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Pair Density Waves from Local Band Geometry.

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Researchers developed a new method to calculate superfluid weight in 2D superconductors. They found that pairing fluctuations can cause a transition from a Bardeen-Cooper-Schrieffer (BCS) state to a pair density wave (PDW) state.

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Area of Science:

  • Condensed Matter Physics
  • Superconductivity Theory
  • Materials Science

Background:

  • Superfluid weight is a crucial property determining the superconducting response.
  • Orbital-dependent pairing in multiorbital systems presents unique theoretical challenges.
  • Understanding phase transitions in superconductors is key to novel electronic applications.

Purpose of the Study:

  • Develop a band-projection formalism to calculate superfluid weight in 2D multiorbital superconductors.
  • Investigate the conditions leading to a transition from a Bardeen-Cooper-Schrieffer (BCS) state to a pair density wave (PDW) state.
  • Establish the existence of a geometric BCS-PDW transition in topological flat bands.

Main Methods:

  • Development of a band-projection formalism.
  • Calculation of the band geometric superfluid stiffness tensor.
  • Analysis of pairing fluctuations and their impact on superfluid weight.
  • Study of two-orbital superconductor models and generic topological flat bands.

Main Results:

  • The band geometric superfluid stiffness tensor can be locally nonpositive definite in specific Brillouin zone regions.
  • Pairing fluctuations can render the total superfluid weight nonpositive definite.
  • A geometric BCS to PDW state transition occurs when these nonpositive definite regions are significant or contain nodal singularities.
  • Proof of the existence of this geometric BCS-PDW transition in generic topological flat bands.

Conclusions:

  • The developed formalism accurately captures the superfluid weight in complex superconducting systems.
  • Orbital-dependent pairing and band geometry play critical roles in driving novel phase transitions.
  • The findings provide a theoretical framework for understanding and potentially engineering pair density wave states in topological materials.