Bond-ordered states and 
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-wave pairing of spinless fermions on the honeycomb lattice

Heßelmann, Stephan; Scherer, Daniel D.; Scherer, Michael M.; Wessel, Stefan

doi:10.1103/physrevb.98.045142

Cited by 13 publications

(4 citation statements)

References 60 publications

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“…This observation is in agreement with Ref. [105], where the authors carried out a non-perturbative functional RG analysis for the NN repulsive interaction. Note that only the f -wave pairing was found in this study, which, however, considered spinless fermions in MLG that does not permit s-wave pairing, due to the requisite antisymmetry property of the electronic wave function.…”

Section: Summary and Discussionsupporting

confidence: 92%

Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

Szabo,

Roy

2021

Preprint

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Performing a leading-order renormalization group analysis, here we compute the effects of generic local or short-range electronic interactions in monolayer and Bernal bilayer graphene. Respectively in these two systems chiral quasiparticles display linear and biquadratic band touching, leading to linearly vanishing and constant density of states. Consequently, the former system remains stable for weak enough local interactions, and supports a variety of ordered phases only beyond a critical strength of interactions. By contrast, ordered phases can nucleate for sufficiently weak interactions in bilayer graphene. By tuning the strength of all symmetry allowed local interactions, we construct various cuts of the phase diagram at zero and finite temperature and chemical doping. Typically, at zero doping insulating phases (such as charge-density-wave, antiferromagnet, quantum anomalous and spin Hall insulators) prevail at the lowest temperature, while gapless nematic or smectic liquids stabilize at higher temperatures. On the other hand, at finite doping the lowest temperature ordered phase is occupied by a superconductor. Besides anchoring such an organizing principle among the candidate ordered phases, we also establish a selection rule between them and the interaction channel responsible for the breakdown of linear or biquadrtic chiral nodal Fermi liquid. In addition, we also demonstrate the role of the normal state band structure in selecting the pattern of symmetry breaking from a soup of preselected incipient competing orders. As a direct consequence of the selection rule, while an antiferromagnetic phase develops in undoped monolayer and bilayer graphene, the linear (biquadratic) band dispersion favors condensation of a spin-singlet nematic (translational symmetry breaking Kekulé) superconductor in doped monolayer (bilayer) graphene, when the on site Hubbard repulsion dominates in these systems. On the other hand, nearest-neighbor (next-nearest-neighbor) repulsion accommodates charge-density-wave (quantum spin Hall insulator) and s + if (s-wave) pairing at zero and finite chemical doping in both systems, respectively.

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Section: Summary and Discussionsupporting

confidence: 92%

Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

Szabo,

Roy

2021

Preprint

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“…[31-37, 42-49, 66-69]). However, earlier theories have not discussed the role of deformations in determining the superconducting properties of BLG 50,[52][53][54] .…”

Section: Introductionmentioning

confidence: 99%

Symmetry of superconducting correlations in displaced bilayers of graphene

2019

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Using a Green's function approach, we study phonon-mediated superconducting pairing symmetries that may arise in bilayer graphene where the monolayers are displaced in-plane with respect to each other. We consider a generic coupling potential between the displaced graphene monolayers, which is applicable to both shifted and commensurate twisted graphene layers; study intralayer and interlayer phonon-mediated BCS pairings; and investigate AA and AB(AC) stacking orders. Our findings demonstrate that at the charge neutrality point, the dominant pairings in both AA and AB stackings with intralayer and interlayer electron-electron couplings can have even-parity s-wave class and odd-parity p-wave class of symmetries with the possibility of invoking equal-pseudospin and odd-frequency pair correlations. At a finite doping, however, the AB (and equivalently AC) stacking can develop pseudospin-singlet and pseudospin-triplet d-wave symmetry, in addition to s-wave, p-wave, f -wave, and their combinations, while the AA stacking order, similar to the undoped case, is unable to host the d-wave symmetry. When we introduce a generic coupling potential, applicable to commensurate twisted and shifted bilayers of graphene, d-wave symmetry can also appear at the charge neutrality point. Inspired by a recent experiment where two phonon modes were observed in a twisted bilayer graphene, we also discuss the possibility of the existence of two-gap superconductivity, where the intralayer and interlayer phonon-mediated BCS picture is responsible for superconductivity. These analyses may provide a useful tool in determining the superconducting pairing symmetries and mechanism in bilayer graphene systems.

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“…Proposals of f -wave pairing have been put forward in heavy-fermion UPt 3 , [68] twisted bilayer gaphene, [69] monolayer MoS 2 , [70], cold atom optical lattice, [71] pdoped semiconductors, [72] honeycomb lattices, [73], and other superconductors. [74] However, apart from indirect hints of such pairing symmetry in UPt 3 , [68] this state has not been directly realized in other families.…”

Section: Discussionmentioning

confidence: 99%

Prediction of $f$-wave pairing symmetry in YBa$_2$Cu$_3$O$_{6+x}$ cuprates

Adhikary,

Das

2020

Preprint

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We perform a numerical simulation of a three-band Hubbard model with two CuO2 planes and a single CuO chain layer for YBCO cuprates. The spin-fluctuation mediated pairing interaction is computed within the multiband random-phase approximation, and its pairing eigenvalues and eigenfunctions are solved as a function of chain state filling factor nc. We find that for the intrinsic value of nc in YBCO samples, one obtains the usual d-wave pairing symmetry. However, if we dope the chain layers with holes, while keeping the plane states doping fixed, the leading pairing symmetry solution becomes a unconventional f -wave symmetry. The mechanism behind the f -wave pairing is the competition between the plane states antiferromagnetic nesting and chain states' uniaxial nesting. We also find that the pairing strength is strongly augmented when the flat band bottom of the chain state passes the Fermi level for a fixed plane states doping. The f -wave pairing symmetry can be realized in YBCO cuprates in future experiments where self-doping mechanism between the chain and plane states can be minimized so that only chain state can be selectively hole-doped.

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Bond-ordered states and f -wave pairing of spinless fermions on the honeycomb lattice

Cited by 13 publications

References 60 publications

Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

Symmetry of superconducting correlations in displaced bilayers of graphene

Prediction of $f$-wave pairing symmetry in YBa$_2$Cu$_3$O$_{6+x}$ cuprates

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