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Related Concept Videos

Band Theory02:35

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When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
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Consider a conductor in electrostatic equilibrium. The net electric field inside a conductor vanishes, and extra charges on the conductor reside on its outer surface, regardless of where they originate.
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Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
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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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Gauss's Law01:07

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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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Electric Field Inside a Conductor01:20

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When a conductor is placed in an external electric field, the free charges in the conductor redistribute and very quickly reach electrostatic equilibrium. The resulting charge distribution and its electric field have many interesting properties, which can be investigated with the help of Gauss's law.
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Emergent gauge fields in band insulators.

Zhaoyu Han1, Steven A Kivelson1

  • 1Department of Physics, Stanford University, Stanford, CA 94305.

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|April 7, 2025
PubMed
Summary

Electronically trivial band insulators with specific vibrational properties can exhibit a resonating valence-bond state, featuring emergent gauge fields and mobile charges. This quantum phase may be found in certain ferroelectric materials.

Keywords:
electron–phonon couplingsemergent gauge fieldsice ruleresonating valence bond

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials Science

Background:

  • Electronically trivial band insulators typically lack exotic electronic properties.
  • Vibrational (phonon) degrees of freedom are often considered separately from electronic band structures.

Purpose of the Study:

  • To demonstrate that a specific type of band insulator can host a quantum phase with emergent phenomena.
  • To identify the characteristics of such a quantum phase and its potential material realizations.

Main Methods:

  • Explicit microscopic construction of a quantum vertex model.
  • Mapping the system to a model obeying the "ice rule."

Main Results:

  • An electronically trivial band insulator with phonon degrees of freedom can host a resonating valence-bond state.
  • This state features emergent gauge fields and deconfined excitations with nonquantized mobile charges.
  • Emergent gapless "photon" modes are identifiable characteristics of this phase.

Conclusions:

  • Resonating valence-bond states are not limited to conventional topological insulators.
  • Nearly ferroelectric materials are potential candidates for hosting these novel quantum phases.
  • The interplay between electronic and vibrational degrees of freedom can lead to emergent quantum phenomena.