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Crystal Field Theory
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The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily interpreted using 2-dimensional (2D) NMR. Unlike 1D NMR, 2D NMR has two frequency axes that provide the coupling information between the nucleus A and nucleus B in a molecule. The process from which 2D spectra are obtained has four steps.
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Imaging two-dimensional generalized Wigner crystals.

Hongyuan Li1,2,3, Shaowei Li4,5,6,7, Emma C Regan1,2,3

  • 1Department of Physics, University of California at Berkeley, Berkeley, CA, USA.

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|September 30, 2021
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Summary
This summary is machine-generated.

Physicists have directly visualized two-dimensional (2D) Wigner crystals in WSe2/WS2 moiré heterostructures. A novel non-invasive scanning tunnelling microscopy (STM) technique revealed distinct lattice configurations at fractional electron fillings.

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Quantum mechanics

Background:

  • Wigner crystals, theorized 90 years ago, are exotic electronic states.
  • Previous observations were indirect or lacked real-space visualization.
  • 2D Wigner crystals were previously seen in 2D electron gases and moiré superlattices.

Purpose of the Study:

  • To achieve direct real-space imaging of 2D Wigner crystals.
  • To overcome limitations of conventional scanning tunnelling microscopy (STM).
  • To investigate Wigner crystal states in WSe2/WS2 moiré heterostructures.

Main Methods:

  • Developed a non-invasive STM spectroscopy technique using a graphene sensing layer.
  • Utilized the modulation of local STM tunnel current by the Wigner crystal lattice.
  • Applied the technique to WSe2/WS2 moiré heterostructures.

Main Results:

  • Successfully visualized 2D Wigner crystals in real space.
  • Observed distinct lattice configurations for fractional electron fillings (n=1/3, 1/2, 2/3).
  • Identified triangular (n=1/3), honeycomb (n=2/3), and stripe (n=1/2) phases, with the n=1/2 state breaking C3 symmetry.

Conclusions:

  • The study provides the first direct real-space imaging of 2D Wigner crystals in WSe2/WS2 moiré heterostructures.
  • The non-invasive STM technique is a powerful tool for studying fragile correlated electron states.
  • This approach can be generalized for imaging novel electronic lattices in other quantum materials.