[Paper Review] Multiorbital spin-triplet pairing and spin resonance in the heavy-fermion superconductor $\mathrm{UTe_2}$

Lei Chen, Haoyu Hu+4 more|arXiv (Cornell University)|Dec 29, 2021

Iron-based superconductors research4 citations

TL;DR

This paper resolves the paradox of spin-triplet superconductivity coexisting with antiferromagnetic spin resonance in UTe₂ by proposing a multiorbital spin-triplet pairing state where the pairing matrix does not commute with the kinetic Hamiltonian. The resulting intraband pairing component naturally generates a spin resonance at the antiferromagnetic wavevector, reconciling triplet pairing with AF spin fluctuations through orbital degrees of freedom in a strongly correlated system.

ABSTRACT

The heavy-fermion system $\mathrm{UTe_2}$ is a candidate for spin-triplet superconductivity, which is of considerable interest to quantum engineering. Among the outstanding issues is the nature of the pairing state. A recent surprising discovery is the observation of a resonance in the spin excitation spectrum at an antiferromagnetic wavevector [C. Duan {\it et al.}, Nature extbf{600}, 636 (2021)], which stands in apparent contrast to the ferromagnetic nature of the interactions expected in this system. We show how the puzzle can be resolved by a multiorbital spin-triplet pairing constructed from local degrees of freedom. Because it does not commute with the kinetic part of the Hamiltonian, the pairing contains both intra- and inter-band terms in the band basis. We demonstrate that the intraband pairing component naturally yields a spin resonance at the antiferromagnetic wavevector. Our work illustrates how orbital degrees of freedom can enrich the nature and properties of spin-triplet superconductivity of strongly-correlated quantum materials.

Motivation & Objective

• To resolve the apparent contradiction between spin-triplet superconductivity and the observation of an antiferromagnetic spin resonance in UTe₂.
• To understand how spin-triplet pairing can emerge in a system dominated by antiferromagnetic spin fluctuations.
• To demonstrate that orbital degrees of freedom in strongly correlated UTe₂ enable a pairing state that supports both triplet pairing and an AF spin resonance.
• To establish a theoretical framework where the pairing matrix's non-commutativity with the kinetic term leads to mixed intra- and inter-band pairing components.
• To lay the foundation for future quantitative studies of the spin resonance energy and multiple pairing gaps in UTe₂.

Proposed method

• Construct a multiorbital spin-triplet pairing state using local degrees of freedom, including sublattice and orbital degrees associated with U-sites in the unit cell.
• Model the pairing as a matrix in both spin and orbital space, which does not commute with the kinetic part of the Hamiltonian.
• Transform the pairing into the band basis, revealing both intra-band and inter-band pairing components.
• Show that the intraband component of the spin-triplet pairing naturally produces a spin resonance at the antiferromagnetic wavevector.
• Use a minimal model to demonstrate the proof-of-principle mechanism, focusing on the interplay between ferromagnetic dimer interactions and antiferromagnetic inter-cell interactions.
• Generalize the framework to include non-unitary pairing, allowing for time-reversal symmetry breaking and additional splitting in the Bogoliubov-de Gennes spectrum.

Experimental results

Research questions

• RQ1 How can spin-triplet superconductivity coexist with antiferromagnetic spin fluctuations in UTe₂?
• RQ2 What mechanism allows a spin-triplet pairing state to produce a spin resonance at the antiferromagnetic wavevector?
• RQ3 How do orbital degrees of freedom in UTe₂ influence the structure and properties of the superconducting pairing state?
• RQ4 Why does the observed spin resonance in the superconducting state not contradict the expected ferromagnetic nature of interactions in UTe₂?
• RQ5 Can a multiorbital pairing framework explain both the triplet pairing and the emergence of a resonance at the AF wavevector?

Key findings

• The multiorbital spin-triplet pairing state in UTe₂ is non-commuting with the kinetic Hamiltonian, leading to mixed intra- and inter-band pairing components in the band basis.
• The intraband pairing component naturally gives rise to a spin resonance at the antiferromagnetic wavevector, resolving the central paradox of the system.
• The pairing mechanism is enabled by dominant ferromagnetic interactions within dimers and antiferromagnetic interactions between units, consistent with observed spin fluctuations.
• The spin-triplet nature of the pairing is preserved overall, even though the resonance arises from the intra-band component.
• The framework is robust to generalization to non-unitary pairing, which can break time-reversal symmetry and introduce additional splitting in the Bogoliubov-de Gennes spectrum.
• The model provides a conceptual bridge to other correlated systems, such as iron-based superconductors and CeCu₂Si₂, suggesting broad relevance of multiorbital pairing in quantum materials.