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A superconductor is a substance that offers zero resistance to the electric current when it drops below a critical temperature. Zero resistance is not the only interesting phenomenon as materials reach their transition temperatures. A second effect is the exclusion of magnetic fields. This is known as the Meissner effect. A light, permanent magnet placed over a superconducting sample will levitate in a stable position above the superconductor. High-speed trains that levitate on strong...
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A substance that reaches superconductivity, a state in which magnetic fields cannot penetrate, and there is no electrical resistance, is referred to as a superconductor. In 1911, Heike Kamerlingh Onnes of Leiden University, a Dutch physicist, observed a relation between the temperature and the resistance of the element mercury. The mercury sample was then cooled in liquid helium to study the linear dependence of resistance on temperature. It was observed that, as the temperature decreased, the...
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Microscopic study of the intermediate mixed state in intertype superconductors.

Vyacheslav D Neverov1,2, Alexander V Kalashnikov3, Andrey V Krasavin2,3

  • 1Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russian Federation.

Beilstein Journal of Nanotechnology
|January 14, 2026
PubMed
Summary

This study reveals key features of intertype superconductivity, including nonmonotonic vortex interactions and cluster formation. Microscopic calculations establish a foundation for understanding this regime beyond critical temperatures.

Keywords:
Bogoliubov–de Gennes equationsintertype regimemicroscopic calculationssuperconductivityvortices in superconductors

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Area of Science:

  • Condensed Matter Physics
  • Superconductivity Theory

Background:

  • The intermediate mixed state (intertype or IT regime) in superconductors bridges Type I and Type II behaviors.
  • Understanding vortex interactions and configurations in this regime is crucial for fundamental physics and potential applications.

Purpose of the Study:

  • To conduct a comprehensive microscopic investigation of the intermediate mixed state in superconductors.
  • To analyze vortex configurations and interactions across the full temperature range below the critical temperature (Tc).
  • To establish a microscopic foundation for intertype superconductivity.

Main Methods:

  • Utilized fully self-consistent Bogoliubov-de Gennes calculations.
  • Employed a lattice model to simulate few-vortex configurations.
  • Analyzed superconducting behavior across the temperature range 0 < T < Tc.

Main Results:

  • Demonstrated nonmonotonic vortex interactions and the formation of vortex clusters, characteristic of IT superconductivity.
  • Constructed a "temperature-coupling" phase diagram showing distinct superconducting regimes converging at a Bogomolnyi point.
  • Identified a deep IT region with irregular vortex configurations influenced by many-body vortex effects.

Conclusions:

  • The study provides a robust microscopic basis for understanding intertype superconductivity.
  • The findings extend the description of IT superconductivity beyond the immediate vicinity of the critical temperature.
  • Results align with and extend predictions from extended Ginzburg-Landau theory.