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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, 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 equation framework that considers spin-fluctuation-driven 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., 11 pages, 5 figures (plus 6 pages, 4 figures)

Unconventional symmetry breaking due to nonlocal order parameters has attracted considerable attention in many strongly correlated metals. Famous examples are the nematic order in Fe-based superconductors and the star-of-David charge density order in kagome metals. Such exotic symmetry breaking in metals is a central issue of modern condensed matter physics, while its theoretical foundation is still unclear in comparison with the well-established theory of superconductivity. To overcome this difficulty, here we introduce the "form factor" that generalizes the nonlocal order parameter into the Luttinger-Ward (LW) Fermi liquid theory. We then construct a rigorous formalism of the "density-wave equation" that gives the thermodynamically stable form factor, similarly to the superconducting-gap equation. In addition, a rigorous expression of the Ginzburg-Landau free-energy for the unconventional order is presented to calculate various thermodynamic properties. In the next stage, we apply the derived formalism to a typical Fe-based superconductor FeSe, by using the one-loop LW function that represents the free-energy gain due to the interference among paramagnons. The following key experiments are naturally explained: (i) Lifshitz transition (=disappearance of an electron-pocket) due to the bond+orbital order below $T_c$. (ii) Curie-Weiss behavior of the nematic susceptibility at higher T, and the deviation from the Curie-Weiss behavior at lower T near the nematic quantum-critical-point. (iii) Scaling relation of the specific heat jump at $T_c$, $\Delta C/T_c \propto T_c^b$ with $b \sim 3$. (Note that b=0 in the BCS theory.) These results lead to a conclusion that the nematicity in FeSe is the bond+orbital order due to the "paramagnon interference mechanism". The present theory paves the way for solving various unconventional phase transition systems., Comment: 19 pages, 10 figures

To seek high-$T_c$ pairing mechanism, many scientists have focused on the mysterious spontaneous rotational symmetry breaking above Tc, such as nematic order at $q=0$ and smectic order at $q\ne0$. Such exotic correlation-driven symmetry breaking in metals has become a central issue in condensed matter physics. We demonstrate the emergence of the nematic and smectic orders due to orbital polarization ($n_{xz}\ne n_{yz}$) and the symmetry breaking in the correlated intersite hopping (= bond order $\delta t_{i,j}$) in Fe-based and cuprate superconductors. In addition, we discuss exotic spontaneous loop current orders driven by the pure imaginary $\delta t_{i,j}$. These interesting ``unconventional density-waves'' originate from the quantum interference between different spin fluctuations that is described by the vertex correction (VC) in the field theory. In the next stage, we discuss electron-correlation driven superconductivity due to the fluctuations of unconventional density-waves. For this purpose, we suggest the beyond-Migdal-Eliashberg gap equation by including the VCs into the equation. In Fe-based superconductors, high-$T_c$ $s$-wave superconductivity can be mediated by nematic and smectic fluctuations because the pairing interaction is magnified by the VCs. We also discuss the multipolar fluctuation pairing mechanism in heavy fermion systems, owing to the cooperation between the strong spin-orbit interaction and the strong electron correlation. To summarize, we suggest that the quantum interference mechanism described by the VCs is the key ingredients to explain not only various unconventional density-waves, but also exotic superconducting states in many strongly correlated metals. We finally discuss some interesting future issues with respect to the quantum interference mechanism., Comment: 98 pages, 50 figures, to be published in Advances in Physics

The authors reveal the mechanism of incommensurate charge-density-wave in transition metal dichalcogenide (TMD) 1T-TaS${}_{2}$.

FeSe is a unique high-$$T_c$$ T c iron-based superconductor in which nematicity, superconductivity, and magnetism are entangled with each other in the P-T phase diagram. We performed $$^{77}$$ 77 Se-nuclear magnetic resonance measurements under pressures of up to 3.9 GPa on 12% S-substituted FeSe, in which the complex overlap between the nematicity and magnetism are resolved. A pressure-induced Lifshitz transition was observed at 1.0 GPa as an anomaly of the density of states and as double superconducting (SC) domes accompanied by different types of antiferromagnetic (AF) fluctuations. The low-$$T_{\mathrm{c}}$$ T c SC dome below 1 GPa is accompanied by strong AF fluctuations, whereas the high-$$T_{\mathrm{c}}$$ T c SC dome develops above 1 GPa, where AF fluctuations are fairly weak. These results suggest the importance of the $$d_{xy}$$ d xy orbital and its intra-orbital coupling for the high-$$T_{\mathrm{c}}$$ T c superconductivity.

The authors propose the emergence of $d$-wave smectic bond order in organic superconductor $\ensuremath{\kappa}$-(BEDT-TTF)${}_{2}$X due to the paramagnon interference mechanism.

Unconventional symmetry breaking without spin order,such as the rotational symmetry breaking (=nematic or smectic) orders as well as the spontaneous loop-current orders, have been recently reported in cuprate superconductors and their related materials.They are theoretically represented by non-$A_{1g}$ symmetry breaking in self-energy, which we call the form factor $f_{k,q}$.In this paper, we analyze typical Hubbard models by applying the renormalization-group (RG) method, and find that various unconventional ordering emerges due to the quantum interference among spin fluctuations. Due to this mechanism,nematic ($q=0$) and smectic ($q \ne 0$)bond orders with $d$-wave form factor appear $f_{k,q}\propto \cos k_x - \cos k_y$ in both cuprates and $\kappa$-(BEDT-TTF)$_2$X. The derived bond orders naturally explain the pseudogap behaviors in these compounds. The quantum interference also induces various current orders with odd-parity form factor. For example, we find the emergence of the charge and spin loop-current orders with $p$-wave form factor in geometrically frustrated Hubbard models. Thus, rich quantum phase transitions with $d$- and $p$-wave form factors are driven by the paramagnon interference in many low-dimensional Hubbard models., Comment: 13 pages, 13 figures

In cuprate superconductors, superconductivity appears below the CDW transition temperature $T_{CDW}$. However, many-body electronic states under the CDW order are still far from understood. Here, we study the development of the spin fluctuations under the presence of $d$-wave bond order (BO) with wavevector $q=(\pi/2,0),(0,\pi/2)$, which is derived from the paramagnon interference mechanism in recent theoretical studies. Based on the $4 \times 1$ and $4 \times 4$ cluster Hubbard models, the feedback effects between spin susceptibility and self-energy are calculated self-consistently by using the fluctuation-exchange (FLEX) approximation. It is found that the $d$-wave BO leads to a sizable suppression of the nuclear magnetic relaxation rate $1/T_1$. In contrast, the reduction in $T_c$ is small, since the static susceptibility $\chi^s(Q_s)$ is affected by the BO just slightly. It is verified that the $d$-wave BO scenario is consistent with the experimental electronic properties below $T_{CDW}$., Comment: 8 pages,7 figures, to be published in J. Phys. Soc. Jpn

Spontaneous current orders due to odd-parity order parameters attract increasing attention in various strongly correlated metals. Here, we discover a novel spin-fluctuation-driven charge loop current (cLC) mechanism based on the functional renormalization group (fRG) theory. The present mechanism leads to the ferro-cLC order in a simple frustrated chain Hubbard model. The cLC appears between the antiferromagnetic and $d$-wave superconducting ($d$SC) phases. While the microscopic origin of the cLC has a close similarity to that of the $d$SC, the cLC transition temperature $T_{\rm cLC}$ can be higher than the $d$SC one for wide parameter range. Furthermore, we reveal that the ferro cLC order is driven by the strong enhancement of the forward scatterings $g_2$ and $g_4$ owing to the two dimensionality based on the $g$-ology language. The present study indicates that the cLC can emerge in metals near the magnetic criticality with geometrical frustration, Comment: 11 pages, 15 figures, has been published in Phys. Rev. B

Exotic quantum phase transitions in metals, such as the nematic and smectic states, were discovered one after another and found to be universal now. The emergence of unconventional density-wave order in frustrated kagome metal AV$_3$Sb$_5$ and its interplay with exotic superconductivity attract increasing attention. We reveal that the smectic bond-density-wave is naturally caused by the paramagnon interference mechanism, because strong scatterings among different van-Hove singularity points are induced. In addition, the fluctuations of the bond-order induce sizable "beyond-Migdal" pairing glue, and therefore both singlet nodal $s$-wave pairing and triplet $p$-wave pairing states are expected to emerge. The coexistence of both states would explain exotic superconducting states. Unexpected similarities between kagome metal and some Fe-based superconductors are discussed. This study enables us to understand the exotic density wave, superconductivity and their interplay in kagome metals based on the interference mechanism., Comment: 18 pages, 16 figures

We report the electronic properties of single crystals of candidate nodal-line semimetal CaAgP. The transport properties of CaAgP are understood within the framework of a hole-doped nodal-line semimetal. In contrast, Pd-doped CaAgP shows a drastic increase of magnetoresistance at low magnetic fields and a strong decrease of electrical resistivity at low temperatures probably due to weak antilocalization. Hall conductivity data indicated that the Pd-doped CaAgP has not only hole carriers induced by the Pd doping, but also high-mobility electron carriers in proximity of the Dirac point. Electrical resistivity of Pd-doped CaAgP also showed a superconducting transition with onset temperature of 1.7-1.8 K., 6 pages, 3 figures, accepted for publication in Phys. Rev. B

Unconventional symmetry-breaking phenomena due to nontrivial order parameters attract increasing attention in strongly correlated electron systems. Here, we predict theoretically the occurrence of nanoscale spontaneous spin-current, called the spin loop-current (sLC) order, as a promising origin of the pseudogap and electronic nematicity in cuprates. We reveal that the sLC is driven by the odd-parity electron-hole condensation that are mediated by transverse spin fluctuations around the pseudogap temperature $T^*$. At the same temperature, odd-parity magnon pair condensation occurs. The sLC order is "hidden" in that neither internal magnetic field nor charge density modulation is induced, whereas the predicted sLC with finite wavenumber naturally gives the Fermi arc structure. In addition, the fluctuations of sLC order work as attractive pairing interaction between adjacent hot spots, which enlarges the d-wave superconducting transition temperature $T_c$. The sLC state will be a key ingredient in understanding the pseudogap, electronic nematicity as well as superconductivity in cuprates and other strongly correlated metals., Comment: 13 pages, 15 figures, to be published in Phys. Rev. Research

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 disappears when the hole-pocket vanishes at $x \sim 0.03$. With increasing $x$ further, the spin fluctuations remain small, whereas orbital fluctuations gradually increase with $x$ due to the VCs. The negative feedback due to the self-energy is crucial to explain experimental phase diagram. Thanks to both vertex and self-energy corrections, the orbital-fluctuation-mediated $s_{++}$-wave state appears for a wide doping range, consistent with experiments., 10 pages, 8 figures

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 - x S x , in which the nematicity is suppressed by isoelectronic sulfur substitution and a nematic critical point (NCP) appears at [Formula: see text] We find that, in the whole nematic regime ([Formula: see text]), 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 ([Formula: see text]), the larger gap becomes strongly anisotropic, demonstrating an abrupt change in the superconducting gap structure at the NCP. Near the NCP, charge fluctuations of [Formula: see text] and [Formula: see text] 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.

An iron-based superconductor ${\mathrm{LaFeAsO}}_{1\ensuremath{-}x}{\mathrm{H}}_{x}\phantom{\rule{0.16em}{0ex}}(0\ensuremath{\le}x\ensuremath{\le}0.6)$ undergoes two antiferromagnetic (AF) phases upon H doping. We investigated the second AF phase ($x=0.6$) using NMR techniques under pressure. At pressures up to 2 GPa, the ground state is a spin-density-wave state with a large gap; however, the gap closes at 4.0 GPa, suggesting a pressure-induced quantum critical point. Interestingly, the gapped excitation coexists with gapless magnetic fluctuations at pressures between 2 and 4 GPa. This coexistence is attributable to the lift up of the ${d}_{xy}$ orbital to the Fermi level, a Lifshitz transition under pressure.

We report the synthesis, electronic properties, and electronic structure of LaIrSi-type BaPtP with a noncentrosymmetric cubic crystal structure. Electrical resistivity and heat capacity data taken by using polycrystalline samples indicated that BaPtP is a metal, which was further supported by first principles calculations. A polycrystalline sample of BaPtP showed a zero resistivity below 0.2 K due to the superconducting transition. The first principles calculation results indicated that the spin splitting at around the Fermi energy is large in BaPtP. These results suggest that BaPtP is likely to exhibit interesting physical properties caused by a strong spin-orbit coupling of 5d electrons in the Pt atoms., Comment: 4 pages, 4 figures, JPS Conf. Proc., accepted

To elucidate the pairing states in Fe-based superconductors, we perform a careful calculation of the dynamical spin susceptibility ${\ensuremath{\chi}}^{S}(\mathbit{q},\ensuremath{\omega})$ at very low temperatures ($T\ensuremath{\gtrsim}1\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$). The feedback effect on both the self-energy and ${\ensuremath{\chi}}^{S}(\mathbit{q},\ensuremath{\omega})$ from the superconducting gap is self-consistently analyzed based on the fluctuation-exchange (FLEX) approximation. In the ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave state, which has sign reversal in the gap function, ${\ensuremath{\chi}}^{S}(\mathbit{q},\ensuremath{\omega})$ at the nesting momentum $\mathbit{q}=\mathbit{Q}$ shows a resonance peak even when the system is away from the magnetic quantum critical point (QCP). In the ${s}_{++}$-wave state that has no sign reversal, ${\ensuremath{\chi}}^{S}(\mathbit{q},\ensuremath{\omega})$ shows a large hump structure when the system is close to the magnetic QCP. This result confirms the validity of a self-energy driven resonancelike peak in the ${s}_{++}$-wave state proposed in our previous semimicroscopic study: The enhancement in ${\ensuremath{\chi}}^{S}(\mathbit{q},\ensuremath{\omega})$ due to the self-energy effect exceeds the suppression due to the coherence factor effect near the magnetic QCP. We stress that the hump structure in the ${s}_{++}$-wave state given by the FLEX method smoothly changes to a resonancelike sharp peak structure as the system approaches the magnetic QCP, which was not reported in our previous studies. The obtained $\ensuremath{\omega}$ and $T$ dependence of ${\ensuremath{\chi}}^{S}(\mathbit{q},\ensuremath{\omega})$ in the ${s}_{++}$-wave states resembles the resonancelike feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe.

The pairing mechanism and gap structure in Ba122 pnictides have been hotly discussed for a 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 $U\phantom{\rule{0.28em}{0ex}}(U\ensuremath{-}\mathrm{VCs})$, which are totally dropped in conventional Migdal-Eliashberg formalism. The $U\ensuremath{-}\mathrm{VC}$ in the charge susceptibility induces strong orbital fluctuations, and the $U\ensuremath{-}\mathrm{VC}$ enlarges the orbital-fluctuation-driven attractive interaction. By analyzing the effective multiorbital Hubbard model for Ba122 pnictides, we find that the orbital fluctuations develop in all four $d$ orbitals (${t}_{2g}$ and ${z}^{2}$ orbitals) by which the Fermi surfaces (FSs) are composed. For this reason, nearly isotropic gap functions appear on all the hole-type FSs, including the outer hole FS around the $Z$ point composed of the ${z}^{2}$ orbital. In contrast, nodal gap structure appears on the electron FSs for the wide parameter range. The obtained nodal $s$-wave state changes to a fully gapped $s$-wave state without sign reversal (${s}_{++}$-wave state) by introducing a small amount of impurities, accompanied by a small reduction in ${T}_{\mathrm{c}}$. The present microscopic theory naturally explains the important characteristics of the gap structure of both hole and electron FSs in Ba122 pnictides without introducing any phenomenological pairing interaction.

To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The position-dependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The present study predicts the emergence of nontrivial spin-fluctuation-driven phenomena near the edge, like the quantum criticality, edge superconductivity, and the bond-density-wave order., 18 pages, 7 figures, to be published in J. Phys. Soc. Jpn

Electronic nematicity that spontaneously breaks the rotational symmetry of the underlying crystal lattice has been a growing issue in high-temperature superconductivity of iron pnictides/chalcogenides and cuprates. FeSe1 − xSx, in which the nematicity can be tuned by isoelectronic sulfur substitution, offers a fascinating opportunity to clarify the direct relationship between the nematicity and superconductivity. Here, we discover a dramatic change in the superconducting gap structure at the critical concentration of sulfur where the nematicity disappears, i.e., nematic critical point. Our observation provides direct evidence that the orbital-dependent nature of the critical nematic fluctuations has a strong impact on the superconducting pairing interaction.

One of key challenges in current material research is to search for new topological materials with inverted bulk-band structure. In topological insulators, the band inversion caused by strong spin-orbit coupling leads to opening of a band gap in the entire Brillouin zone, whereas an additional crystal symmetry such as point-group and nonsymmorphic symmetries sometimes prohibits the gap opening at/on specific points or line in momentum space, giving rise to topological semimetals. Despite many theoretical predictions of topological insulators/semimetals associated with such crystal symmetries, the experimental realization is still relatively scarce. Here, using angle-resolved photoemission spectroscopy with bulk-sensitive soft x-ray photons, we experimentally demonstrate that hexagonal pnictide CaAgAs belongs to a new family of topological insulators characterized by the inverted band structure and the mirror reflection symmetry of crystal. We have established the bulk valence-band structure in three-dimensional Brillouin zone, and observed the Dirac-like energy band and ring-torus Fermi surface associated with the line node, where bulk valence and conducting bands cross on a line in the momentum space under negligible spin-orbit coupling. Intriguingly, we found that no other bands cross the Fermi level and therefore the low-energy excitations are solely characterized by the Dirac-like band. CaAgAs provides an excellent platform to study the interplay among low-energy electron dynamics, crystal symmetry, and exotic topological properties., Comment: 23 pages, 3 figures

We found that whisker crystals of Mo-doped Nb4SiTe4 show high thermoelectric performances at low temperatures, indicated by the largest power factor of 70 microW cm-1 K-2 at 230-300 K, much larger than those of Bi2Te3-based practical materials. This power factor is smaller than the maximum value in the 5d analogue Ta4SiTe4, but is comparable to that with a similar doping level. First principles calculation results suggest that the difference in thermoelectric performances between Nb and Ta compounds is caused by the much smaller band gap in Nb4SiTe4 than that in Ta4SiTe4, due to the weaker spin-orbit coupling in the former. We also demonstrated that the solid solution of Nb4SiTe4 and Ta4SiTe4 shows a large power factor, indicating that their combination is promising as a practical thermoelectric material, as in the case of Bi2Te3 and Sb2Te3. These results advance our understanding of the mechanism of high thermoelectric performances in this one-dimensional telluride system, as well as indicating the high potential of this system as a practical thermoelectric material for low temperature applications., Comment: 5 pages, 5 figures

Recently, complex phase transitions accompanied by the rotational symmetry breaking have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various charge susceptibilities in an unbiased way, by applying the functional-renormalization-group method to the realistic $d$-$p$ Hubbard model. Without assuming the wavevector of the order parameter, we reveal that the most dominant instability is the uniform ($q = 0$) charge modulation on the $p_x$ and $p_y$ orbitals, which possesses the d-symmetry. This uniform nematic order triggers another nematic p-orbital density wave along the axial (Cu-Cu) direction at $Q_a = (\pi/2,0)$. It is predicted that uniform nematic order is driven by the spin fluctuations in the pseudogap region, and another nematic density-wave order at $q = Q_a$ is triggered by the uniform order. The predicted multistage nematic transitions are caused by the Aslamazov-Larkin-type fluctuation-exchange processes., Comment: 10 pages, 10 figures

We have investigated the superconducting (SC) gap on hole Fermi surfaces (FSs) of optimally substituted $\mathrm{Ba}(\mathrm{F}{\mathrm{e}}_{0.65}\mathrm{R}{\mathrm{u}}_{0.35}{)}_{2}\mathrm{A}{\mathrm{s}}_{2}$ by angle-resolved photoemission spectroscopy (APRES) using bulk-sensitive 7 eV laser and synchrotron radiation. It was found that, whereas the gap is isotropic in the ${k}_{x}\ensuremath{-}{k}_{y}$ plane, the gap magnitudes of two resolved hole FSs show similar ${k}_{z}$ dependences and decrease as ${k}_{z}$ approaches $\ensuremath{\sim}2\phantom{\rule{0.16em}{0ex}}\ensuremath{\pi}/c$ (i.e., around the $Z$ point), unlike the other Fe-based superconductors reported so far, where the SC gap of only one hole FS shows a strong ${k}_{z}$ dependence. This unique gap structure can be understood in the scenario that the ${d}_{{z}^{2}}$ orbital character is mixed into both hole FSs due to finite spin-orbit coupling (SOC) and is reproduced by calculation within the random phase approximation including the SOC.

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 ($\chi$-VC). In addition, the charge-channel attractive interaction is enlarged by the VC for the coupling-constant ($U$-VC), which is significant when the interaction has prominent $q$-dependences so the Migdal theorem fails. Due to both $\chi$-VC and $U$-VC, the plain $s$-wave state is caused by the small electron-phonon interaction near the magnetic criticality against the repulsive Coulomb interaction. We find that the direct Coulomb repulsion for the plain $s$-wave Cooper pair is strongly reduced by the "multiorbital screening effect"., Comment: 10 pages, 10 figures, We explain that the significance of the AL-processes has been confirmed by the recent functional-renormalization-group analysis, in which the higher-order vertex corrections are generated in a systematic and unbiased manner

We report the discovery of a very large thermoelectric power over -400 microV K-1 in the whisker crystals of a one-dimensional telluride Ta4SiTe4, while maintaining a low electrical resistivity of rho = 2 mohm cm, yielding a very large power factor of P = 80 microW cm-1 K-2 at an optimum temperature of 130 K. This temperature is widely controlled from the cryogenic temperature of 50 K to room temperature by chemical doping, resulting in the largest P of 170 microW cm-1 K-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., Comment: 5 pages, 3 figures

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., Comment: 16 pages, 9 figures

We study polycrystalline samples of the hexagonal pnictides, CaAgP and CaAgAs, both of which are ideal candidates for line-node Dirac semimetals. The polycrystalline samples of CaAgP and CaAgAs obtained in this study are low-carrier metals, where hole carriers are dominant. By combining the hole carrier densities estimated from Hall coefficients and the electronic structures calculated by first principles calculations, both samples are found to have a ring-torus Fermi surface, derived from a ring-shaped Dirac line node. In the phosphide sample, the Fermi energy EF is located at around the end of the linear dispersion region of the electronic bands, while the EF in the arsenide sample exists in the middle of this region, suggesting that the arsenide is a more promising system for uncovering the physics of line-node Dirac semimetals., 6 pages, 5 figures

We report the synthesis, electronic properties, and electronic structure of ullmannite-type PtSbS, which has a cubic crystal structure without space inversion symmetry. Electrical resistivity and magnetization measured at low temperatures suggested that this compound is a bulk superconductor with a superconducting transition temperature of Tc = 0.15 K. First principles calculations indicated that Fermi surfaces of PtSbS include strongly nested hole pockets, which can make this compound interesting if they contribute to the emergence of superconductivity., 5 pages, 5 figures

An electron-doped high-T c pnictide LaFeAsO1−x H x is recently known for having double superconducting (SC) domes in the phase diagram. We have performed nuclear magnetic resonance (NMR) measurements in an H-overdoped regime to investigate the second SC dome on a microscopic level. We unexpectedly discovered that the linewidths of both 75As and 1H spectra broaden at low temperatures for the 58 and 62.5 % H-doped samples, indicating that the antiferromagnetic (AF) ordering returns in the heavily H-doped regime. The finding itself is rare because an excess carrier doping tends to cause Fermi-liquid behavior in strongly correlated electron systems. We demonstrate that the new AF ordering originates from the nesting between electron pockets.

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 ${\mathrm{BaTi}}_{2}{(\mathrm{As},\mathrm{Sb})}_{2}\mathrm{O}$, 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 ${\mathrm{BaTi}}_{2}{(\mathrm{As},\mathrm{Sb})}_{2}\mathrm{O}$. 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.

Nematicity and magnetism are two key features in Fe-based superconductors, and their interplay is one of the most important unsolved problems. In FeSe, the magnetic order is absent below the structural transition temperature $T_{str}=90$K, in stark contrast that the magnetism emerges slightly below $T_{str}$ in other families. To understand such amazing material dependence, we investigate the spin-fluctuation-mediated orbital order ($n_{xz}\neq n_{yz}$) by focusing on the orbital-spin interplay driven by the strong-coupling effect, called the vertex correction. This orbital-spin interplay is very strong in FeSe because of the small ratio between the Hund's and Coulomb interactions ($\bar{J}/\bar{U}$) and large $d_{xz},d_{yz}$-orbitals weight at the Fermi level. For this reason, in the FeSe model, the orbital order is established irrespective that the spin fluctuations are very weak, so the magnetism is absent below $T_{str}$. In contrast, in the LaFeAsO model, the magnetic order appears just below $T_{str}$ both experimentally and theoretically. Thus, the orbital-spin interplay due to the vertex correction is the key ingredient in understanding the rich phase diagram with nematicity and magnetism in Fe-based superconductors in a unified way., Comment: 15 pages, 11 figures, to appear in Phys. Rev. X

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, $U^0$, 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 $(U_{eff}^c/U^0)^2 >> 1$. In contrast, the spin fluctuation pairing interaction is suppressed by the spin-channel $U$-VC, because of the relation $U_{eff}^s << U^0$. 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., 10 pages, 9 figures, to be published in Phys. Rev. B

The discovery of the charge-density-wave formation in the high-${T}_{c}$ 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 ${p}_{x}$ and ${p}_{y}$ 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.

In high-superconducting transition temperature (${T}_{\mathrm{c}}$) iron-based superconductors, interband sign reversal (${s}_{\ifmmode\pm\else\textpm\fi{}}$) and sign preserving (${s}_{++}$) $s$-wave superconducting states have been primarily discussed as the plausible superconducting mechanism. We study Co impurity scattering effects on the superconductivity in order to achieve an important clue on the pairing mechanism using single-crystal ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{Se}$ and depict a phase diagram of a FeSe system. Both superconductivity and structural transition/orbital order are suppressed by the Co replacement on the Fe sites and disappear above $x$ = 0.036. These correlated suppressions represent a common background physics behind these physical phenomena in the multiband Fermi surfaces of FeSe. By comparing experimental data and theories so far proposed, the suppression of ${T}_{\mathrm{c}}$ against the residual resistivity is shown to be much weaker than that predicted in the case of general sign reversal and full gap ${s}_{\ifmmode\pm\else\textpm\fi{}}$ models. The origin of the superconducting paring in FeSe is discussed in terms of its multiband electronic structure.

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 $O = n_{xz} - n_{yz}$, which is driven by the spin fluctuations on xz,yz orbitals through the intra-orbital 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., 11 pages, 10 figures. The pressure Hamiltonian of FeSe introduced in the present study has been confirmed by the first principles analysis

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 inter-pocket attractive force, which is as important as 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., Comment: 12 pages, 10 figures

The main features in iron-based superconductors would be (i) the orthorhombic transition accompanied by remarkable softening of shear modulus, (ii) high- T c superconductivity close to the orthorhombic phase, and (iii) nematic transition in the tetragonal phase. In this paper, we present a unified explanation for them, based on the orbital fluctuation theory, considering both the e -ph and the Coulomb interaction. It is found that a small e -phonon coupling constant ( λ ∼ 0.2 ) is enough to produce large orbital ( = charge quadrupole O x z / y z ) fluctuations, which causes the s -wave superconductivity without sign reversal ( s + + -wave state). The derived orbital fluctuations also cause the instability toward the structure transition due to the bound state formation of two orbitons with opposite momenta, which is called the “two-orbiton process”. Moreover, impurity-induced non-local orbital order with C 2 -symmetry is obtained when the orbital fluctuations are strong. This “impurity-induced nematic state” explains the in-plane anisotropy of resistivity in detwinned samples. We stress that (i)–(iii) are reproducible only when orbital fluctuations with respect to O x z and O y z charge quadrupoles are the most divergent. This fact ensures the reliability of the present model Hamiltonian and calculation.

We investigate the electronic states and the superconductivity in the two-dimensional 16-band d – p model extracted from a tight-binding fit to the band structure of iron pnictides, in the presence of both the Coulomb interaction between Fe d -electrons and the electron–lattice coupling g with the orthorhombic mode which is crucial for reproducing the recently observed ultrasonic softening of the elastic constant C 66 . Due to the cooperative effects of these interactions, the ferro-orbital order with different occupations of d y z and d z x orbitals occurs and induces the tetragonal-orthorhombic structural transition at T s , together with the stripe-type antiferromagnetic (AFM) order below T N . For a large g case, we obtain the phase diagram consistent with the doped iron pnictides with T s > T N for x > 0 , where the s + + -wave superconductivity is mediated by the ferro-orbital fluctuation which is largely enhanced near the ferro-orbital QCP at x c with T s → 0 . On the other hand, for a small g case, the simultaneous phase transition occurs at T s = T N even for x > 0 , where the s ± -wave superconductivity is mediated by the AFM fluctuation. Both the s -wave states with full superconducting gaps are consistent with most of the experiments but only the former is considered to account for the small T c -suppression against nonmagnetic impurities.