Induced spin-triplet pairing in the coexistence state of antiferromagnetism and singlet superconductivity: Collective modes and microscopic properties

Abstract

The close interplay between superconductivity and antiferromagnetism in several quantum materials can lead to the appearance of an unusual thermodynamic state in which both orders coexist microscopically, despite their competing nature. A hallmark of this coexistence state is the emergence of a spin-triplet superconducting gap component, called π-triplet, which is spatially modulated by the antiferromagnetic wave-vector, reminiscent of a pair-density wave. In this paper, we investigate the impact of these π-triplet degrees of freedom on the phase diagram of a system with competing antiferromagnetic and superconducting orders. Although we focus on a microscopic two-band model that has been widely employed in studies of iron pnictides, most of our results follow from a Ginzburg-Landau analysis, and as such should be applicable to other systems of interest, such as cuprates and heavy fermions. The Ginzburg-Landau functional reveals not only that the π-triplet gap amplitude couples tri-linearly with the singlet gap amplitude and the staggered magnetization magnitude, but also that the π-triplet d-vector couples linearly with the magnetization direction. While in the mean field level this coupling forces the d-vector to align parallel or anti-parallel to the magnetization, in the fluctuation regime it promotes two additional collective modes -a Goldstone mode related to the precession of the d-vector around the magnetization and a massive mode, related to the relative angle between the two vectors, which is nearly degenerate with a Leggett-like mode associated with the phase difference between the singlet and triplet gaps. We also investigate the impact of magnetic fluctuations on the superconducting-antiferromagnetic phase diagram, showing that due to their coupling with the π-triplet order parameter, the coexistence region is enhanced. This effect stems from the fact that the π-triplet degrees of freedom promote an effective attraction between the antiferromagnetic and singlet superconducting degrees of freedom, highlighting the complex interplay between these two orders, which goes beyond mere competition for the same electronic states.

Ground State Phase Diagram of the $t$-$t'$-$J$ model

“…We further verify that this relation holds when a global d-wave singlet pairfield is applied. This relation is qualitatively consistent with several studies where there is coexistence of AFM, d-wave singlet pairing and (π, π) p−wave triplet pairing [36,46,47]. This further implies that this (π, π)pwave triplet pairing is purely parasitic and relies on the existence of both AFM and d-wave singlet pairing.…”

Strong In-Plane Magnetic Field-Induced Reemergent Superconductivity in the van der Waals Heterointerface of NbSe2 and CrCl3

“…Theoretically, to the best of our knowledge, the nature of intriguing reemergent superconducting phase observed in the NbSe2/CrCl3 heterostructure in the in-plane magnetic field could be understood through the mechanisms of that (i) the disorder induced flux-pinning nature 35,36 ; (ii) the exchange field compensation effect 37,38 ; (iii) the triplet pairing SC induced by the enhancement of interfacial spin-orbit coupling 48,49 ; and (iv) the FFLO state 11,12 . intertwined with vortex and defects [53][54][55] .…”

Disentangling superconducting and magnetic orders in NaFe1−xNixAs using muon spin rotation

“…Itinerant AFM and SC orders are generally expected to compete strongly for the same electronic states; this behavior can be captured within a simple Ginzburg-Landau free energy for the AFM and SC order parameters, M and ∆, respectively (in the context of Fe-HTS, see for instance Refs. 14,[31][32][33]:…”