Time-Reversal Symmetry Breaking Superconductivity in the Coexistence Phase with Magnetism in Fe Pnictides

Abstract

We argue that superconductivity in the coexistence region with spin-density-wave (SDW) order in weakly doped Fe-pnictides differs qualitatively from the ordinary s +− state outside the coexistence region, as it develops an additional gap component which is a mixture of intra-pocket singlet (s ++ ) and inter-pocket spin-triplet pairings (the t−state). The coupling constant for the t−channel is proportional to the SDW order and involves interactions that do not contribute to superconductivity outside of the SDW region. We argue that the s +− and t−type superconducting orders coexist at low temperatures, and the relative phase between the two is in general different than 0 or π, manifesting explicitly the breaking of the time-reversal symmetry promoted by long-range SDW order. We show that this exotic state emerges already in the simplest model of Fe-pnictides, with one hole pocket and two symmetry-related electron pockets. We argue that in some parameter range time-reversal gets broken even before long-range superconducting order develops. IntroductionIron-based superconductors (FeSCs) have been the subject of intense study since 20081 . Their rich phase diagram includes the regions of superconductivity (SC), spin density wave (SDW), nematic order, and a region where SDW, SC, and nematic order coexist 2 . Outside the SDW/nematic region, SC develops in the spin-singlet channel and in most of Fe-based superconductors has s−wave symmetry with a π phase shift between the SC order parameters on hole and on electron pockets ( s +− gap structure) 3,4 . It has been recently argued by several groups that the multiband structure of FeSCs allows for superconducting states with more exotic properties 5-11,14-21 . Of particular interest are SC states that break time-reversal symmetry (TRS), as such states have a plethora of interesting properties like, e.g., novel collective modes 12,13,15,20 . TRS-broken states emerge when the phase differences ψ i between SC order parameters on different Fermi surfaces (FS) are not multiples of π.The two current proposals for TRS breaking in FeSCs are s + id 5,[9][10][11]19 and s + is states 6,15,20,21 . The first emerges when attractions in the d−wave and s−wave channels are of near-equal strength. The second emerges when there is a competition between different s +− states favored by inter-pocket and intra-pocket interactions. Both of these proposals were, however, argued to be applicable only to strongly hole or electron-doped FeSCc. For weakly/moderately doped FeSCs the common belief is that s +− superconductivity is robust. In this communication we argue that an exotic state which breaks TRS can emerge already at low doping, in a range where SC is known [22][23][24][25][26][27][28][29][30] to emerge from a pre-existing SDW state. Previous works on SC in the coexistence region focused on the SDW-induced modification of the form of s +− gap 31-37 . We argue that there is another effect -SDW order also induces attraction in another pairing channel, for which the order parameter is an admix...

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

“…46 ). For instance, in the equation above, setting M = ∆ s = 0 and assuming perfect nesting yields the following linearized equation for ∆ t…”

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Coexistence of Charge-Density-Wave and Pair-Density-Wave Orders in Underdoped Cuprates

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Interplay between unidirectional and bidirectional charge-density-wave orders in underdoped cuprates

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