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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
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Spin-Depairing-Induced Exceptional Fermionic Superfluidity.

Soma Takemori1, Kazuki Yamamoto1, Akihisa Koga1

  • 1Institute of Science Tokyo, Department of Physics, Meguro, Tokyo 152-8551, Japan.

Physical Review Letters
|January 20, 2026
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Summary
This summary is machine-generated.

Spin depairing in non-Hermitian systems stabilizes an exceptional fermionic superfluid. This unique phase features exceptional points within the superfluid state, unlike previous models where they only signal breakdown.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Topological Physics

Background:

  • Non-Hermitian (NH) systems exhibit unique phenomena not found in Hermitian systems.
  • Fermionic superfluidity is a key state in condensed matter physics.
  • Spin-resolved asymmetric hopping introduces nonreciprocity.

Purpose of the Study:

  • Investigate the non-Hermitian attractive Hubbard model with spin depairing.
  • Characterize the novel superfluid state stabilized by spin depairing.
  • Understand the role of exceptional points (EPs) in this NH superfluid.

Main Methods:

  • Theoretical analysis of the NH attractive Hubbard model.
  • Examination of spin-resolved asymmetric hopping.
  • Analysis of complex energy dispersion and density of states.
  • Investigating the interplay between EPs and system properties.

Main Results:

  • Spin depairing stabilizes a unique NH superfluid state.
  • This 'exceptional fermionic superfluidity' is characterized by EPs within the superfluid phase.
  • EPs emerge from the interplay of EPs and the effective density of states.
  • The superfluid state breaks down under strong spin depairing on a cubic lattice but remains robust on a square lattice.

Conclusions:

  • Spin depairing creates a novel topological superfluid state in NH systems.
  • Exceptional points are integral to the superfluid phase, not just its boundary.
  • Lattice geometry influences the robustness of this exceptional superfluid state.