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1. Nodal band-off-diagonal superconductivity in twisted graphene superlattices

   https://doi.org/10.1038/s41467-023-42471-4  

   Christos, Maine ; Sachdev, Subir ; Scheurer, Mathias S. ( December 2023 , Nature Communications)

   The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiralp-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

    

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2. Two-fold symmetric superconductivity in few-layer NbSe2

   https://doi.org/10.1038/s41567-021-01219-x  

   Hamill, Alex ; Heischmidt, Brett ; Sohn, Egon ; Shaffer, Daniel ; Tsai, Kan-Ting ; Zhang, Xi ; Xi, Xiaoxiang ; Suslov, Alexey ; Berger, Helmuth ; Forró, László ; et al ( April 2021 , Nature Physics)

   null (Ed.)

   The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to ~35 T, and could lead to topological superconductivity. Here we report a two-fold rotational symmetry of the superconducting state in few-layer NbSe2 under in-plane external magnetic fields, in contrast to the three-fold symmetry of the lattice. Both the magnetoresistance and critical field exhibit this two-fold symmetry, and it also manifests deep inside the superconducting state in NbSe2/CrBr3 superconductor-magnet tunnel junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behaviour to the mixing between two closely competing pairing instabilities, namely the conventional s-wave instability typical of bulk NbSe2 and an unconventional d- or p-wave channel that emerges in few-layer NbSe2. Our results demonstrate the unconventional character of the pairing interaction in few-layer transition metal dichalcogenides and highlight the exotic superconductivity in this family of two-dimensional materials. 

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3. Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations

   https://doi.org/10.1038/s41467-022-30302-x  

   Jiang, Weilun ; Liu, Yuzhi ; Klein, Avraham ; Wang, Yuxuan ; Sun, Kai ; Chubukov, Andrey V. ; Meng, Zi Yang ( May 2022 , Nature Communications)

   The origin of the pseudogap behavior, found in many high-T_csuperconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a “gap-filling rather than “gap-closing behavior, similar to the one observed in cuprate superconductors. Our results present direct evidence of the pseudogap state, driven by superconducting fluctuations.

    

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4. A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4

   https://doi.org/10.1038/s41535-020-0245-1  

   Kivelson, Steven Allan ; Yuan, Andrew Chang ; Ramshaw, Brad ; Thomale, Ronny ( December 2020 , npj Quantum Materials)

   null (Ed.)

   Abstract A variety of precise experiments have been carried out to establish the character of the superconducting state in Sr 2 RuO 4 . Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here we propose that these results can be reconciled if we assume that there is a near-degeneracy between a $${d}_{{x}^{2}-{y}^{2}}$$ d x 2 − y 2 (B 1 g in group theory nomenclature) and a $${g}_{xy({x}^{2}-{y}^{2})}$$ g x y ( x 2 − y 2 ) (A 2 g ) superconducting state. From a weak-coupling perspective, such an accidental degeneracy can occur at a point at which a balance between the on-site and nearest-neighbor repulsions triggers a d -wave to g -wave transition. 

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5. Multiband mean-field theory of the d+ig superconductivity scenario in Sr2RuO4

   https://doi.org/10.1103/PhysRevB.108.014502  

   Yuan, Andrew C ; Berg, Erez ; Kivelson, Steven A ( July 2023 , Physical Review B)

   Many seemingly contradictory experimental findings concerning the superconducting state in Sr2RuO4 can be accounted for on the basis of a conjectured accidental degeneracy between two patterns of pairing that are unrelated to each other under the (D4h) symmetry of the crystal: a dx2-y2-wave (B1g) and a gxy(x2-y2)-wave (A2g) superconducting state. In this paper, we propose a generic multiband model in which the g-wave pairing involving the xz and yz orbitals arises from second-nearest-neighbor BCS channel effective interactions. Even if timereversal symmetry is broken in a d + ig state, such a superconductor remains gapless with a Bogoliubov Fermi surface that approximates a (vertical) line node. The model gives rise to a strain-dependent splitting between the critical temperature Tc and the time-reversal symmetry-breaking temperature TTRSB that is qualitatively similar to some of the experimental observations in Sr2RuO4. 

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