Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals.

In kagome metals, the chiral current order parameter [Formula: see text] with time-reversal-symmetry-breaking 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 [Formula: see text] are still unsolved. Here, we reveal that tiny uniform orbital magnetization [Formula: see text] 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 ([Formula: see text])-induced Ginzburg-Landau (GL) free energy expression [Formula: see text], which enables us to elucidate the field-induced current-bond phase transitions in kagome metals. The emergent current-bond-[Formula: see text] trilinear coupling term in the free energy, [Formula: see text], 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 [Formula: see text] 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.

Correlation-driven electronic nematicity in the Dirac semimetal BaNiS2.

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-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.

SU(4) Valley+Spin Fluctuation Interference Mechanism for Nematic Order in Magic-Angle Twisted Bilayer Graphene: The Impact of Vertex Corrections.

In the magic-angle twisted bilayer graphene (MATBG), one of the most remarkable observations is the C_{3}-symmetry-breaking nematic state. We identify that the nematicity in MATBG is the E-symmetry ferro bond order, which is the modulation of correlated hopping integrals owing to the E-symmetry particle-hole pairing condensation. The nematicity in MATBG originates from prominent quantum interference among SU(4) valley+spin composite fluctuations. This novel "valley+spin fluctuation interference mechanism" is revealed by the density wave equation analysis for the realistic multiorbital Hubbard model for MATBG. We find that the nematic state is robust once three van Hove singularity points exist in each valley. This interference mechanism also causes novel time-reversal-symmetry-broken valley polarization accompanied by a charge loop current. We discuss interesting similarities and differences between MATBG and Fe-based superconductors.

Abrupt change of the superconducting gap structure at the nematic critical point in FeSe1-xSx.

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.

Sign-Reversing Orbital Polarization in the Nematic Phase of FeSe due to the C_{2} Symmetry Breaking in the Self-Energy.

To understand the nematicity in Fe-based superconductors, nontrivial k dependence of the orbital polarization [ΔE_{xz}(k), ΔE_{yz}(k)] in the nematic phase, such as the sign reversal of the orbital splitting between Γ 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 k_{y} and k_{x} 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.

Spin-Fluctuation-Driven Nematic Charge-Density Wave in Cuprate Superconductors: Impact of Aslamazov-Larkin Vertex Corrections.

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=(Δ(FS),0), (0,Δ(FS)) appears when the spin fluctuations are strong, due to the strong charge-spin interference represented by the VC. Here, Δ(FS) 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.

Linear response theory for shear modulus C66 and Raman quadrupole susceptibility: evidence for nematic orbital fluctuations in Fe-based superconductors.

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 C(66) and the Raman quadrupole susceptibility χ(x)(2)-y(2))(Raman). Because of the Aslamazov-Larkin vertex correction, the nematic-type orbital fluctuations are induced, and they enhance both 1/C(66) and χ(x(2)-y(2))(Raman) strongly. However, χ(x)(2)-y(2))(Raman) remains finite even at the structure transition temperature T(S), 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.

High-Tc superconductivity near the anion height instability in Fe-based superconductors: analysis of LaFeAsO(1-x)H(x).

The isostructural transition in the tetragonal phase with a sizable change in the anion height, is realized in heavily H-doped LaFeAsO 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 LaFeAsO(1-x)H(x) 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.

Orbital nematic instability in the two-orbital Hubbard model: renormalization-group + constrained RPA analysis.

Motivated by the nematic electronic fluid phase in Sr(3)Ru(2)O(7), we develop a combined scheme of the renormalization-group method and the random-phase-approximation-type method, and analyze orbital susceptibilities of the (d(xz), d(yz))-orbital Hubbard model with high accuracy. It is confirmed that the present model exhibits a ferro-orbital instability near the magnetic or superconducting quantum criticality, due to the Aslamazov-Larkin-type vertex corrections. This mechanism of orbital nematic order presents a natural explanation for the nematic order in Sr(3)Ru(2)O(7), and is expected to be realized in various multiorbital systems, such as Fe-based superconductors.

Charge-loop current order and Z3 nematicity mediated by bond order fluctuations in kagome metals.

Recent experiments on geometrically frustrated kagome metal AV3Sb5 (A = K, Rb, Cs) have revealed the emergence of the charge loop current (cLC) order near the bond order (BO) phase. However, the origin of the cLC and its interplay with other phases have been uncovered. Here, we propose a novel mechanism of the cLC state, by focusing on the BO phase common in kagome metals. The BO fluctuations in kagome metals, which emerges due to the Coulomb interaction and the electron-phonon coupling, mediate the odd-parity particle-hole condensation that gives rise to the topological current order. Furthermore, the predicted cLC+BO phase gives rise to the Z3-nematic state in addition to the giant anomalous Hall effect. The present theory predicts the close relationship between the cLC, the BO, and the nematicity, which is significant to understand the cascade of quantum electron states in kagome metals. The present scenario provides a natural understanding.

Self-consistent vertex correction analysis for iron-based superconductors: mechanism of Coulomb interaction-driven orbital fluctuations.

We study the mechanism of orbital or 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 (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 antiferro-orbital and ferro-orbital (=nematic) fluctuations simultaneously develop for J/U~0.1, both of which contribute to the s-wave superconductivity. Especially, the ferro-orbital fluctuations give the orthorhombic structure transition as well as the softening of shear modulus C(66).

Mechanism of exotic density-wave and beyond-Migdal unconventional superconductivity in kagome metal AV3Sb5 (A = K, Rb, Cs).

Exotic quantum phase transitions in metals, such as the electronic nematic state, have been discovered one after another and found to be universal now. The emergence of unconventional density-wave (DW) order in frustrated kagome metal AV3Sb5 and its interplay with exotic superconductivity attract increasing attention. We find that the DW in kagome metal is the bond order, because the sizable intersite attraction is caused by the quantum interference among paramagnons. This mechanism is important in kagome metals because the geometrical frustration prohibits the freezing of paramagnons. In addition, we uncover that moderate bond-order fluctuations mediate sizable pairing glue, and this mechanism gives rise to both singlet s-wave and triplet p-wave superconductivity. Furthermore, characteristic pressure-induced phase transitions in CsV3Cb5 are naturally understood by the present theory. Thus, both the exotic density wave and the superconductivity in geometrically frustrated kagome metals are explained by the quantum interference mechanism.

Orbital-fluctuation-mediated superconductivity in iron pnictides: analysis of the five-orbital Hubbard-Holstein model.

In iron pnictides, we find that the moderate electron-phonon interaction due to the Fe-ion oscillation can induce the critical d-orbital fluctuations, without being prohibited by the Coulomb interaction. These fluctuations give rise to the strong pairing interaction for the s-wave superconducting (SC) state without sign reversal (s(++)-wave state), which is consistent with experimentally observed robustness of superconductivity against impurities. When the magnetic fluctuations due to Coulomb interaction are also strong, the SC state shows a smooth crossover from the s-wave state with sign reversal (s(+/-)-wave state) to the s(++)-wave state as impurity concentration increases.

Violation of Anderson's theorem for the sign-reversing s-wave state of iron-pnictide superconductors.

Based on the five-orbital model, we study the effect of local impurity in iron pnictides, and find that the interband impurity scattering is promoted by the d-orbital degree of freedom. This fact means that the fully gapped sign-reversing s-wave state, which is predicted by spin fluctuation theories, is very fragile against impurities. In the BCS theory, only 1% impurities with intermediate strength induce huge pair breaking, resulting in the large in-gap state and prominent reduction in Tc, contrary to the prediction based on simple orbital-less models. The present study provides a stringent constraint on the pairing symmetry and the electronic states in iron pnictides.

Unconventional pairing originating from the disconnected Fermi surfaces of superconducting LaFeAsO1-xFx.

For a newly discovered iron-based high T_{c} superconductor LaFeAsO1-xFx, we have constructed a minimal model, where inclusion of all five Fe d bands is found to be necessary. The random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin-fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended s-wave pairing, while d-wave pairing can also be another candidate.

Nernst coefficient and magnetoresistance in high-T(c) superconductors: the role of superconducting fluctuations.

In high-T(c) cuprates, the Nernst coefficient (nu) as well as the magnetoresistance (Deltarho/rho) increases drastically below the pseudogap temperature, T(*), which attracts much attention as a key phenomenon in the pseudogap region. We study these transport phenomena in terms of the fluctuation-exchange+T-matrix approximation. In this present theory, the d-wave superconducting (SC) fluctuations, which are mediated by antiferromagnetic (AF) correlations, become dominant below T(*). We especially investigate the vertex corrections both for the charge current and the heat one to keep the conservation laws. As a result, the mysterious behaviors of nu and Deltarho/rho are naturally explained as the reflection of the enhancement of the SC fluctuation, without assuming thermally excited vortices. The present result suggests that the pseudogap phenomena are well described in terms of the Fermi liquid with AF and SC fluctuations.