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Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
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Tetrahedral Complexes
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
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Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
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When Infrared (IR) radiation passes through a covalently bonded molecule, the bonds transition from lower to higher vibrational levels. The fundamental vibrational motions that result in infrared absorption can be classified as stretching or bending vibrations.
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Intrinsic superflat bands in general twisted bilayer systems.

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Light, Science & Applications
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Summary

Researchers discovered superflat bands in general twisted bilayer systems, extending beyond magic-angle graphene. These bands arise from localized states due to lattice dislocations, offering tunable properties for various wave systems.

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Wave phenomena

Background:

  • Twisted bilayer systems, like twisted bilayer graphene, are known for unique physical properties arising from moiré superlattices and magic angles.
  • Existing research primarily focuses on low-energy physics in magic-angle twisted systems.

Purpose of the Study:

  • To discover and characterize superflat bands in general twisted bilayer systems beyond the established magic-angle phenomena.
  • To investigate the role of continuous lattice dislocations in forming these superflat bands and associated localized states.

Main Methods:

  • Theoretical analysis of general twisted bilayer systems incorporating continuous lattice dislocations.
  • Identification of intrinsic localized states governed by an effective energy potential well.
  • Analysis of inter-cell coupling and parameter space for superflat band formation.
  • Exploration of mimicking these systems using twisted bilayer nanophotonic analogs.

Main Results:

  • Discovery of a new class of superflat bands in general twisted bilayer systems.
  • Identification of spectrally isolated, intrinsic localized states centered around AA stacked regions.
  • Demonstration that these localized states lead to negligible inter-cell coupling.
  • Formation of superflat bands supported across a wide, continuous parameter space.
  • Successful mimicry of these phenomena in twisted bilayer nanophotonic systems.

Conclusions:

  • General twisted bilayer systems offer a broader platform for realizing superflat bands compared to magic-angle systems.
  • Continuous lattice dislocations are key to creating tunable localized states and superflat bands.
  • These findings open possibilities for controlling photonic, phononic, and mechanical waves in engineered materials.