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Related Concept Videos

Energy Associated With a Charge Distribution01:21

Energy Associated With a Charge Distribution

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
The Hall Effect01:30

The Hall Effect

Edwin H. Hall, in the year 1879, devised an experiment that could be used to identify the polarity of the predominant charge carriers in a conducting material. From a historical perspective, this experiment was the first to demonstrate that the charge carriers in most metals are negative.
Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
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Induced Electric Fields: Applications01:27

Induced Electric Fields: Applications

An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge distribution. Specifically, the induced electric field is nonconservative because it does not work in moving a charge over a closed path. In contrast, the electrostatic field is conservative and does no net work over a closed path. Hence, electric potential can be associated with the electrostatic field but not the induced field. The following...
Diamagnetic Shielding of Nuclei: Local Diamagnetic Current01:14

Diamagnetic Shielding of Nuclei: Local Diamagnetic Current

An applied magnetic field causes the electrons present in the molecule to circulate, setting up a local diamagnetic current within the molecule. The local diamagnetic current arising from circulating sigma-bonding electrons induces a magnetic field, Blocal that opposes the applied magnetic field, B0. The effective magnetic field experienced by these nuclei is given by the difference between the applied and local magnetic fields in a phenomenon called local diamagnetic shielding. Essentially,...

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Related Experiment Video

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All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
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Density functional study of collective electron localization: detection by persistent current.

Marc Siegmund1, Markus Hofmann, Oleg Pankratov

  • 1Lehrstuhl für Theoretische Festkörperphysik, Universität Erlangen-Nürnberg, Staudtstrasse 7 B2, D-91058 Erlangen, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 10, 2011
PubMed
Summary
This summary is machine-generated.

The study reveals that persistent current in quantum rings signals Wigner crystal formation when electron-electron interactions exceed a threshold. This macroscopic current indicates the emergence of correlated electron states, crucial for understanding condensed matter systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Chemistry
  • Computational Physics

Background:

  • Persistent currents in quantum systems are sensitive to electron-electron interactions and external potentials.
  • Symmetry breaking can alter the relationship between current and interaction strength.
  • Density Functional Theory (DFT) provides a framework for studying correlated electron systems.

Purpose of the Study:

  • To investigate the impact of electron-electron interactions on persistent currents in a quantum ring model.
  • To determine the threshold for correlated electron state formation using DFT.
  • To establish macroscopic current as an indicator of Wigner crystal formation.

Main Methods:

  • Application of the optimized effective potential (OEP) implementation of DFT.
  • Modeling interacting spinless electrons on a quantum ring with a magnetic flux.
  • Inclusion of a weak Gaussian-shaped impurity potential to break rotational symmetry.

Main Results:

  • Persistent current remains constant for weak electron-electron interactions (r(S) < 2.05).
  • Current decays exponentially above a critical interaction strength (r(S) ≈ 2.05), indicating Wigner crystal formation.
  • Electron density exhibits periodic modulation above the threshold, characteristic of a second-order phase transition.

Conclusions:

  • Macroscopic persistent current serves as a direct indicator of correlated electron state formation in DFT.
  • The DFT-OEP approach accurately captures the transition to an electron Wigner crystal.
  • Understanding these transitions is vital for designing novel electronic materials and devices.