Determining the symmetry of the order parameter of unconventional superconductors remains a recurrent topic and non-trivial task in the field of strongly correlated electron systems. Here we show that the behavior of Dirac points away from the Fermi energy is a potential tool to unveil the orbital structure of a superconducting state. In particular, we show that gap openings in such Dirac crossings are a signature of non-unitary multiorbital superconducting order. Consequently, also spectral features at higher energy can help us to identify broken symmetries of superconducting phases and the orbital structure of non-unitary states. Our results show how angle-resolved photo-emission spectroscopy measurements can be used to detect non-unitary multiorbital superconductivity.
We show the emergence of a new class of superconductivity in multiorbital systems, focusing on non-Kramers f$^2$ states. The Cooper pairs in this class of superconductivity mainly consist of local pairs with the same symmetry as the local f$^2$ ground states. When the local ground state is an anisotropic representation, the superconducting gap has nodes on the Fermi surface. This nodal superconductivity is mediated by the strong onsite inter-orbital attractions as a consequence of negative-$U$ physics generalized to multiorbital systems. We show that this is indeed realized in a simple two-orb…
We develop an efficient approach for computing two-particle response functions and interaction vertices for multiorbital strongly correlated systems based on fluctuation around rotationally-invariant slave-boson saddle-point. The method is applied to the degenerate three-orbital Hubbard-Kanamori model for investigating the origin of the s-wave orbital antisymmetric spin-triplet superconductivity in the Hund's metal regime, previously found in the dynamical mean-field theory studies. By computing the pairing interaction considering the particle-particle and the particle-hole scattering channels…
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…
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 study the orbital-dependent superconducting pairing in a five-orbital t-J1-J2 model for iron pnictides. Depending on the orbital selectivity of electron correlations and the orbital characters along the Fermi surface, the superconducting gap in an A_{1g} pairing state may exhibit anisotropy. This anisotropy varies with the degree of J1-J2 magnetic frustration. We have also calculated the dynamical spin susceptibility in the superconducting state. The frequency dependence of the susceptibility at the antiferromagnetic wavevector (π,0) shows a resonance, whose width is enhanced by the orbital…
We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our Ansatz is an optimized linear superposition of Affleck-Kennedy-Lieb-Tasaki valence bond states, rendering the combination a valence bond liquid dubbed Orbital Resonant Valence Bond. We show that the undoped (one electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer…
Superconductivity with a remarkably high $T_c$ has recently been found in Sr-doped NdNiO$_2$ thin films. While this system bears strong similarities to the cuprates, some differences, such as a weaker antiferromagnetic exchange coupling and possible high-spin moments on the doped Ni sites have been pointed out. Here, we investigate the effect of Hund coupling and crystal field splitting in a simple model system and argue that a multiorbital description of nickelate superconductors is warranted, especially in the strongly hole-doped regime. We then look at this system from the viewpoint of the …
Multiorbital systems such as the iron-based superconductors provide a new avenue to attack the longstanding problem of superconductivity in strongly correlated systems. In this work we study the superconductivity driven by a generic bosonic mechanism in a multiorbital model including the full dynamical electronic correlations induced by the Hubbard U and the Hund's coupling. We show that superconductivity survives much more in a Hund's metal than in an ordinary correlated metal with the same degree of correlation. The crucial role of the redistribution of spectral weight in the Hund's metal re…
The heavy-fermion system $\mathrm{UTe_2}$ is a candidate for spin-triplet superconductivity, which is of considerable interest to quantum engineering. Among the outstanding issues is the nature of the pairing state. A recent surprising discovery is the observation of a resonance in the spin excitation spectrum at an antiferromagnetic wavevector [C. Duan {\it et al.}, Nature \textbf{600}, 636 (2021)], which stands in apparent contrast to the ferromagnetic nature of the interactions expected in this system. We show how the puzzle can be resolved by a multiorbital spin-triplet pairing constructed…
In the framework of a multiorbital Hubbard model description of superconductivity, a matrix formulation of the superconducting pairing interaction that has been widely used is designed to treat spin, charge and orbital fluctuations within a random phase approximation (RPA). In terms of Feynman diagrams, this takes into account particle-hole ladder and bubble contributions as expected. It turns out, however, that this matrix formulation also generates additional terms which have the diagrammatic structure of vertex corrections. Here we examine these terms and discuss the relationship between th…
Multiorbital character of the density wave in trilayer nickelate superconductors
Max-Planck-Institute for Solid State Research（马克斯·普朗克固体研究所）；Facultad de Ciencias Exactas, Ingeniería y Agrimensura and Instituto de Física Rosario (UNR-CONICET)（罗萨里奥大学精确科学、工程与测量学院及罗萨里奥物理研究所（UNR-CONICET））；RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心 (iTHEMS)）
The predominant Ni-multiorbital nature of infinite-layer neodynium nickelate at stoichiometry and with doping is revealed. We investigate the correlated electronic structure of NdNiO$_2$ at lower temperatures and show that first-principles many-body theory may account for Kondo(-lattice) features. Yet those are not only based on localized Ni-$d_{x^2-y^2}$ and a Nd-dominated self-doping band, but heavily builds on the participation of Ni-$d_{z^2}$ in a Hund-assisted manner. In a tailored three-orbital study, the half-filled regime of the former inplane Ni orbital remains surprisingly robust eve…
We propose a concept of superconductivity controlled by orbital degree of freedom taking CeMIn5 (M= Co, Rh, and Ir) as typical examples. A microscopic multiorbital model for CeMIn5 is analyzed by fluctuation exchange approximation. Even though the Fermi-surface structure is unchanged, the ground state is found to change significantly among paramagnetic, antiferromagnetic, and d-wave superconducting phases, depending on the dominant orbital component in the band near the Fermi energy. We show that our picture naturally explains the different low-temperature properties of CeMIn5 by carefully ana…
Recent experiments revealed that the plain $s$-wave state without any sign-reversal emerges in various metals near the magnetic criticality. To understand this counter-intuitive phenomenon, we study the gap equation for the multiorbital Hubbard-Holstein model, by analyzing the vertex correction (VC) due to the higher-order electron-correlation effects. We find that the phonon-mediated orbital fluctuations are magnified by the VC for the susceptibility ($χ$-VC). In addition, the charge-channel attractive interaction is enlarged by the VC for the coupling-constant ($U$-VC), which is significant …
In various multiorbital systems, the emergence of the orbital fluctuations and its role on the pairing mechanism attract increasing attention. To archive deep understanding on these issues, we perform the functional-renormalization-group (fRG) study for the two-orbital Hubbard model. The vertex corrections for the electron-boson coupling ($U$-VC), which are dropped in the Migdal-Eliashberg gap equation, are obtained by solving the RG equation. We reveal that the dressed electron-boson coupling for the charge-channel, $U_{eff}^c$, becomes much larger than the bare Coulomb interaction, $U^0$, du…
The interplay between electronic orders and superconductivity is central to the physics of unconventional superconductors, and is particularly pronounced in the iron-based superconductors. Motivated by recent experiments on FeSe, we study the superconducting pairing in its nematic phase in a multiorbital model with frustrated spin-exchange interactions. The electron correlations in the presence of the nematic order give rise to an enhanced orbital selectivity in the superconducting pairing amplitudes. This orbital-selective pairing produces a large gap anisotropy on the Fermi surface. Our resu…
We study the effect of a uniform external magnetization on p-wave superconductivity on the (001) surface of the crystalline topological insulator(TCI) Pb$_{1-x}$Sn$_{x}$Te. It was shown by us in an earlier work that a chiral p-wave finite momentum pairing (FFLO) state can be stabilized in this system in the presence of weak repulsive interparticle interactions. In particular, the superconducting instability is very sensitive to the Hund's interaction in the multiorbital TCI, and no instabilities are found to be possible for the "wrong" sign of the Hund's splitting. Here we show that for a fini…
We study the mechanism of the triplet superconductivity in Sr2RuO4 based on the multiorbital Hubbard model. The electronic states are studied using the renormalization group method. Thanks to the vertex correction (VC) for the susceptibility, which is dropped in the mean-field-level approximations, strong orbital and spin fluctuations at $Q=(2π/3,2π/3)$ emerge in the quasi one-dimensional Fermi surfaces composed of $d_{xz}$ and $d_{yz}$ orbitals. Due to the cooperation of both fluctuations, we obtain the triplet superconductivity in the $E_u$ representation, in which the superconducting gap is…
Recent experiments on Zn-doped 122-type iron pnictides, Ba(Fe$_{1-x-y}$Co$_y$Zn$_x$)$_2$As$_2$, are challenging our understanding of electron doping the 122s and the interplay between doping and impurity scattering. To resolve this enigma, we investigate the disorder effects of nonmagnetic Zn impurities in the strong (unitary) scattering limit on various properties of the system in the $s_{\pm}$-wave superconducting pairing state. The lattice Bogoliubov-de Gennes equation (BdG) is solved self-consistently based on a minimal two-orbital model with an extended range of impurity concentrations. W…
To understand the amazing variety of the superconducting states of Fe-based superconductors, we analyze the multiorbital Hubbard models for LaFeAsO and LiFeAs going beyond the random-phase approximation (RPA), by calculating the vertex correction (VC) and self-energy correction. Due to the spin+orbital mode coupling described by the VC, both orbital and spin fluctuations mutually develop, consistently with the experimental phase diagram with the orbital and magnetic orders. Due to both fluctuations, the s-wave gap function with sign-reversal ($s_{\pm}$-wave), without sign-reversal ($s_{++}$-wa…
High-Tc pairing mechanism absent of hole-pockets in heavily electron-doped FeSe is one of the key unsolved problems in Fe-based superconductors. Here, this problem is attacked by focusing on the higher-order many-body effects neglected in conventional Migdal-Eliashberg formalism. We uncover two significant many-body effects for high-Tc superconductivity: (i) Due to the "vertex correction", the dressed multiorbital Coulomb interaction acquires prominent orbital dependence for low-energy electrons. The dressed Coulomb interaction not only induces the orbital fluctuations, but also magnifies the …
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-orb…
Correlation-driven enhancement of pairing in a nematic Hund's metal
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；HUN-REN-BME-BCE Quantum Technology Research Group（匈牙利研究与创新网络-布达佩斯技术与经济大学-布达佩斯理工大学量子技术研究组）；Istituto dei Sistemi Complessi (ISC-CNR)（复杂系统研究所）
We study the mechanism of the triplet superconductivity (TSC) in Sr$_2$RuO$_4$ based on the multiorbital Hubbard model. The electronic states are studied using the recently developed renormalization group method combined with the constrained random-phase-approximation, called the RG+cRPA method. Thanks to the vertex correction (VC) for the susceptibility, which is dropped in the mean-field-level approximations, strong orbital and spin fluctuations at $Q \approx(2π/3,2π/3)$ emerge in the quasi one-dimensional Fermi surfaces (FSs) composed of $d_{xz}+d_{yz}$ orbitals. Due to the cooperation of b…
Structural symmetry effects on the competition of density waves and superconductivity in bilayer nickelates
Ruhr-Universität Bochum（波鸿鲁尔大学）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所（北京凝聚态物理国家研究中心））；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
In order to gain a deep insight into $f$-electron properties of filled skutterudite compounds from a microscopic viewpoint, we investigate the multiorbital Anderson model including Coulomb interactions, spin-orbit coupling, and crystalline electric field effect. For each case of $n$=1$\sim$13, where $n$ is the number of $f$ electrons per rare-earth ion, the model is analyzed by using the numerical renormalization group (NRG) method to evaluate magnetic susceptibility and entropy of $f$ electron. In order to make further step to construct a simplified model which can be treated even in a period…
The pairing mechanism and gap structure in Ba122 pnictides have been hotly discussed for long time as one of the central issues in Fe-based superconductors. Here, we attack this problem by taking account of the vertex corrections (VCs) for the Coulomb interaction $U$ ($U$-VCs), which are totally dropped in conventional Migdal-Eliashberg formalism. The $U$-VC in the charge susceptibility induces strong orbital fluctuations, and the $U$-VC also enlarges the orbital-fluctuation-mediated attractive interaction. By analyzing the effective multiorbital Hubbard model for Ba122 pnictides, we find that…
Precise gap structure in LiFeAs (Tc = 18 K) given by ARPES studies offers us significant information to understand the pairing mechanism in iron-based superconductors. The most remarkable characteristics in LiFeAs gap structure would be that "the largest gap emerges on the tiny hole-pockets around Z point". This result had been naturally explained in terms of the orbital-fluctuation scenario (T. Saito et al., Phys. Rev. B 90, 035104 (2014)), whereas an opposite result is obtained by the spin-fluctuation scenario. In this paper, we study the gap structure in LiFeAs by taking the spin-orbit inte…
We study the mechanism of orbital/spin fluctuations due to multiorbital Coulomb interaction in iron-based superconductors, going beyond the random-phase-approximation. For this purpose, we develop a self-consistent vertex correction (SC-VC) method, and find that multiple orbital fluctuations in addition to spin fluctuations are mutually emphasized by the "multimode interference effect" described by the VC. Then, both the antiferro-orbital and ferro-orbital (=nematic) fluctuations simultaneously develop for $J/U \sim 0.1$, both of which contribute to the s-wave superconductivity. Especially, th…
We study tunneling currents in a model consisting of two non-unitary ferromagnetic spin-triplet superconductors separated by a thin insulating layer. We find a novel interplay between ferromagnetism and superconductivity, manifested in the Josephson effect. This offers the possibility of tuning dissipationless currents of charge and spin in a well-defined manner by adjusting the magnetization direction on either side of the junction.
Hund's coupling assisted orbital-selective superconductivity in Ba1-xKxFe2As2
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Geballe Laboratory for Advanced Materials, Department of Applied Physics and Physics, Stanford University（斯坦福大学应用物理与物理系，Geballe先进材料实验室）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Department of Applied Physics, KTH-Royal Institute of Technology（瑞典皇家理工学院应用物理系）；National Institute of Advanced Industrial Science and Technology (AIST)（日本产业技术综合研究所）；Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory（SLAC国家加速器实验室斯坦福同步辐射光源）；Department of Material Science, Stanford University（斯坦福大学材料科学系）
We investigate the competition between antiferromagnetism and triplet superconductivity in quasi one-dimensional electron systems. We show that the two order parameters can be unified using a SO(4) symmetry and demonstrate the existence of such symmetry in one dimensional Luttinger liquids of interacting electrons. We argue that approximate SO(4) symmetry remains valid even when interchain hopping is strong enough to turn the system into a strongly anisotropic Fermi liquid. For unitary triplet superconductors SO(4) symmetry requires a first order transition between antiferromagnetic and superc…
Muon spin rotation and relaxation experiments on the centrosymmetric intermetallic superconductor LaNiGa$_2$ are reported. The appearance of spontaneous magnetic fields coincides with the onset of superconductivity, implying that the superconducting state breaks time reversal symmetry, similarly to non-centrosymmetric LaNiC$_2$. Only four triplet states are compatible with this observation, all of which are non-unitary triplets. This suggests that LaNiGa$_2$ is the centrosymmetric analogue of LaNiC$_2$. We argue that these materials are representatives of a new family of paramagnetic non-unita…
Motivated by the recent low-tempearture experiments on bulk FeSe, we study the electron correlation effects in a multiorbital model for this compound in the nematic phase using the U(1) slave-spin theory. We find that a finite nematic order helps to stabilize an orbital selective Mott phase. Moreover, we propose that when the d- and s-wave bond nematic orders are combined with the ferro-orbital order, there exists a surprisingly large orbital selectivity between the xz and yz orbitals even though the associated band splitting is relatively small. Our results explain the seemingly unusual obser…
We study a multiorbital Hubbard model coupled to local Jahn-Teller phonons to investigate the superconducting state realized in fullerides. A weak-coupling approach is employed in combination with a local self-energy approximation. In addition to the normal and anomalous self-energies of the electrons, we consider the phonon self-energy, which allows a self-consistent treatment of the energetics. The frequency dependence of the self-energies and their characteristic coefficients, such as renormalization factors and dampings, are investigated in detail using numerical calculations. It is clarif…
An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region, and a suppression in the composite ordered phase. The doping dependent…
The main features in iron-pnictide superconductors are summarized as (i) the orthorhombic transition accompanied by remarkable softening of shear modulus, (ii) high-Tc superconductivity close to the orthorhombic phase, and (iii) stripe-type magnetic order induced by orthorhombicity. To present a unified explanation for them, we analyze the multiorbital Hubbard-Holstein model with Fe-ion optical phonons based on the orbital fluctuation theory. In the random-phase-approximation (RPA), a small electron-phonon coupling constant ($λ~ 0.2$) is enough to produce large orbital (=charge quadrupole) flu…
A weak-coupling formalism for superconducting states possessing both singlet (even parity) and triplet (odd parity) components of the order parameter in centrosymmetric crystals is developed. It is shown that the quasiparticle energy spectrum may be non-degenerate even if the triplet component is unitary. The superconducting gap of a mixed-parity state may have line nodes in the strong spin-orbit coupling limit. The pseudospin carried by the superconducting electrons is calculated, from which follows a prediction of a kink anomaly in the temperature dependence of muon spin relaxation rate. The…
The pairing glue of high-$T_{\rm c}$ superconductivity in heavily electron-doped (e-doped) FeSe, in which hole-pockets are absent, has been an important unsolved problem. Here, we focus on a heavily e-doped bulk superconductor Li$_{1-x}$Fe$_x$OHFeSe ($T_{\rm c} \sim 40$K). We construct a multiorbital model beyond the rigid band approximation and analyze the spin and orbital fluctuations by taking both vertex corrections (VCs) and self-energy into consideration. Without e-doping ($x=0$), the ferro-orbital order without magnetism in FeSe is reproduced by the VCs.The orbital order quickly disappe…
The pseudogap phenomena in the cuprate superconductors requires a theory beyond the mean field BCS level. A natural candidate is to include strong pairing fluctuations, and treat the two-particle and single particle Green's functions self-consistently. At the same time, impurities are present in even the cleanest samples of the cuprates. Some impurity effects can help reveal whether the pseudogap has a superconducting origin and thus test various theories. Here we extend the pairing fluctuation theory for a clean system [Phys. Rev. Lett. 81, 4708 (1998)] to the case with nonmagnetic impurities…
Scanning tunneling spectroscopic studies of $Ba(Fe_{1-x}Co_x)_2As_2$ (x = 0.06, 0.12) single crystals reveal direct evidence for predominantly two-gap superconductivity. These gaps decrease with increasing temperature and vanish above the superconducting transition $T_c$. The two-gap nature and the slightly doping- and energy-dependent quasiparticle scattering interferences near the wave-vectors $(\pm π, 0)$ and $(0, \pm π)$ are consistent with sign-changing $s$-wave superconductivity. The excess zero-bias conductance and the large gap-to-$T_c$ ratios suggest dominant unitary impurity scatteri…
