In this work, we study the magnetic-impurity resonance states in superconducting phase of twisted bilayer graphene for different pairing symmetries. Using the two-orbital model proposed by Yuan and Fu in [Phys. Rev. B 98, 045103 (2018)], we find that when the impurity is located at one site of the emergent honeycomb lattice, the spacial distributions of the resonance states will break both the threefold and twofold rotation symmetries of $D_3$ group for pairing symmetries which belong to the irreducible representations of this point group. When the magnetic impurity is located at the center of the emergent honeycomb lattice, the appearance of resonance peak at the position close to the impurity can be considered as a strong evidence of non-$s$-wave pairing.
Non-magnetic impurities can lift the accidental degeneracy of unconventional pairing states, such as the $(d + i g)$-wave state recently proposed for Sr$_2$RuO$_4$. This type of effect would lead to a superconducting double transition upon impurity doping. In a model calculation it is shown how this behavior depends on material parameters and how it could be detected.
We study the impurity states in bilayer graphene in the unitary limit using Green's function method. Unlike in single layer graphene, the presence of impurities at two non-equivalent sites in bilayer graphene produce different impurity states which is understood as the change in the band structure due to interlayer hopping of electrons. The impurity states can also be tuned by changing the band structure of bilayer grahene through external electric field bias.
We investigate the twisted bilayer graphene by a two-orbital Hubbard model on the honeycomb lattice. The model is studied near 1/4 band filling by using the singular-mode functional renormalization group theory. Spin-triplet $f$-wave pairing is found from weak to moderate coupling limit of the local interactions, and is associated with the Hund's rule coupling and incommensurate spin fluctuations at moderate momenta.
We investigate phonon-mediated Cooper pairing in flat electronic band systems by solving the full-bandwidth multiband Eliashberg equations for superconductivity in magic angle twisted bilayer graphene using a realistic tight-binding model. We find that Cooper pairing away from the Fermi level contributes decisively to superconductivity by enhancing the critical temperature and ensures a robust finite superfluid density. We show that this pairing yields particle-hole asymmetric superconducting domes in the temperature-gating phase diagram and gives rise to distinct spectroscopic signatures in t…
The pairing symmetry of an effective Hamiltonian for interacting fermions on a twisted bilayer graphene superlattice is studied with the determinant quantum Monte Carlo method. The model has the symmetry of a triangle lattice and a nearly-flat low energy band, features which underlie the magic-angle twisted bilayer graphene superlattice. We show that the low temperature phase is insulating at half-filling, even for relatively weak interactions. The natures of the spin and pairing correlations upon doping are determined, and exhibit an electron-hole asymmetry consistent with experiment. Among t…
We have studied the effect of a single nonmagnetic impurity in the recently discovered (K,Tl)Fe$_x$Se$_2$ superconductors, within both a toy two-band model and a more realistic five-band model. We have found that, out of five types of pairing symmetry under consideration, only the $d_{x^2-y^2}$-wave pairing gives rise to impurity resonance states. The intra-gap states have energies far away from the Fermi energy. The existence of these intra-gap states is robust against the presence or absence of inter-band scattering. However, the inter-band scattering does tune the relative distribution of l…
Superconducting transition temperature is calculated for differently doped bilayer cuprates. Superexchange is assumed to be the dominating mechanism of high-temperature superconductivity, but the contribution from the phonon potential is not negligible, which qualitatively explains the observed weak isotopic effect. The calculated value 2$Δ_{max}/k_B T_C \simeq 4.5$ is close to the experiment in the case of optimum doping.
We study the non-local superconducting pairing of two interacting Anderson impurities, which has an instability near the quantum critical point from the competition between the Kondo effect and an antiferromagnetic inter-impurity spin exchange interaction. As revealed by the dynamics over the whole energy range, the superconducting pairing fluctuations acquire considerable strength from an energy scale much higher than the characteristic spin fluctuation scale while the low energy behaviors follow those of the staggered spin susceptibility. We argue that the glue to the superconducting pairing…
We investigate a magnetic impurity in Bernal stacked bilayer graphene by a non-perturbative numerical exact approach. In the two cases we study, impurity is placed on the top of two different sublattices (A and B) in bilayer graphene. We find that similar to the monolayer case, magnet moment of the impurity could still be tuned in a wide range through changing the chemical potential. However, the property of the impurity depends strongly on its location due to the broken symmetry between sublattices A and B caused by the Bernal stacking. This difference becomes more apparent with the increase …
The bilayer Hubbard model with an intra-layer hopping $t$ and an inter-layer hopping $t_\perp$ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half-filling, if the splitting between the bonding and anti-bonding bands $t_\perp/t$ is sma…
Motivated by the recent discovery of noncentrosymmetric superconductors, such as $CePt_{3}Si$, $CeRhSi_{3}$ and $CeIrSi_{3}$, we investigate theoretically the impurity resonance states with coexisting $s$- and p-wave pairing symmetries. Due to the nodal structure of the gap function, we find single nonmagnetic impurity-induced resonances appearing in the local density of state (LDOS). In particular, we analyze the evolution of the local density of states for coexisting isotropic s-wave and p-wave superconducting states and compare with that of anisotropic s-wave and p-wave symmetries of the su…
The effect of impurities which induce local interlayer tunneling in bilayer exciton condensates is discussed. We show that a localized single fermion bound state emerges inside the gap for any strength of impurity scattering and calculate the dependence of the impurity state energy and wave function on the potential strength. We show that such an impurity induced single fermion state enhances the interlayer coherence around it, and is similar to the superconducting proximity effect. As a direct consequence of these single impurity states, we predict that a finite concentration of such impuriti…
Two scenarios, i.e., the anisotropic s-wave pairing (the s-wave scenario) and the d-wave pairing coexisting with antiferromagnetism (the coexisting scenario) have been introduced to understand some of seemingly s-wave like behaviors in electron doped cuprates. We considered the electronic structure in the presence of a nonmagnetic impurity in the coexistence scenario. We found that even if the AF order opens a full gap in quasi-particle excitation spectra, the mid-gap resonant peaks in local density of states (LDoS) around an impurity can still be observed in the presence of a d-wave pairing g…
We study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moiré supercells. With increasing the pairing potential, the system evolves from the mixed nontopological $d+id$ and $p+ip$ phase to the $s+p+d$ phase via the first-order phase transition. In the time-reversal symmetry breaking $d+id$ and $p+ip$ phase, vortex and antivortex lattices accompanying spontaneous supercurrent are induced by the twist. The superconducting order parameter is nonuniform in the moiré unit cell. Nevertheless, the superconducting gap …
The superconducting transition temperature, Tc, of bilayers comprising underdoped La2-xSrxCuO4 films capped by a thin heavily overdoped metallic La1.65Sr0.35CuO4 layer, is found to increase with respect to Tc of the bare underdoped films. The highest Tc is achieved for x = 0.12, close to the 'anomalous' 1/8 doping level, and exceeds that of the optimally-doped bare film. Our data suggest that the enhanced superconductivity is confined to the interface between the layers. We attribute the effect to a combination of the high pairing scale in the underdoped layer with an enhanced phase stiffness …
Using both the self-consistent Bogoliubov-de Gennes formulation and non-self-consistent T-matrix approach, we perform a comprehensive investigation of the in-gap bound states induced by a localized single impurity in iron-based superconductors. We focus on studying signatures associated with the unconventional sign-changed s-wave pairing symmetry. For a non-magnetic impurity, we find that there are two in-gap bounds, symmetric with respect to zero energy, only in the sign changed s-wave pairing state, not in the sign-unchanged s-wave state, due to the existence of non-trivial Andreev bound sta…
The effect of non-magnetic Zn impurity on superconductivity in LaFe$_{1-y}$Zn$_y$AsO$_{1-x}$F$_x$ system is studied systematically. In the presence of Zn impurity, the superconducting transition temperature increases in the under-doped regime, remains unchanged in the optimally doped regime, and is severely suppressed in the over-doped regime. Our results suggest a switch of the symmetry of the superconducting order parameters from a $s$-wave to $s_{\pm}$ or $d$-wave states as the charge carrier doping increases in FeAs-based superconductors.
A system of self-consistent integral equations for the superconducting gap is formulated and solved taking account of the instability of the normal phase of bilayered cuprates against charge-density waves. The critical parameters are calculated as a function of the wave vector, temperature, and doping index. It is found that the region in which superconductivity coexists with d-type charge-density waves depends strongly on the doping index. The effective energy-gap parameter, determined as the interval between the peaks of the density of states, can have a local minimum at temperatures T$<$T$_…
We study the localized magnetic states of impurity in biased bilayer and trilayer graphene. It is found that the magnetic boundary for bilayer and trilayer graphene presents the mixing features of Dirac and conventional fermion. For zero gate bias, as the impurity energy approaches the Dirac point, the impurity magnetization region diminishes for bilayer and trilayer graphene. When a gate bias is applied, the dependence of impurity magnetic states on the impurity energy exhibits a different behavior for bilayer and trilayer graphene due to the opening of a gap between the valence and the condu…
We derive the polarizability of an electron system in (i) the superconducting phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azymuthal …
In a recent Letter [PRL 103, 186402 (2009)], the energy band structure of Fe-As-based superconductors is fitted with a tight-binding model with two Fe ions per unit cell and two degenerate xz and yz orbitals per Fe ion. The author claims that the proposed model, which differs markedly from a model previously used by other authors for the same two orbitals in the same compounds, possesses the symmetry required to describe the Fe-As planes in iron-pnictide superconductors. In this comment we argue that this is not the case.
We use quantum Monte Carlo method to study a magnetic impurity located next to a vacancy in bilayer graphene with Bernal stacking. Due to the broken symmetry between two sublattices in bilayer system, there exist two different types of vacancy induced localized state. We find that the magnetic property of the adatom located on the adjacent site of the vacancy depends on whether the vacancy belongs to A or B sublattice. In general, local moment is more strongly suppressed if the vacancy belongs to the sublattice A when $μ\sim 0$. We switch the values of the chemical potential and study the basi…
We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Due to the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of …
Interacting many-body systems combining confined and extended dimensions, such as ladders and few layer systems are characterized by enhanced quantum fluctuations, which often result in interesting collective properties. Recently two-dimensional bilayer systems, such as twisted bilayer graphene or ultracold atoms, have sparked a lot of interest because they can host rich phase diagrams, including unconventional superconductivity. Here we present a theoretical proposal for realizing high temperature pairing of fermions in a class of bilayer Hubbard models. We introduce a general, highly efficie…
One of the outstanding questions in the study of twisted bilayer graphene -- from both experimental and theoretical points of view -- is the nature of its superconducting phase. In this work we perform a comprehensive synthesis of existing experiments, and argue that experimental constraints are strong enough to allow the structure of the superconducting order parameter to be nearly uniquely determined. In particular, we argue that the order parameter is nodal, and is formed from an admixture of spin-singlet and spin-triplet Cooper pairs. This argument is made on phenomenological grounds, with…
To shed light on the symmetry of the superconducting order parameter in Na_xCoO_2-yH_2O, the Mn doping effects are studied. X-ray absorption spectroscopy verifies that the doped Mn impurities occupy the Co sites and are with a valance close to +4. Impurity scattering by Mn is in the unitary limit that, however, does not lead to strong Tc suppression. This absence of the strong impurity effects on T_c is not consistent with the simple picture of a sign-changing order parameter. Coexistence of the s-wave and unconventional order parameters is proposed to reconcile all existing experiments and ha…
Based on our revised perturbational-band theory, we study possible pairing states driven by interaction in the electron-doped quasicrystal 30\degree-twisted bilayer graphene. Our mean-field study on the related t-J model predicts that, the beneath-van-Hove and beyond-van-Hove low doping regimes are covered by the chiral $d+id$ and $g+ig$ topological superconductivities (TSCs) respectively. The $g+ig$-TSC possesses a pairing angular momentum 4, and hence following each effective $C_{12}$- rotation by $Δϕ=nπ/6$, the pairing phase changes $4Δϕ$. This intriguing TSC is novel, as it belongs to a sp…
We investigate the interplay of magnetic fluctuations and Cooper pairing in twisted bilayer graphene from a purely microscopic model within a large-scale tight-binding approach resolving the Ångström scale. For local onsite repulsive interactions and using the random-phase approximation for spin fluctuations, we derive a microscopic effective pairing interaction that we use for self-consistent solutions of the Bogoliubov-de-Gennes equations of superconductivity. We study the predominant pairing types as function of interaction strength, temperature and band filling. For large regions of this p…
We consider the symmetric single-impurity Anderson model in the presence of pairing fluctuations. In the isotropic limit, the degrees of freedom of the local impurity are separated into hybridizing and non-hybridizing modes. The self-energy for the hybridizing modes can be obtained exactly, leading to two subbands centered at $\pm U/2$. For the non-hybridizing modes, the second order perturbation yields a singular resonance of the marginal Fermi liquid form. By multiplicative renomalization, the self-energy is derived exactly, showing the resonance is pinned at the Fermi level, while its stren…
We show that unconventional nematic superconductors with multi-component order parameter in lattices with three-fold and six-fold rotational symmetries support a charge-$4e$ vestigial superconducting phase above $T_c$. The charge-$4e$ state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is non-superconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities…
Using the functional renormalization group technique we demonstrate a route for potentially high-temperature odd-parity superconductivity in ferromagnetic materials caused by repulsive electron interactions, where the superconducting pairing is driven by charge-density wave fluctuations. Our model is directly applicable to a lightly cobalt-doped LaNiO$_3$ bilayer grown in the (111) direction. As the on-site repulsive interaction grows, a charge-density wave state with a charge pattern that respects all point-group symmetries of the bilayer is replaced by a superconducting state with an f-wave …
In the low-energy two-band as well as four-band continuum models, we study the supercritical instability in gapped bilayer graphene in the field of a charged impurity. It is found that the screening effects are crucially important in bilayer graphene. If they are neglected, then the critical value for the impurity charge as the lowest-energy bound state dives into the lower continuum tends to zero as the gap $Δ$ vanishes. If the screened Coulomb interaction is considered, then the critical charge tends to a finite value for $Δ\to 0$. The different scalings of the kinetic energy of quasiparticl…
We report the observation by angle-resolved photoemission spectroscopy of an impurity state located inside the superconducting gap of Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ and vanishing above the superconducting critical temperature, for which the spectral weight is confined in momentum space near the Fermi wave vector positions. We demonstrate, supported by theoretical simulations, that this in-gap state originates from weak non-magnetic scattering between bands with opposite sign of the superconducting gap phase. This weak scattering, likely due to off-plane Ba/K disorders, occurs mostly among nei…
We discuss the composite fermion pairing state in bilayer quantum Hall systems. After the evaluation of the range of the inter-layer separation in which the quantum Hall state is stabilized, we discuss the effect of inter-layer tunneling on the composite fermion pairing state at ν=1/2. We show that there is a cusp at the transition point between the Halperin (3,3,1) state and the Pfaffian state.
We study bilayer fermionic cold atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth and first Haldane pseudopotentials, at total Landau level filling factor 1/2. Our numerical results on the TCTP model indicates that Haldane-Rezayi state describes the critical point between strong and weak d-wave pairing quantum Hall phases. Further increasing the attractive zeroth pseudopotentials, the system transits from the strong-pairing phase to a stripe phase, and then to a cluster phase (or phase separation). The dipolar in…
Starting from a continuum-model description, we develop a microscopic weak-coupling theory for superconductivity in twisted double-bilayer graphene. We study both electron-phonon and entirely electronic pairing mechanisms. In each case, the leading superconducting instability transforms under the trivial representation, $A$, of the point group $C_3$ of the system, while the subleading pairing phases belong to the $E$ channel. We explicitly compute the momentum dependence of the associated order parameters and find that the leading state has no nodal points for electron-phonon pairing but exhib…
Triple point fermions are elusive electronic excitations that generalize Dirac and Weyl modes beyond the conventional high energy paradigm. Yet, finding real materials naturally hosting these excitations at the Fermi energy has remained challenging. Here we show that twisted bilayer graphene is a versatile platform to realize robust triple point fermions in two dimensions. In particular, we establish that the introduction of localized impurities lifts one of the two degenerate Dirac cones, yielding triple point fermions at charge neutrality. Furthermore, we show that the valley polarization is…
We consider an atomic chain of magnetic impurities on the surface of a spin-orbit coupled superconductor with a dominating $d$-wave and sub-dominating $s$-wave order parameters. In particular, we investigate the properties of the Majorana bound states (MBSs) emerging at the chain end points in the topological phase and how MBSs are affected by the $d$-wave order parameter. We provide a comprehensive picture by both studying time-reversal invariant and breaking superconducting substrates as well as chains oriented in different directions relative to the $d$-wave rotation. We show that increasin…
In conventional superconductors, magnetic interactions and magnetic impurity atoms are destructive to superconductivity. By contrast, in some unconventional systems, e.g. superfluid 3He and superconducting UGe2, superconductivity or superfluidity is actually mediated by magnetic interactions. A magnetic mechanism has also been proposed for high temperature superconductivity (HTSC) in which an electron magnetically polarizes its environment resulting in an attractive pairing-interaction for oppositely polarized spins. Since a magnetic impurity atom would apparently not disrupt such a pairing-in…
Triplon-mediated pairing and the superconducting gap structure in bilayer nickelates
National Laboratory of Solid State Microstructures and School of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
By using the determinant Quantum Monte Carlo method, the magnetic and pairing correlation of the Na$_{x}$CoO$_{2}\cdot$yH$_{2}$O system are studied within the Hubbard model on a bilayer triangular lattice. The temperature dependence of spin correlation function and pairing susceptibility with several kinds of symmetries at different electron fillings and inter layer coupling terms are investigated. It is found that the system shows an antiferromagnetic correlation around the half filling, and the $fn$-wave pairing correlation dominates over other kinds of pairing symmetry in the low doping reg…
The local properties of bilayer graphene (BLG) due to the spatial inhomogeneity of its sublattices are of interest. We apply Anderson impurity model to consider the local moment formation on a magnetic impurity which could be adsorbed on different sublattices of BLG. We find different features for the impurity magnetization when it is adsorbed A and B sublattices. The impurity adsorbed on A sublattice can magnetize even when the impurity level is above the Fermi level and the on-site coulomb energy is very small. But when the impurity is adsorbed on B sublattice the magnetization is possible f…
Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. The evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition, and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a $d+id$ superconducti…
Motivated by recent discoveries of novel superconductors such as Na$_x$CoO$_2\cdot y$H$_2$O and Sr$_2$RuO$_4$, we analysize features of quasi-particle scattering due to impurities and interfaces for possible gapful $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ Cooper pairing. A bound state appears near a local impurity, and a band of bound states form near an interface. We obtained analytically the bound state energy, and calculated the space and energy dependent local density of states resolvable by high-resolution scanning tunnelling microscopy. For comparison we also sketch results of impurity and s…
