywords:
Condensed matter physicsMagnetismNanomaterials

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Area of Science:

  • Condensed Matter Physics
  • Materials Science

Background:

  • Topological phases like the quantum anomalous Hall (QAI) and Chern insulator phases require broken time-reversal symmetry, often achieved through magnetic interactions.
  • Flat band models are crucial for realizing exotic electronic phases due to strong electron correlations.

Purpose of the Study:

  • To investigate topological phases in a minimal flat band model incorporating Rashba spin-orbit coupling and spontaneous ferromagnetism.
  • To explore interaction-driven phase transitions and identify novel topological states.

Main Methods:

  • Analysis of interaction-driven phase diagrams.
  • Band structure calculations.
  • Investigation of topological edge states and topological invariants.

Main Results:

  • Demonstrated a platform for realizing normal insulators, semimetals, and Chern insulators.
  • Identified unique high-Chern-number insulators.
  • Discovered valley-polarized Chern insulators with single-valley edge channels and near-complete valley polarization.

Conclusions:

  • Interaction-driven systems offer a versatile platform for novel topological phases.
  • The discovered phases hold promise for future applications in topology electronics and valleytronics.