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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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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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Intrinsic semiconductors are highly pure materials with no impurities. At absolute zero, these semiconductors behave as perfect insulators because all the valence electrons are bound, and the conduction band is empty, disallowing electrical conduction. The Fermi level is a concept used to describe the probability of occupancy of energy levels by electrons at thermal equilibrium. In intrinsic semiconductors, the Fermi level is positioned at the midpoint of the energy gap at absolute zero. When...
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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
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The contact of metal and semiconductor can lead to the formation of a junction with either Schottky or Ohmic behavior.
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Punctured-Chern Topological Invariants for Semimetallic Band Structures.

Ankur Das1, Eyal Cornfeld1, Sumiran Pujari2

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|May 19, 2023
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Researchers developed a new "punctured-Chern" invariant to classify complex topological phases in materials. This method accurately characterizes topological transitions and semimetallic nodal defects, advancing condensed matter physics.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Mechanics

Background:

  • Topological insulators classify gapped electronic bands, but nontrivial topology exists in systems with multiple gap-closing points.
  • Existing methods struggle to capture the complex topology of systems with multiple bands and gapless points.

Purpose of the Study:

  • To introduce a general wave-function-based invariant, the "punctured-Chern" invariant, for classifying nontrivial band topology.
  • To demonstrate the invariant's applicability to diverse gapless topological systems.
  • To provide a unified framework for understanding topological phase transitions and semimetallic nodal defects.

Main Methods:

  • Construction of a general wave-function-based "punctured-Chern" invariant.
  • Analysis of a two-dimensional fragile topological model to study band-topological transitions.
  • Analysis of a three-dimensional triple-point nodal defect model to characterize semimetallic topology.

Main Results:

  • The "punctured-Chern" invariant successfully captures nontrivial topology in systems with multiple bands and gap-closing points.
  • The invariant characterizes topological transitions in a 2D fragile topological model.
  • The invariant describes the semimetallic topology of a 3D triple-point nodal defect, yielding half-integer topological charges relevant to anomalous transport.

Conclusions:

  • The "punctured-Chern" invariant offers a powerful tool for classifying complex topological phases beyond traditional topological insulators.
  • The invariant provides a unified approach to understanding diverse gapless topological phenomena.
  • The classification of Nexus triple points (Z×Z) is confirmed under specific symmetry conditions.