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Energy Bands in Solids01:01

Energy Bands in Solids

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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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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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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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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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There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
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Topological phase transitions with zero indirect band gaps.

Giandomenico Palumbo1

  • 1School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|April 4, 2024
PubMed
Summary

This study reveals a new type of topological phase transition in 1D systems, characterized by a robust zero indirect band gap. This transition, linked to persymmetry, offers novel insights into topological physics.

Keywords:
Floquet theorytopological insulatorstopological phase transitions

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Area of Science:

  • Condensed Matter Physics
  • Topological Materials
  • Quantum Mechanics

Background:

  • Topological phase transitions typically involve band gap closing and nodal structures.
  • One-dimensional systems offer unique platforms for exploring novel topological phenomena.

Purpose of the Study:

  • To investigate a distinct type of topological phase transition in 1D systems.
  • To characterize transitions marked by a robust zero indirect band gap.

Main Methods:

  • Analysis of a 1D trimer chain model with particle-hole and chiral-inversion symmetries.
  • Introduction of a deforming parameter breaking individual symmetries while preserving their combination.
  • Investigation of the Hamiltonian's persymmetry.

Main Results:

  • Observation of a robust zero indirect band gap over a range of the deforming parameter.
  • Identification of a Dirac-like point at the initial critical point.
  • The zero indirect gap is linked to the Hamiltonian's persymmetry.

Conclusions:

  • A novel topological phase transition characterized by a zero indirect band gap exists in 1D systems.
  • This transition is robust and related to persymmetry, distinct from traditional band gap closing.
  • Potential for realization in tight-binding models via Floquet driving.