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Related Concept Videos

Phase Diagrams02:39

Phase Diagrams

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Valence Bond Theory

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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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Correlation-driven topological phases in magic-angle twisted bilayer graphene.

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Magic-angle twisted bilayer graphene reveals six new topological phases driven by strong electronic interactions. These phases, mapped using scanning tunnelling microscopy, emerge from correlation-induced symmetry breaking in a magnetic field.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Materials

Background:

  • Magic-angle twisted bilayer graphene (MATBG) displays correlated phenomena due to strong electron-electron interactions.
  • These interactions cause Fermi surface reconstruction and the formation of various correlated phases.
  • The local microscopic and topological properties of many MATBG phases remain undetermined.

Purpose of the Study:

  • To map the topological phases in MATBG under a finite magnetic field.
  • To determine the local microscopic properties and topological character of emergent phases.
  • To investigate the influence of electronic interactions on MATBG band structure.

Main Methods:

  • Utilized scanning tunnelling microscopy (STM) to probe MATBG.
  • Mapped the local density of states at the Fermi level.
  • Created a local Landau fan diagram by varying electrostatic doping and magnetic field.

Main Results:

  • Discovered six distinct topological phases arising from integer fillings in finite magnetic fields.
  • Identified these phases originate from correlation-driven symmetry-breaking transitions.
  • Observed significant modifications to the charge-neutrality Landau spectrum, including electron-hole asymmetry and large zero Landau level splitting.

Conclusions:

  • Strong electronic interactions fundamentally alter the MATBG band structure.
  • These interactions enable the formation of novel, correlation-driven topological phases.
  • The findings provide insights into the complex interplay of correlations, topology, and magnetism in 2D materials.