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In kagome metals, the chiral current order parameter η with time-reversal-symmetrybreaking is the source of various exotic electronic states, while the method of controlling the current order and its interplay with the star-of-David bond order ϕ are still unsolved. Here, we reveal that tiny uniform orbital magnetizationMorb[η, ϕ] is induced by the chiral current order, and its magnitude is prominently enlarged under the presence of the bond order. Importantly, we derive the magnetic-field (hz)-induced Ginzburg-Landau (GL) free energy expression ΔF[hz, η, ϕ] ∝ -hzMorb[η, ϕ], which enables us to elucidate the field-induced current-bond phase transitions in kagome metals. The emergent current-bond-hz trilinear coupling term in the free energy, -m1hzη Δ ϕ, naturally explains the characteristic magnetic-field sensitive electronic states in kagome metals, such as the field-induced current order and the strong interplay between the bond and current orders. The GL coefficients of ΔF[hz, η, ϕ] derived from the realistic multiorbital model are appropriate to explain various experiments. Furthermore, we discuss the field-induced loop current orders in the square lattice models that have been studied in cuprate superconductors. [ABSTRACT FROM AUTHOR]

We present a microscopic derivation of the nematic charge-density wave (CDW) formation in cuprate superconductors based on the three-orbital d-p Hubbard model by introducing the vertex correction (VC) into the charge susceptibility. The CDW instability at q = (ΔFS, 0), (0, ΔFS) appears when the spin fluctuations are strong, due to the strong charge-spin interference represented by the VC. Here, ΔFS is the wave number between the neighboring hot spots. The obtained spin-fluctuation-driven CDW is expressed as the "intra-unit-cell orbital order" accompanied by the charge transfer between the neighboring atomic orbitals, which is actually observed by the scanning tunneling microscope measurements. We predict that the cuprate CDW and the nematic orbital order in Fe-based superconductors are closely related spin-fluctuation-driven phenomena. [ABSTRACT FROM AUTHOR]

We study the mechanism of the triplet superconductivity (TSC) in Sr2RuO4 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 ≈ (2π/3,2π/3) emerge in the quasi-one-dimensional Fermi surfaces (FSs) composed of dxz + dyz orbitals. Due to the cooperation of both fluctuations, we obtain the triplet superconductivity in the Eu representation, in which the superconducting gap is given by the linear combination of (Δx(k),Δy(k)) ∼ (sin3kx, sin 3Ky). Very similar results are obtained by applying the diagrammatic calculation called the self-consistent VC method. Thus, the idea of "orbital + spin fluctuation mediated TSC" is confirmed by both the RG + cRPA method and the self-consistent VC method. We also revealed that the large superconducting gap on the dxy-orbital Fermi surface is induced from gaps on the quasi-one-dimensional FSs, in consequence of the large orbital mixture due to the 4d spin-orbit interaction. [ABSTRACT FROM AUTHOR]

The emergence of the nematic order and fluctuations has been discussed as a central issue in Fe-based superconductors. To clarify the origin of the nematicity, we focus on the shear modulus C66 and the Raman quadrupole susceptibility XRamanx²-y². Because of the Aslamazov-Larkin vertex correction, the nematic-type orbital fluctuations are induced, and they enhance both 1/C66 and XRamanx²-y² strongly. However, XRamanx²-y² remains finite even at the structure transition temperature TS, because of the absence of the band Jahn-Teller effect and the Pauli (intraband) contribution, as proved in terms of the linear response theory. The present study clarifies that the origin of the nematicity in Fe-based superconductors is the nematic orbital order and fluctuations. [ABSTRACT FROM AUTHOR]

The isostructural transition in the tetragonal phase with a sizable change in the anion height, is realized in heavily H-doped LaFeAs and (La,P) codoped CaFe2As2. In these compounds, the superconductivity with higher Tc (40-50 K) is realized near the isostructural transition. To find the origin of the anion-height instability and the role in realizing the higher-Tc state, we develop the orbital-spin fluctuation theory by including the vertex correction. We analyze LaFeAsO1-xHx and find that the non-nematic orbital fluctuations, which induce the anion-height instability, are automatically obtained at x ∼ 0.5, in addition to the conventional nematic orbital fluctuations at x∼0. The non-nematic orbital order triggers the isostructural transition, and its fluctuation would be a key ingredient to realize higher-Tc superconductivity of order 50 K. [ABSTRACT FROM AUTHOR]

We propose that an impurity-induced electronic nematic state is realized above the orthorhombic structure transition temperature TS in iron-pnictide superconductors. In the presence of strong orbital fluctuations near TS, it is theoretically revealed that a single impurity induces local orbital order with C2 symmetry, consistently with recent Scanning Tunneling Microscopy/Spectroscopy (STM/STS) measuremenTS. Each impurity-induced C2-symmetric nanostructure aligns along the a axis by applying tiny uniaxial pressure along the b axis. In this impurity-induced nematic phase, the resistivity shows sizable in-plane anisotropy (ρb/ρa∼ 2) even above TS, actually observed in various "detwinned" samples. The present study indicates the existence of strong orbital fluctuations in iron-pnictide superconductors. [ABSTRACT FROM AUTHOR]

In BaNiS2, a Dirac nodal line band structure exists within a two-dimensional Ni square lattice system, in which significant electronic correlation effects are anticipated. Using scanning tunneling microscopy (STM), we discover signs of correlated-electron behavior, namely electronic nematicity appearing as a pair of C2-symmetry striped patterns in the local density-of-states at ~60 meV above the Fermi energy. In observations of quasiparticle interference, as well as identifying scattering between Dirac cones, we find that the striped patterns in real space stem from a lifting of degeneracy among electron pockets at the Brillouin zone boundary. We infer a momentum-dependent energy shift with d-form factor, which we model numerically within a density wave (DW) equation framework that considers spin-fluctuationdriven nematicity. This suggests an unusual mechanism driving the nematic instability, stemming from only a small perturbation to the Fermi surface, in a system with very low density of states at the Fermi energy. The Dirac points lie at nodes of the d-form factor and are almost unaffected by it. These results highlight BaNiS2 as a unique material in which Dirac electrons and symmetry-breaking electronic correlations coexist. [ABSTRACT FROM AUTHOR]

To understand the rich electronic phase diagram in FeSe under pressure that vividly demonstrates the strong interplay between the nematicity, magnetism, and superconductivity, we analyze the electronic states by including the higher-order many-body effects called the vertex correction (VC). We predict the pressure-induced emergence of xy-orbital hole pocket based on the first-principles analysis. Due to this pressure-induced Lifshitz transition, the spin fluctuations on the xy orbital are enhanced, whereas those on xz,yz orbitals are gradually reduced. For this reason, nonmagnetic orbital order O=nxz-nyz, which is driven by the spin fluctuations on xz,yz orbitals through the intraorbital VCs, is suppressed, and it is replaced with the magnetism of xy-orbital d electrons. The nodal s-wave state at ambient pressure (O≠0) and the enhancement of Tc under pressure are driven by the cooperation between the spin and orbital fluctuations. [ABSTRACT FROM AUTHOR]

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 electron-boson coupling constant. Therefore, moderate orbital fluctuations give strong attractive pairing interaction. (ii) The "multi-fluctuation-exchange pairing process" causes large interpocket attractive force, which is as important as the usual single-fluctuation-exchange process. Due to these two significant effects dropped in the Migdal-Eliashberg formalism, the anisotropic s++-wave state in heavily electron-doped FeSe is satisfactorily explained. The proposed "inter-electron-pocket pairing mechanism" will enlarge Tc in other Fe-based superconductors. [ABSTRACT FROM AUTHOR]

Multiple line nodes in energy-band gaps are found in semimetals preserving mirror-reflection symmetry. We classify possible configurations of multiple line nodes with crossing points (crossing line nodes) under point-group symmetry. Taking the spin-orbit interaction (SOI) into account, we also classify topological phase transitions from crossing-line-node Dirac semimetals to other topological phases, e.g., topological insulators and point-node semimetals. This study enables one to find crossing-line-node semimetal materials and their behavior in the presence of SOI from the band structure in the absence of SOI without detailed calculations. As an example, the theory applies to hexagonal rare-earth trihydrides with the HoD3 structure and clarifies that it is a crossing-line-node Dirac semimetal hosting three line nodes. [ABSTRACT FROM AUTHOR]

In various multiorbital systems, the emergence of the orbital fluctuations and their role on the pairing mechanism attract increasing attention. To achieve deep understanding on these issues, we perform a 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 Ueffˆc becomes much larger than the bare Coulomb interaction Uˆ0 due to the U-VC in the presence of moderate spin fluctuations. For this reason, the attractive pairing interaction due to the charge or orbital fluctuations is enlarged by the factor (Ueffˆc/Uˆ0)²≫1. In contrast, the spin fluctuation pairing interaction is suppressed by the spin-channel U-VC, because of the relation Ueffˆs≪Uˆ0. The present study demonstrates that the orbital or charge fluctuation pairing mechanism can be realized in various multiorbital systems thanks to the U-VC, such as in Fe-based superconductors. [ABSTRACT FROM AUTHOR]

The electronic nematic state without magnetization emerges in various strongly correlated metals such as Fe-based and cuprate superconductors. To understand this universal phenomenon, we focus on the nematic state in Ti oxypnictide BaTi2(As,Sb)2O, which is expressed as the three-dimensional ten-orbital Hubbard model. The antiferromagnetic fluctuations are caused by the Fermi surface nesting. Interestingly, we find the spin-fluctuation-driven orbital order due to the strong orbital-spin interference, which is described by the Aslamazov-Larkin vertex correction (AL-VC). The predicted intra-unit-cell nematic orbital order is consistent with the recent experimental reports on BaTi2(As,Sb)2O. Thus, the spin-fluctuation-driven orbital order due to the AL-VC mechanism is expected to be universal in various two- and three-dimensional multiorbital metals. [ABSTRACT FROM AUTHOR]

To understand the nematicity in Fe-based superconductors, nontrivial k dependence of the orbital polarization [ΔExz(k), ΔEyz(k)] in the nematic phase, such as the sign reversal of the orbital splitting between Δ and X, Y points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole and electron pockets are elongated along the ky and kx axes, respectively, consistently with experiments. In addition, an electron pocket splits into two Dirac cone Fermi pockets while increasing the orbital polarization. The orbital order in Fe-based superconductors originates from the strong positive feedback between the nematic orbital order and spin susceptibility. [ABSTRACT FROM AUTHOR]

The discovery of the charge-density-wave formation in the high-Tc cuprate superconductors has activated intensive theoretical studies for the pseudogap states. However, the microscopic origin of the charge-density-wave state has been unknown so far since the many-body effects beyond the mean-field-level approximations, called the vertex corrections, are essential. Toward solving this problem, we employ the recently developed functional renormalization group method, by which we can calculate the higher-order vertex corrections in a systematic and unbiased way with high numerical accuracy. We discover the critical development of the p-orbital-density-wave (p-ODW) instability in the strong-spin-fluctuation region. The obtained p-ODW state possesses the key characteristics of the charge-ordering pattern in Bi- and Y-based superconductors, such as the wave vector parallel to the nearest Cu-Cu direction, and the d-symmetry form factor with the antiphase correlation between px and py orbitals in the same unit cell. In addition, from the observation of the beautiful scaling relation between the spin susceptibility and the p-ODW susceptibility, we conclude that the main driving force of the density wave is the Aslamazov-Larkin vertex correction that becomes very singular near the magnetic quantum-critical point. [ABSTRACT FROM AUTHOR]

The precise gap structure in LiFeAs (Tc = 18K) given by ARPES studies offers significant information that helps us understand the pairing mechanism in iron-based superconductors. The most remarkable characteristic in the LiFeAs gap structure would be that "the largest gap emerges on the tiny hole-pockets around the Z point." This result has been naturally explained in terms of the orbital-fluctuation scenario [T. Saito et al., Phys. Rev. B 90, 035104 (2014)], whereas the opposite result is obtained by the spin-fluctuation scenario. In this paper, we study the gap structure in LiFeAs by taking the spin-orbit interaction (SOI) into account, motivated by the recent ARPES studies that revealed a significant SOI-induced modification of the Fermi surface topology. For this purpose, we construct two possible tight-binding models with finite SOI by referring the band structures given by different ARPES groups. In addition, we extend the gap equation for multiorbital systems with finite SOI, and calculate the gap functions by applying the orbital-spin fluctuation theory. On the basis of both SOI-induced band structures, the main characteristics of the gap structure in LiFeAs are naturally reproduced only in the presence of strong interorbital interactions between (dxz/yz-dxy) orbitals. Thus the experimental gap structure in LiFeAs is a strong evidence for the orbital-fluctuation pairing mechanism. [ABSTRACT FROM AUTHOR]

We investigate the quasiparticle interference (QPI) in Fe-based superconductors in both the s++-wave and s±-wave superconducting states on the basis of the five-orbital model. In the octet model for cuprate superconductors with dxâ'y²-wave state, the QPI signal due to the impurity scattering at q=kiâ'kj (E=|Δ(ki)|, i=1â'8) disappears when the gap functions at ki and kj have the same sign. However, we show that this extinction rule does not hold in Fe-based superconductors with fully gapped s-wave state. The reason is that the resonance condition E=|Δ(ki)| is not satisfied under the experimental condition for Fe-based superconductors. We perform the detailed numerical study of the QPI signal using the T-matrix approximation, and show that the experimentally observed QPI peak around q2=(Ï€,0) can be explained on the basis of both the s++-wave and s±-wave states. Furthermore, we discuss the magnetic field dependence of the QPI by considering the Zeeman effect, and find that the field-induced suppression of the peak intensity around q2 can also be explained in terms of both the s++-wave and s±-wave states. [ABSTRACT FROM AUTHOR]

We report the discovery of a very large thermoelectric power over -400 µV K-1 in the whisker crystals of a one-dimensional telluride Ta4SiTe4, while maintaining a low electrical resistivity of ρ = 2 mΩ cm, yielding a very large power factor of P=80 µW cm-1 K-2 at an optimum temperature of 130 K. This temperature is widely controlled from the cryogenic temperature of 50K to room temperature by chemical doping, resulting in the largest P of 170 µW cm-1K-2 at 220-280 K. These P values far exceed those of the Bi2Te3-Sb2Te3 alloys at around room temperature, offering an avenue for realizing the practical-level thermoelectric cooling at low temperatures. The coexistence of a one-dimensional electronic structure and a very small band gap appearing in the vicinity of the Dirac semimetals probably causes the very large power factors in Ta4SiTe4, indicating that the "one-dimensional Dirac semimetal" is a promising way to find high-performance thermoelectric materials for the low temperature applications. [ABSTRACT FROM AUTHOR]

The absence of nesting between electron and hole pockets in LiFeAs with Tc = 18 K attracts great attention, as an important hint to understand the pairing mechanism of Fe-based superconductors. Here, we study the five-orbital model of LiFeAs based on the recently developed orbital-spin fluctuation theories. It is found that the experimentally observed gap structure of LiFeAs, which is a "fingerprint" of the pairing mechanism, is quantitatively reproduced in terms of the orbital-fluctuation-mediated s++-wave state. Specifically, the largest gap observed on the two small hole pockets composed of (dxz,dyz) orbitals can be explained, and this is a hallmark of the orbital-fluctuation-mediated superconductivity. The s++-wave gap structure becomes more anisotropic in the presence of weak spin fluctuations. As the spin fluctuations increase, we obtain the "hole-s±-wave state," in which only the gap of the large hole pocket made of the dxy orbital is sign reversed, due to the cooperation of orbital and spin fluctuations. This gap structure with "sign reversal between hole pockets" is similar to that recently reported in (Ba,K)Fe2As2. [ABSTRACT FROM AUTHOR]

The emergence of the nematic electronic state that breaks rotational symmetry is one of the most fascinating properties of the iron-based superconductors, and has relevance to cuprates as well. FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering, providing a significant opportunity to investigate the role of nematicity in the superconducting pairing interaction. Here, to reveal how the superconducting gap evolves with nematicity, we measure the thermal conductivity and specific heat of FeSe1-xSx, in which the nematicity is suppressed by isoelectronic sulfur substitution and a nematic critical point (NCP) appears at xc≈ 0:17. We find that, in the whole nematic regime (0⩽x ⩽0:17), the field dependence of two quantities consistently shows two-gap behavior; one gap is small but highly anisotropic with deep minima or line nodes, and the other is larger and more isotropic. In stark contrast, in the tetragonal regime (x = 0:20), the larger gap becomes strongly anisotropic, demonstrating an abrupt change in the superconducting gap structure at the NCP. Near the NCP, charge fluctuations of dxz and dyz orbitals are enhanced equally in the tetragonal side, whereas they develop differently in the orthorhombic side. Our observation therefore directly implies that the orbital-dependent nature of the nematic fluctuations has a strong impact on the superconducting gap structure and hence on the pairing interaction. [ABSTRACT FROM AUTHOR]