An unconventional superconductor is distinguished with two types of gap functions: unitary and non-unitary. This core subject has been concentrated on purely spin-triplet or singlet-triplet mixed superconductors. However, the generalization to a purely spin-singlet superconductor has remained primarily of theoretical interest, which requires at least a multi-orbital correlated electronic systems. In this work, we present a possible establishment of both unitary and non-unitary pairings for spin-singlet superconductors with two atomic orbitals. Then we investigate the effects of atomic spin-orbit coupling and find a new spin-orbit-coupled non-unitary superconductor that supports exotic phenomena. Remarkably, there are mainly three features. Firstly, the atomic spin-orbit coupling locks the electron spins to be out-of-plane, which could give birth to the Type II Ising superconductivity with a large in-plane upper critical field compared to the Pauli limit. Secondly, topological chiral or helical Majorana edge state could be realized even in the absence of external magnetic fields or Zeeman fields. In addition, a spin-polarized superconducting state could even be generated by spin-singlet non-unitary pairings with spontaneous time-reversal breaking, which severs as a smoking gun to detect this exotic state by measuring the spin-resolved density of states. Therefore, our work might pave a new avenue to spin-orbit-coupled superconductors with spin-singlet non-unitary pairing symmetries.
Using an RPA approximation, we have calculated the strengths of the singlet and triplet pairing interactions which arise from the exchange of spin and orbital fluctuations for a 2-orbital model of the Fe-pnictide superconductors. When the system is doped with F, the electron pockets become dominant and we find that the strongest pairing occurs in the singlet d-wave pairing and the triplet p-wave pairing channels, which compete closely. The pairing structure in the singlet d-wave channel corresponds to a superposition of near neighbor intra-orbital singlets with a minus sign phase difference be…
Recent experiments in quantum critical heavy fermion metals have pushed to the fore the question about whether antiferromagnetic fluctuations can promote both spin-singlet and spin-triplet superconductivity. Here we address the issue through non-perturbative calculations in antiferromagnetically correlated Kondo systems. We identify Kondo-destruction quantum critical points in both the SU(2) symmetric and Ising-anisotropic cluster Bose-Fermi Anderson models. The spin-singlet pairing correlations are significantly enhanced near the quantum critical point in the SU(2) case; however, with adequat…
In cuprate superconductors doping is believed to create holes on the O-sites, which couple antiferromagnetically with holes on the Cu-sites to form the so-called Zhang-Rice singlets. Here we study a d-wave pairing state based on the Zhang-Rice singlet states. Upper and lower bounds of an off-diagonal long-range order parameter with d-wave symmetry for this state are estimated. We also introduce a concrete model with on-site Coulomb repulsion and kinds of antiferromagnetic interactions whose ground state is this d-wave pairing state.
The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$T\sb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation functions describing respectively the singlet hopping and the superconducting pairing. Rigorous derivation of their values is reported based on the finding that specific invariant classes of polynomial Green functions in terms of the Wannier overlap coefficients $ν\sb{ij}$ exist.
Based on the degeneracy of the d_{zx} and d_{yz} orbitals in Sr_2RuO_4 it is argued that the Cooper pairs condense in orbital singlets. Together with the spin-triplet wave functions the real-space wave function then is symmetric. Considering interaction effects the order parameter is found to have A_{1g} symmetry consistent with a number of experimental observations. The sensitivity of the material on non-magnetic impurities follows in a straightforward manner from the orbital-singlet configuration.
Have you been lying awake wondering what symmetries determine whether a superconductor is spin singlet, triplet, or both? We show that if BCS theory is supplied with additional degrees of freedom, spin singlet can coexist with spin triplet superconductivity. In the first part, we didactically guide the reader to the most general superconducting state using symmetry arguments. If both singlet and triplet pairing channels are present, a magnetic field can convert between spin singlet and triplet states. In the second part, we discuss two possible singlet-triplet superconductors: CeRh$_2$As$_2$ a…
Recently, a strongly enhanced xy anisotropy of magnetic excitations was observed in YBa_2Cu_3O_y (YBCO_y) with y=6.45 and Tc=35 K [Science 319, 597 (2008)]. Unlike the observation in YBCO_6.6 and YBCO_6.85, the anisotropy grows to be pronounced at lower temperature and at lower energy, and is not suppressed by the onset of superconductivity. We propose that the effect of singlet pairing is substantially reduced in YBCO_6.45. This reduction concomitantly enhances an order competing with singlet pairing, a strong tendency of the so-called d-wave Pomeranchuk instability, leading to the magnetic e…
We propose a two-dimensional exciton model showing the possibility of two-exciton pairing in cuprates, both in singlet and in triplet states. The former is assumed to be responsible for the superconductivity and the latter for the unusual normal state properties. The ground state is found to be a projection of the Bose condensation of N/2 mobile bosons with a ηprojection operator which is a generalization of the Gutzwiller projection operator. The phase diagram of the model shows insulator-superconductivity and superconductivity-metal transitions with doping.
In the present paper, we propose the parity even,orbital singlet and spin triplet pairing state as the ground state of the newly discovered super-conductor $LaO_{1-x}F_xFeAs$.The pairing mechanism involves both the special shape of the electron fermi surface and the strong ferromagnetic fluctuation induced by Hund's rule coupling.The special behavior of the Bogoliubov quasi-particle spectrum may leads to "Fermi arc" like anisotropy super-conducting gap, which can be detected by angle resolved photo emission(ARPES).The impurity effects are also discussed.
We study spin-half fermions in a one-dimensional extended Hubbard chain at low filling. We identify three triplet and one singlet pairing channels in the system, which are independently tunable as a function of nearest-neighbor charge and spin interactions. In a large-size system with translational invariance, we derive gap equations for the corresponding pairing gaps and obtain a Bogoliubov-de Gennes Hamiltonian with its non-trivial topology determined by the interplay of these gaps. In an open-end system with a fixed number of particles, we compute the exact many-body ground state and identi…
The model of local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems is studied for anisotropic pairing symmetry. The phase diagram is presented and the phase fluctuations effects are analyzed within the Kosterlitz-Thouless scenario.
I present a microscopic theory I proposed recently to describe high-T_c superconductivity in cuprates. I show that coherent pairing states consisting of extended singlet Cooper pairs and triplet $π$ pairs can manifest both the Mott insulating antiferromagnetic order and the d-wave superconducting order. From this configuration of coherent pairing states, I can describe both the single electron properties and the low energy collective excitations in high T_c superconductivity in the same framework. The quasiparticle can be derived directly with respect to the coherent pairing states. While, the…
Recent experiments in multiband Fe-based and heavy-fermion superconductors have challenged the long-held dichotomy between simple $s$- and $d$-wave spin-singlet pairing states. Here, we advance several time-reversal-invariant irreducible pairings that go beyond the standard singlet functions through a matrix structure in the band/orbital space, and elucidate their naturalness in multiband systems. We consider the $sτ_{3}$ multiorbital superconducting state for Fe-chalcogenide superconductors. This state, corresponding to a $d+d$ intra- and inter-band pairing, is shown to contrast with the more…
We investigate the influence of critical spin fluctuations on electromagnetic responses in the odd-frequency superconductivity. It is shown that the Meissner kernel of the odd-frequency superconductivity is strongly reduced by the critical spin fluctuation or the massless spin wave mode in the antiferromagnetic phase. These results imply that the superfluid density is reduced, and the London penetration depth is lengthened for the odd-frequency pairing. It is also shown that the zero field Flude-Ferrell-Larkin-Ovchinnikov pairing is spontaneously realized both for even- and odd-frequency in th…
We show how in principle a coherent coupling between two superconductors of opposite parity can be realized in a three-layer oxide heterostructure. Due to strong intraionic spin-orbit coupling in the middle layer, singlet Cooper pairs are converted into triplet ones and vice versa. This results in a large enhancement of the triplet superconductivity, persisting well above the native triplet critical temperature.
Recently synthesized Kagome compounds AV$_3$Sb$_5$ attract great attention due to the unusual coexistence of the topology, charge density wave and superconductivity. In this {\it Letter}, based on the band structures for CsV$_3$Sb$_5$ in pristine phase, we fit an effective 6-band model for the low-energy processes; utilizing the random phase approximation (RPA) on the effective minimal model, we obtain the momentum-resolved static spin susceptibility attributing the spin-fluctuation pairing mechanism, we find that the superconducting pairing strengths increase with the lift of the Coulomb corr…
We present precise measurements of the upper critical field (Hc2) in the recently discovered cobalt oxide superconductor. We have found that the critical field has an unusual temperature dependence; namely, there is an abrupt change of the slope of Hc2(T) in a weak field regime. In order to explain this result we have derived and solved Gor'kov equations on a triangular lattice. Our experimental results may be interpreted in terms of the field-induced transition from singlet to triplet superconductivity.
Monovalent metals contain half filled band (HFB) of s-electrons. Emphasizing importance of Coulomb repulsions in HFB in 2D and 1D monovalent systems we sketched a theory (2018) for ambient temperature granular superconductivity reported by Thapa and Pandey (2018) in Au-Ag nanostructures (updated by Thapa et al., 2019). Sharpening our theory, we suggest that \textit{Coulomb repulsions in certain structurally perturbed regions (atomic clusters, stacking faults, grain boundaries etc.) create nanoscale reservoirs of singlet electron pairs}. These low dimensional patches are hybridized to a backgro…
We suggest that superconductivity (SC) in the organic charge transfer solids (CTS) is reached from a Bond-Charge Density Wave (BCDW). We discuss an effective model for the BCDW to SC transition, an attractive U extended Hubbard Hamiltonian with repulsive nearest neighbor interaction V. We discuss experimental consequences of the theory for different classes of CTS superconductors as well as related inorganic materials.
We discuss phase diagrams obtained by calculating temperature dependent correlation functions for superconductivity and density waves for a single (5,0) carbon nanotube (CN). We use one-loop renormalization group method within logarithmic accuracy. In this system we must specify scattering channels in terms of momentum along the circumferential direction as well as the axis direction, since (5,0) CN has two degenerate bands crossing the Fermi energy with circumferential momenta. We find singlet-superconducting phase with $5\hbar$ circumferential angular momentum. Critical exponents for each co…
We study the possible superconducting pairing symmetry mediated by spin and charge fluctuations on the honeycomb lattice using the extended Hubbard model and the random-phase-approximation method. From $2\%$ to $20\%$ doping levels, a spin-singlet $d_{x^{2}-y^{2}}+id_{xy}$-wave is shown to be the leading superconducting pairing symmetry when only the on-site Coulomb interaction $U$ is considered, with the gap function being a mixture of the nearest-neighbor and next-nearest-neighbor pairings. When the offset of the energy level between the two sublattices exceeds a critical value, the most fav…
Confirmation of the phononic origin of Cooper pair formation in superconductors came with the demonstration that the interaction was retarded and that the corresponding energy scales were associated with phonons. Using cellular dynamical mean-field theory for the two-dimensional Hubbard model, we identify such retardation effects in d-wave pairing and associate the corresponding energy scales with short-range spin fluctuations. We find which frequencies are relevant for pairing as a function of interaction strength and doping and show that the disappearance of superconductivity on the overdope…
The recent observation of fully-gapped superconductivity in Yb doped CeCoIn5 poses a paradox, for the disappearance of nodes suggests that they are accidental, yet d-wave symmetry with protected nodes is we ll established by experiment. Here, we show that composite pairing provides a natural resolution: in this scenario, Yb doping drives a Lifshitz transition of the nodal Fermi surface, forming a fully-gapped d-wave molecular superfluid of composite pairs. The T4 dependence of the penetration depth associated with the sound mode of this condensate is in accord with observation.
To pinpoint the microscopic mechanism for superconductivity has proven to be one of the most outstanding challenges in the physics of correlated quantum matter. Thus far, the most direct evidence for an electronic pairing mechanism is the observation of a new symmetry of the order-parameter, as done in the cuprate high-temperature superconductors. Like distinctions based on the symmetry of a locally defined order-parameter, global, topological invariants allow for a sharp discrimination between states of matter that cannot be transformed into each other adiabatically. Here we propose an unconv…
A possibility of the realization of the p-wave spin-singlet superconductivity ($p$SS), whose gap function is odd both in momentum and in frequency, is investigated by solving the gap equation with the phenomenological interaction mediated by the antiferromagnetic spin fluctuation. The $p$SS is realized prevailing over the d-wave singlet superconductivity ($d$SS) in the vicinity of antiferromagnetic quantum critical pint (QCP) both on the paramagnetic and on the antiferromagnetic sides. Off the QCP in the paramagnetic phase, however, the $d$SS with line-nodes is realized as \textit{conventional…
We argue that the pseudogap phase may be an attribute of the non-BCS pairing of quantum-critical, diffusive fermions near the antiferromagnetic quantum critical point. We derive and solve a set of three coupled Eliashberg-type equations for spin-mediated pairing and show that in some $T$ range below the pairing instability, there is no feedback from superconductivity on fermionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the superconducting condensate but preserve the leading edge gap in the fermio…
The phase diagram of order parameters for pairing and phase coherence in hole-doped cuprates is discussed. By examining carefully some recent inelastic neutron scattering data obtained on hole-doped cuprates and heavy fermion compound UPd2Al3 in which the superconductivity is mediated by spin fluctuations, we conclude that the coherent gap in hole-doped cuprates has most likely the magnetic origin and scales with Tc, on average, as 2Dc/kBTc = 5.4. We discuss a model of the superconductivity in hole-doped cuprates and the symmetries of two order parameters.
To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference (QPI) imaging, to reveal quantitatively the momentum-space (k-space) structu…
Different models for doping of two-orbital chains with mobile $S=1/2$ fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S=1 spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnetic (AF) and FM order leads to a rich phase diagram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the pr…
Effects of inhomogeneous doping on the high-$T_c$ cuprate superconductors are studied within the framework of the t-J model. Especially, the boundary between two non-superconducting regions with doping rates much higher and lower than the optimal one is examined. It is found that, although there is no superconductivity in the bulk, a superconducting region appears at the boundary because singlet resonating valence bond order and holon condensation occur simultaneously in this region. The critical temperature of the induced superconductivity can be higher than that of the optimally doped sample…
Kinematic constraint arising in the case of superconducting pairing with large momentum results in a cutoff of the screened Coulomb potential excluding large momentum transfers. This leads to a pairing potential oscillating in the real space that ensures a rise of bound singlet pairs. In multilayer cuprates, there is strong Coulomb interaction between particles composing the pair not only in the same cuprate layer but in the neighboring layers as well. In the framework of such a scenario, we explain a universal dependence of the superconducting transition temperature on the number of layers in…
We report a ^{59}Co Knight shift measurement in a single crystal of the cobalt oxide superconductor Na_{x}CoO_2\cdot1.3H_2O (T_c=4.25 K). We find that the shift due to the spin susceptibility, K^s, is substantially large and anisotropic, with the spin shift along the a-axis K^s_a being two times that along the c-axis K^s_c. The shift decreases with decreasing temperature (T) down to T\sim100 K, then becomes a constant until superconductivity sets in. Both K^s_a and K^s_c decrease below T_c. Our results indicate unambiguously that the electron pairing in the superconducting state is in the spin…
A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting Tc by taking into account the pairing mediated by charge and spi…
Despite of many experimental and theoretical efforts, the pairing symmetry of superconductivity in Sr$_2$RuO$_4$ remains undecided. The accidentally degenerate $d_{x^2-y^2}+ig$ is consistent with most current experiments and seems to be one of the most probable candidates, but we still lack a satisfactory theoretical mechanism for its appearance. Here we construct a phenomenological model combining realistic electronic band structures and all symmetry-allowed multipole fluctuations as potential pairing glues, and make a systematic survey of major pairing states within the Eliashberg framework.…
Pairing in superconductors occurs in a variety of channels and can be produced by various mechanisms. Here, we show that, in the presence of strong correlations, a novel singlet-pair superconducting phase can occur in ladder geometries with the fermions in the pairs residing on different sides of a Mott insulating stripe. The antiferromagnet correlations in the Mott stripe provide the pairing "glue" in such a phase. We study, using the density matrix renormalization group method, the ground state of four-leg t-J ladders with Mott insulating stripes in the inner two legs. Pairing and supercondu…
Under the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we argue that the pairing symmetry in all measured iron-based superconductors is universally consistent with the A_{1g} s-wave. The robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high T_c superconducting mechanisms: (1) the correspondence principle: the short range magnetic exchange interactions and the Fermi surfaces act collaboratively to achieve high T_c superconduc…
Superconductivity in many strongly correlated materials appears in proximity to a density-wave or nematic order and is believed to be mediated by quantum-critical (QC) fluctuations of the corresponding order parameter. We argue that fingerprints of QC pairing can be extracted from the angular dependence of the gap $Δ(θ)$. We consider pairing by QC nematic fluctuations and show that there exist multiple pairing instabilities within the same symmetry ($s-$wave in our case), with closely spaced transition temperatures $T_{c,n}$. The corresponding $Δ_n (θ)$ change sign $8n$ times along the FS. Onl…
We propose a phase diagram of quasi-low-dimensional type II superconductors in parallel magnetic fields, when antiferromagnetic fluctuations contribute to the pairing interactions. We point out that pairing interactions mediated by antiferromagnetic fluctuations necessarily include both singlet channels and triplet channels as attractive interactions. Usually, a singlet pairing is favored at zero field, but a triplet pairing occurs at high fields where the singlet pairing is suppressed by the Pauli paramagnetic pair-breaking effect. As a result, the critical field increases divergently at low …
By paying attention to the hole-doped two-dimensional systems of antiferromagnetically (strongly) correlated electrons, we discuss the cause of hole-rich phase formation in association with phase separation. We show that the phase diagram obtained from the Maxwell's construction in the plane of temperature vs. hole density is consistent with one derived from the evaluation of hole-rich and electron-rich phases in real space. We observe that the formation of a hole-rich phase is attributed to the aggregation of hole pairs induced by spin singlet pairs present in the pseudogap phase and that a d…
A theoretical study is presented on the odd-frequency spin-singlet pairing that arises in nonuniform even-frequency superconductors as a consequence of broken translation symmetry. The effect of the odd-frequency pairing on the superfluid density and the spin susceptibility is analyzed by using the quasiclassical theory of superconductivity. It is shown that (1) the superfluid density is reduced by the formation of the odd-frequency singlet pairs and (2) the odd-frequency pairing increases the spin susceptibility even though its spin symmetry is singlet. The two unusual phenomena are related t…
We formulate a general framework for addressing both odd- and even-frequency superconductivity in Dirac semimetals and demonstrate that the odd-frequency or the Berezinskii pairing can naturally appear in these materials because of the chirality degree of freedom. We show that repulsive frequency-dependent interactions favor the Berezinskii pairing while an attractive electron-electron interaction allows for the BCS pairing. In the case of compensated Dirac and Weyl semimetals, both the conventional BCS and odd-frequency Berezinskii pairings require critical coupling. Since these pairings coul…
In order to probe the effect of charge fluctuations on triplet pairing, we study the pairing symmetry in the one-band Hubbard model having the off-site Coulomb repulsion ($V$) on top of the on-site repulsion as a model for the $γ$ band of Sr$_2$RuO$_4$, a strong candidate for triplet pairing superconductor. The result, obtained with the dynamical cluster approximation combined with the quantum Monte-Carlo method, and confirmed from the fluctuation exchange approximation, shows that while $d_{x^2-y^2}$-pairing dominates over $p$ in the absence of $V$, introduction of $V$ makes $p_{x+y}$ and $d_…
The Kondo lattice model describes a quantum phase transition between the antiferromagnetic state and heavy-fermion states. Applying the dual-fermion approach, we explore possible superconductivities emerging due to the critical antiferromagnetic fluctuations. The d-wave pairing is found to be the leading instability only in the weak-coupling regime. As the coupling is increased, we observe a change of the pairing symmetry into a p-wave spin-singlet pairing. The competing superconductivities are ascribed to crossover between small and large Fermi surfaces, which occurs with formation of heavy q…
We show that the newly discovered BiS$_2$-based superconductors may have a dominant triplet pairing component, in addition to a subdominant singlet component arising from the spin-orbital coupling. The pairing respects time-reversal symmetry. The dominant triplet gap causes gap sign changes between the spin-split Fermi pockets. Within a pocket, the gap function respects $d^*_{x^2-y^2}$-wave symmetry, where the star indicates joint spin-lattice rotations. Below the Lifshitz filling level the gap is nodelss and the superconducting state is weak topological. Above the Lifshitz points the gap beco…
The normal and pairing self-energies are the microscopic quantities which reflect and characterize the underlying interaction in superconductors. The momentum and frequency dependence of the self-energies, therefore, provides the experimental criteria which can single out the long sought-after pairing interaction among many proposed ideas. This line of research to pin down the pairing interaction for the cuprate superconductors has been carried out with some success by analyzing the momentum distribution curves of laser angle-resolved photo-emission spectroscopy (ARPES) data. Some progress and…
The microscopic origin of triplet superconductivity in Sr$_2$RuO$_4$ is discussed, paying attention to the role of Coulomb interaction, $U_{pp}$, at the O site. It is shown on the $d$-$p$ model that $U_{pp}$ induces a ferromagnetic exchange interaction between "d-electrons" (molecular orbital with $d_{xy}$-symmetry) at adjacent Ru sites, leading to short-range ferromagnetic correlations and promoting Cooper pairing with ($\sin p_x\pm\ii\sin p_y$)-symmetry on the $γ$-band. The reason why such ferromagnetic correlations work effectively may be traced back to the fact that the level of 4d-electro…
Hund's pairing refers to Cooper pairing generated by onsite interactions that become attractive due to large Hund's exchange $J$. This is possible in multiorbital systems even when all local bare interactions are repulsive, since attraction in specific channels are given by certain linear combinations of interaction parameters. On the other hand, pairing processes such as the exchange of spin fluctuations, are also present. We compare these two mechanisms on an equal footing using electronic bands appropriate for different classes of multiorbital systems over a wide range of interaction parame…
The superconducting state in uranium compounds UGe2, URhGe and UCoGe is formed at temperatures far below the Curie temperature pointing on nonconventional nature of superconductivity in these materials - namely the superconductivity with triplet pairing. The emergence of superconductivity is accompanied by the slight magnetization expulsion typical for the type-II superconductors. Following classic Abrikosov paper I develop the theory of type-II superconductivity in application to two-band ferromagnetic metal with equal spin triplet pairing.
We introduce and analyze a variational wave function for quasi two-dimensional kappa-ET organic salts containing strong local and nonlocal correlation effects. We find an unconventional superconducting ground state for intermediate charge carrier interaction, sandwiched between a conventional metal at weak coupling and a spin liquid at larger coupling. Most remarkably, the excitation spectrum is dramatically renormalized and is found to be the driving force for the formation of the unusual superconducting state.
Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for d-wave superconductivity in the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest neighbor hopping $t'$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable $t'$ is necessary to obtain a sizable pairing gap.
Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model on a honeycomb lattice. We find that the $f$-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and non-topological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply quali…
