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Pairing Obstructions in Topological Superconductors.

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This summary is machine-generated.

We introduce a position-space view for topological superconductors, analyzing Cooper pair wave functions and Majorana polarization. This approach reveals distinct behaviors in trivial versus topological phases, aiding in diagnosing complex superconducting states.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Solid State Physics

Background:

  • Topological insulators are understood via position-space Wannier obstructions.
  • A similar position-space perspective is lacking for topological superconductors.
  • Understanding Cooper pair and Majorana fermion behavior is crucial.

Purpose of the Study:

  • To investigate topological superconductors using a position-space framework.
  • To characterize topological phases by analyzing Cooper pair wave function and Majorana polarization.
  • To extend topological quantum chemistry concepts to superconductivity.

Main Methods:

  • Analysis of Cooper pair wave function decay in one-dimensional superconductors.
  • Development of a position-space Majorana representation.
  • Quantification of Majorana polarization to identify topological phases.

Main Results:

  • Cooper pair wave functions exhibit exponential decay in trivial phases and polynomial decay in topological phases.
  • Topological phases are characterized by a nonzero Majorana polarization, indicating quantized separation of Majorana Wannier centers.
  • The framework successfully diagnoses second-order topological superconducting phases in two dimensions.

Conclusions:

  • A position-space perspective provides a new lens for understanding topological superconductivity.
  • Majorana polarization serves as a robust indicator of topological superconductivity.
  • This work lays the foundation for generalizing topological quantum chemistry to superconducting systems.