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Related Concept Videos

Bewley Lattice Diagram01:12

Bewley Lattice Diagram

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The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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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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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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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...
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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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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene.

Yang-Zhi Chou1, Sankar Das Sarma1

  • 1Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

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|July 28, 2023
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We explore emergent Kondo lattice models in magic-angle twisted bilayer graphene. A topological Dirac Kondo semimetal state is identified, potentially explaining the ν=0 correlated state.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Graphene Physics

Background:

  • Magic-angle twisted bilayer graphene exhibits complex correlated electronic states.
  • Understanding these states requires theoretical models that capture strong interactions and topology.

Purpose of the Study:

  • To systematically study emergent Kondo lattice models in twisted bilayer graphene.
  • To identify and characterize novel correlated electronic states, such as topological semimetals.
  • To investigate the stability and phase diagram of these emergent states.

Main Methods:

  • Utilizing the topological heavy fermion representation.
  • Analyzing models at commensurate fillings.
  • Constructing quantum phase diagrams to explore parameter space.

Main Results:

  • Demonstrated symmetric, strongly correlated metallic states driven by hybridization.
  • Realized a (fragile) topological Dirac Kondo semimetal.
  • Provided a potential explanation for the symmetry-preserving correlated state at ν=0.
  • Investigated the interplay between Kondo hybridization and magnetic correlation.

Conclusions:

  • The topological Dirac Kondo semimetal offers a new paradigm for correlated states in graphene.
  • Twisted bilayer graphene may serve as a quantum simulator for novel magnetic orders.
  • Further experimental investigation is warranted to confirm these findings.