D-wave Pairing Research Articles

Quantum magnetic impurity resonance states in monolayer FeSe superconductor with different pairing symmetries

In this work, we study the magnetic impurity resonance states in monolayer FeSe superconductor for different pairing symmetries. When the magnetic impurity is hybridized to one of the two electronic pockets at M point, we find that there will be two in-gap resonance peaks located symmetrically at the two sides of the Fermi energy. The intensities of the two peaks are comparable for s-wave and d-wave pairings. For the p-wave pairing, the intensity of the positive resonance peak is much smaller than the negative one. When the magnetic impurity is hybridized to the two electronic pockets simultaneously and spin-orbit coupling is considered, the two resonance peaks will be split into four for d-wave pairing. This splitting is absent for s-wave and p-wave pairings. These features can be considered as signatures to distinguish the pairing potential symmetries.

Superconducting properties of the hole-doped three-band d−p model studied with minimal-size real-space d -wave pairing operators

The three-band \emph{d-p} model is investigated by means of Variational Monte-Carlo (VMC) method with the BCS-like wave-function supplemented by the Gutzwiller and Jastrow correlators. The VMC optimization leads to $d$-$wave$ superconducting state with a characteristic dome-like shape of the order parameter for hole doping $\delta \lesssim 0.4$, in a good agreement with the experimental observations. Also, the off-diagonal pair-pair correlation functions, calculated within VMC, vindicates the results obtained very recently within the diagrammatic expansion of the Gutzwiller wave function method (DE-GWF) [cf. Phys. Rev. B \textbf{99}, 104511 (2019)]. Subsequently, the nature of the $d$-$wave$ pairing is investigated by means of recently proposed \emph{minimal-size real-space d-wave pairing operators} [Phys. Rev. B \textbf{100}, 214502 (2019)]. An emergence of the long-range superconducting ordering for both $d$ and $p$ orbitals is reported by analysing the corresponding off-diagonal pair-pair correlation functions. The dominant character of \emph{d-wave} pairing on $d$ orbitals is confirmed. Additionally, the trial wave-function is used to investigate the magnetic properties of the system. The analysis of spin-spin correlation functions is carried out and shows antiferromagnetic $\mathbf{q}=(\pi,\pi)$, short-range order, as expected. For the sake of completeness, the charge gap has been estimated, which for the parent compound takes the value $\Delta_{CG}\approx1.78\pm0.51\text{ eV}$, and agrees with values reported experimentally for the cuprates.

Vortical configurations in mesoscopic superconducting square loop with mixed pairing orders

Based on the microscopic Bogoliubov-de Gennes theory, we study vortical configurations in a mesoscopic superconducting square loop with mixed pairing orders. By choosing appropriate interaction strengths and chemical potential, the spin-triplet p-wave and subdominant spin-singlet d-wave pairing symmetries can be stabilized. In a small external magnetic field, unusual elliptical-like vortices in chiral p-wave orders as well as elongated vortices in the d-wave order tend to form in sample diagonals. For an enlarged flux, we find a two-quanta skyrmionic mode for the p-wave components, while the closed domain wall does not appear compared to the previous studies in superconducting systems with a pure p-wave state. Particularly, a novel multi-skyrmionic pattern containing four single-quanta skyrmions takes place with increasing flux. Such a single-quanta vortex structure consisting of two spatially separated half-quantum vortices is analogous to the nematic skyrmion with unit topological charge. In addition, several complex hybrid or multiple skyrmionic configurations are revealed in the strong flux range.

Learning pairing symmetries in disordered superconductors using spin-polarized local density of states

We construct an artificial neural network to study the pairing symmetries in disordered superconductors. For Hamiltonians on square lattice with s-wave, d-wave, and nematic pairing potentials, we use the spin-polarized local density of states near a magnetic impurity in the clean system to train the neural network. We find that, when the depth of the artificial neural network is sufficient large, it will have the power to predict the pairing symmetries in disordered superconductors. In a large parameter regime of the potential disorder, the artificial neural network predicts the correct pairing symmetries with relatively high confidences.

Superconductivity due to cooperation of electron-electron and electron-phonon interactions at quarter filling

We present the results of Quantum Monte Carlo calculations for a two dimensional frustrated Hubbard model coupled to bond phonons. The model is known to have a d-wave superconducting ground state in the limit of large phonon frequency for sufficiently strong electron-phonon coupling. In the absence of electron-phonon coupling the Hubbard interaction U enhances superconducting pairing in the quarter-filled (density $\rho$ = 0.5) band. We show here that at $\rho$ = 0.5 electron-electron and electron-phonon interactions cooperatively reinforce d-wave pairing, while competing with each other at all other densities. Cooperative degrees of freedom are found in many phase transitions and are essential to understanding superconductivity in strongly correlated materials.

Identifying the graphene d-wave superconducting symmetry by an anomalous splitting zero-bias conductance peak

Not until recently, was a gate-tunable, high-temperature superconducting proximity effect in graphene demonstrated experimentally. And usually in d-wave superconductor (SC) hybrid structure, ferromagnetism and spin-triplet states could result in a splitting zero-bias conductance peak (ZBCP). Herein, we theoretically present an anomalous splitting ZBCP in a graphene-based ferromagnet/Rashba spin–orbit coupling (RSOC)/insulator/d-wave SC hybrid structure. With increasing the exchange field from h/EF = 0, the ZBCP starts to turn into a splitting one with a zero-bias conductance dip (ZBCD) sandwiched in between two subpeaks, while from h/EF = 1, the two subpeaks and ZBCD begin to gradually shrink till the ZBCP reappears. The anomalous splitting ZBCP can be modulated by the RSOC strength, magnitude of Fermi wave vector mismatch as well as insulator barrier strength. These peculiar features are ascribed to the novel spin-triplet Andreev reflection in the context of the RSOC, characteristic by the anisotropic d-wave pair symmetry combined with the relativistic nodal fermions, which in turn can be experimentally used to directly identify not only the proximity-induced ferromagnetism and RSOC but d-wave pair symmetry in graphene. These results pave the way to a new class of tunable, high-temperature superconducting spintronic devices based on large-scale graphene.

Superconductivity, Pair Density Wave, and Néel Order in Cuprates**Supported by the National Key Research and Development Program of China under Grant Nos. 2016YFA0300401 and 2016YFA0300202, the National Natural Science Foundation of China under Grant Nos. 11574134, 11874205 and 11774306, and the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDB28000000).

We investigate in underdoped cuprates possible coexistence of the superconducting order at zero momentum and pair density wave (PDW) at momentum Q = (π, π) in the presence of a Néel order. By symmetry, the d-wave uniform singlet pairing dS0 can coexist with the d-wave triplet PDW dTQ, and the p-wave singlet PDW pQ can coexist with the p-wave uniform triplet pT0. At half filling, we find that the novel pSQ+ pT0 state is energetically more favorable than the dS0 + dTQ state. At finite doping, however, the dS0 + dTQ state is more favorable. In both types of states, the variational triplet parameters dTQ and pT0 are of secondary significance. Our results point to a fully symmetric Z2 quantum spin liquid with spinon Fermi surface in proximity to the Néel order at zero doping, which may not be adiabatically connected to the d-wave singlet superconductivity at finite doping with intertwining d-wave triplet PDW fluctuations and spin moment fluctuations. The results are obtained by variational quantum Monte Carlo simulations.

Specific criteria for BCS-type cuprate superconductivity and peculiar isotope effects on the critical superconducting transition temperature

So far, many researchers have been misled to believe that the Bardeen–Cooper–Schrieffer (BCS)-like (s- or d-wave) pairing theory is adequate for explaining high- $$T_\mathrm {c}$$ superconductivity in doped cuprates from underdoped to overdoped regime. We show that the doped cuprates, depending on the Fermi energy ( $$\varepsilon _\mathrm {F}$$ ) and the energy ( $$\varepsilon _\mathrm {A}$$ ) of the effective attraction between pairing carriers, might be either unconventional (non-BCS-type) superconductors (at intermediate doping) or BCS-type superconductors (at higher doping). We argue that specific criteria for BCS-type superconductivity formulated in terms of two ratios $$\varepsilon _\mathrm {A}/\varepsilon _\mathrm {F}$$ and $$\Delta /\varepsilon _\mathrm {F}$$ (where $$\Delta $$ is the BCS-like gap) must be met in these systems. We demonstrate that these criteria are satisfied only in overdoped cuprates but not in underdoped and optimally doped cuprates, where the origin of high- $$T_\mathrm {c}$$ superconductivity is quite different from the BCS-type (s- or d-wave) superconductivity. The BCS-like pairing theory is then used to calculate the critical superconducting transition temperature ( $$T_\mathrm {c}$$ ) and the peculiar oxygen and copper isotope effects on $$T_\mathrm {c}$$ in overdoped cuprates.

Superconductivity at metal-antiferromagnetic insulator interfaces

Magnons in antiferromagnetic insulators couple strongly to conduction electrons in adjacent metals. We show that this interfacial tie can lead to superconductivity in a tri-layer consisting of a metal sandwiched between two antiferromagnetic insulators. The critical temperature is closely related to the magnon gap, which can be in the THz range. We estimate the critical temperature in MnF$_2$-Au-MnF$_2$ to be on the order of 1 K. The Umklapp scattering at metal-antiferromagnet interfaces leads to a d-wave superconductive pairing, in contrast to the p-wave superconductivity mediated by magnons in ferromagnets.

Effect of Next-Nearest-Neighbor Electron Hopping on Superconducting Gap of Cuprate Superconductors

We study here a single band Hamiltonian model to describe the effect of next-nearest-neighbor (NNN) electron hopping on superconducting gap in Cuprates. The Hamiltonian consists of nearest-neighbor (NN) and next-nearest-neighbor (NNN) electron hopping integrals between the copper sides. By taking d-wave pairing symmetry into account, BCS type superconducting interaction is studied. By applying Zubarev’s Green function technique, the total Hamiltonian is solved. From the correlation function, the temperature-dependent superconducting gap (SC) equation is derived and is computed self-consistently by using technique [Formula: see text] grid points of the electron momentum. By varying SC coupling, chemical potential, J-T coupling parameter and second-nearest-neighbor electron hopping integral, the evolution of the order parameter is investigated.

Odd-parity superconductivity driven by octahedra rotations in iridium oxides

Iridium oxides have provided a playground to study novel phases originating from spin-orbit coupling and electron-electron interactions. Among them, the d-wave singlet superconductor was proposed for electron-doped Sr$_2$IrO$_4$, containing two Ir atoms in a unit cell due to the staggered rotation of oxygen octahedra about the c-axis. It was also noted that such oxygen octahedra rotation affects electronic transports. Here we study the role of octahedra tilting away from the c-axis, in determining superconducting pairing symmetry. We show that the octahedra tilting changes the large Fermi surface to a Dirac point, which strongly suppresses the conventional d-wave pairing. Furthermore, it also promotes effective spin-triplet interactions in the strong Hubbard interaction limit, leading to a transition from the even-parity to odd-parity superconducting phase. Thus, tuning octahedra distortions can be used as a tool to engineer a spin triplet superconductor in strongly correlated systems with strong spin-orbit coupling.

Topological d+s wave superconductors in a multiorbital quadratic band touching system

Realization of topological superconductors is one of the most important goals in studies of topological phases in quantum materials. In this work, we theoretically propose a novel way to attain topological superconductors with non-trivial Fermi surfaces of Bogoliubov quasiparticles. Considering the interacting Luttinger model with $j\!=\!3/2$ electrons, we investigate the dominant superconducting channels for a multi-orbital quadratic band-touching system with finite chemical potential, which breaks the particle-hole symmetry in the normal state. Notably, while the system generally favors d-wave pairing, the absence of the particle-hole symmetry necessarily induces parasitic s-wave pairing. Based on the Landau theory with $SO(3)$ symmetry, we demonstrate that two kinds of topological superconductors are energetically favored; uniaxial nematic phase with parasitic $s$ wave pairing ($d_{(3z^2-r^2)}\!+\!s$) and time-reversal-symmetry broken phase with parasitic $s$ wave pairing ($d_{(3z^2-r^2,xy)}\!+\!id_{x^2-y^2}\!+\!s$). These superconductors contain either nodal lines or Fermi pockets of gapless Bogoliubov quasiparticles and moreover exhibit topological winding numbers $\pm2$, leading to non-trivial surface states such as drumhead-like surface states or Fermi arcs. We discuss applications of our theory to relevant families of materials, especially half-heusler compound YPtBi, and suggest possible future experiments.

Quasiparticle interference and symmetry of superconducting order parameter in strongly electron-doped iron-based superconductors

Motivated by recent experimental reports of significant spin–orbit coupling (SOC) and a sign-changing order-parameter in the Li1−xFex(OHFe)1−yZnySe superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states—s-wave, d-wave and helical p-wave—can have a fully gapped density of states consistent with angle-resolved photoemission spectroscopy experiments and, due to SOC, are a mixture of spin singlet and triplet components leading to intra- and inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity A1g (s-wave) and B2g (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.

Strong Spin–Charge Coupling and Its Manifestation in the Quasiparticle Structure, Cooper Instability, and Electromagnetic Properties of Cuprates

The Fermi excitation spectrum, the problem of Cooper instability, and the Londons magnetic field penetration depth in cuprate superconductors are considered using the unified conception based on accounting for the strong coupling between the spin of copper ions and holes at oxygen ions. This coupling leads to strong renormalization of the primary spectrum of oxygen holes with the formation of spin-polaron quasiparticles. Analysis of Cooper instability performed using the spin-polaron concept for different channels has shown that only the superconducting d-wave pairing occurs in the ensemble of spin-polaron quasiparticles, and there are no solutions corresponding to the s-wave pairing. It has been demonstrated that the superconducting d-wave pairing is not suppressed by the Coulomb repulsion of holes located at neighboring oxygen ions. This effect is due to peculiarities in the crystallographic structure of the CuO2 plane and the aforementioned strong spin–fermion coupling. As a result, such interaction of holes is omitted in the kernel of the integral equation for the superconducting order parameter with the d-wave symmetry. It has been shown the Hubbard repulsion of holes and their interaction for the second coordination sphere of the oxygen sublattice for actual intensities of the interaction do not suppress the d-wave type of superconductivity. For the spin-polaron ensemble, we have analyzed the dependence of the Londons magnetic field penetration depth on the temperature and hole concentration. It has been established that the peculiarities of this dependence are closely related to specific features of the spin-polaron spectrum.

Superconductivity in a unique type of copper oxide

The mechanism of superconductivity in cuprates remains one of the big challenges of condensed matter physics. High-T c cuprates crystallize into a layered perovskite structure featuring copper oxygen octahedral coordination. Due to the Jahn Teller effect in combination with the strong static Coulomb interaction, the octahedra in high-T c cuprates are elongated along the c axis, leading to a 3dx 2-y 2 orbital at the top of the band structure wherein the doped holes reside. This scenario gives rise to 2D characteristics in high-T c cuprates that favor d-wave pairing symmetry. Here, we report superconductivity in a cuprate Ba2CuO4-y , wherein the local octahedron is in a very exceptional compressed version. The Ba2CuO4-y compound was synthesized at high pressure at high temperatures and shows bulk superconductivity with critical temperature (T c ) above 70 K at ambient conditions. This superconducting transition temperature is more than 30 K higher than the T c for the isostructural counterparts based on classical La2CuO4 X-ray absorption measurements indicate the heavily doped nature of the Ba2CuO4-y superconductor. In compressed octahedron, the 3d3z 2-r 2 orbital will be lifted above the 3dx 2-y 2 orbital, leading to significant 3D nature in addition to the conventional 3dx 2-y 2 orbital. This work sheds important light on advancing our comprehensive understanding of the superconducting mechanism of high T c in cuprate materials.

Tunneling conductance of the s-wave and d-wave pairing superconductive graphene–normal graphene junction

Within the framework of the Blonder–Tinkham–Klapwijk formalism we calculate and analyze the conductance of the normal graphene — s-wave and independently d-wave pairing superconductive graphene junction. The eigenfunctions, the Andreev and the normal reflection rates are obtained by solving the Dirac–Bogoliubov–de Gennes equations. The Fermi velocity is believed to be different in the normal and in the superconductive regions. We consider the options of gapless and gapped graphene for both cases: s-wave and independently d-wave pairing. It is demonstrated that the characteristics of the junction considered are sensitive to the ratio vFN/vFS where vFN, vFS are the Fermi velocities in the normal and the superconductive graphene respectively. This conclusion refers to the Andreev reflection as well as to the normal one. The first of them is shown to be the dominant process for the formation of the conductivity. These results are true for an arbitrary value of the orientational angle of the d-waves. Each of four cases considered: s-, d-wave pairing and gapless and gapped graphene displays its own specific features of the conductance. The dependence of the conductance on the external electrostatic potential as well as on the Fermi energy is also analyzed in every case. The obtained results may be useful for controlling the transport properties of the normal graphene–superconductive graphene junction.

Phase diagram of the half-filled ionic Hubbard model in the limit of strong correlations

We investigate the ionic Hubbard model (IHM) at half-filling in the limit of strong correlations and large ionic potential. The low energy effective Hamiltonian in this limit, obtained by a similarity transformation, is a modified $t-J$ model with effective second neighbour hopping terms. We explore the possibilities of d-wave pairing and extended s-wave pairing superconducting (SC) phases on a two dimensional square lattice at zero temperature within a Gutzwiller projected renormalized mean field theory. In the sector of solutions that forbid spin ordering, the system shows a finite non-zero d-wave as well as extended s-wave pairing amplitude for $\Delta \sim U \gg t$. The width of the superconducting phase in $U-\Delta$ regime shrinks with increase in $U$ and $\Delta$, though the extended s-wave pairing phase is higher in energy than the d-wave pairing superconducting phase. But in a spin resolved renormalized mean field calculation, which allows for an antiferromagnetic (AF) order along with the d-wave or extended s-wave pairing, the SC phase is no longer viable and the system shows a direct transition from an AF ordered phase to a paramagnetic band insulator. Except for a thin sliver of a half-metallic AF phase close to the AF transition point, most of the AF ordered phase is a Mott insulator. We benchmarked the AF Mott insulator to band insulator transition within the Gutzwiller projected renormalized mean field theory against the dynamical mean field theory (DMFT) solved using continuous time quantum Monte-Carlo (CTQMC). Our work suggests that the ground state phase diagram of the IHM at half-filling in the limit of extreme correlations does not have any SC phase. The SC phase seen in the paramagnetic sector is a metastable phase, being higher in energy than the AF Mott insulator phase.

NΩ dibaryon from lattice QCD near the physical point

The nucleon(N)-Omega(Ω) system in the S-wave and spin-2 channel (S25) is studied from the (2+1)-flavor lattice QCD with nearly physical quark masses (mπ≃146MeV and mK≃525MeV). The time-dependent HAL QCD method is employed to convert the lattice QCD data of the two-baryon correlation function to the baryon-baryon potential and eventually to the scattering observables. The NΩ(S25) potential, obtained under the assumption that its couplings to the D-wave octet-baryon pairs are small, is found to be attractive in all distances and to produce a quasi-bound state near unitarity: In this channel, the scattering length, the effective range and the binding energy from QCD alone read a0=5.30(0.44)(−0.01+0.16)fm, reff=1.26(0.01)(−0.01+0.02)fm, B=1.54(0.30)(−0.10+0.04)MeV, respectively. Including the extra Coulomb attraction, the binding energy of pΩ−(S25) becomes BpΩ−=2.46(0.34)(−0.11+0.04)MeV. Such a spin-2 pΩ− state could be searched through two-particle correlations in p-p, p-nucleus and nucleus-nucleus collisions.

Particle–hole fluctuations and possible superconductivity in doped α-RuCl3**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674158 and 11774152) and the National Key Projects for Research and Development of China (Grant No. 2016YFA0300401). W. Wang was also supported by the Program B for Outstanding PhD Candidate of Nanjing University.

We study various particle–hole excitations and possible superconducting pairings mediated by these fluctuations in doped α-RuCl3 by using multi-band Hubbard model with all t2g orbitals. By performing a random-phase-approximation (RPA) analysis, we find that among all particle–hole excitations, the jeff = 1/2 pseudospin fluctuations are dominant, suggesting the robustness of jeff = 1/2 picture even in the doped systems. We also find that the most favorable superconducting state has a d-wave pairing symmetry.

Strange superconductivity near an antiferromagnetic heavy-fermion quantum critical point

The heavy fermion CeMIn5 family with M = Co, Rh, Ir provide a prototypical example of strange superconductors with unconventional d-wave pairing and strange metal normal state, emerged near an antiferromagnetic quantum critical point. The microscopic origin of strange superconductor and its link to antiferromagnetic quantum criticality and strange metal state are still open issues. We propose a microscopic mechanism for strange superconductor, based on the coexistence and competition between the Kondo correlation and the quasi-2d short-ranged antiferromagnetic resonating-valence-bond spin-liquid near the antiferromagnetic quantum critical point via a large-N Kondo-Heisenberg model and renormalization group analysis beyond the mean-field level. We find the coexistence (competition) between the two types of correlations well explains the overall features of superconducting and strange metal state. The interplay of these two effects provides a qualitative understanding on how superconductivity emerges from the SM state and the observed superconducting phase diagrams for CeMIn5 near the anti-ferromagnetic quantum critical point.