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

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.

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.

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.

Electronic and crystal structures ofLnFeAsO1-xHx(Ln= La, Sm) studied by x-ray absorption spectroscopy, x-ray emission spectroscopy, and x-ray diffraction (part I: carrier-doping dependence)

A carrier doping by a hydrogen substitution in LaFeAsO_1-xH_xis known to cause two superconducting (SC) domes with the magnetic order at both end sides of the doping. In contrast, SmFeAsO_1-xH_xhas a similar phase diagram but shows single SC dome. Here, we investigated the electronic and crystal structures for iron oxynitrideLnFeAsO_1-xH_x(Ln= La, Sm) with the range ofx= 0-0.5 by using x-ray absorption spectroscopy, x-ray emission spectroscopy, and x-ray diffraction. For both compounds, we observed that the pre-edge peaks of x-ray absorption spectra near the Fe-Kedge were reduced in intensity on doping. The character arises from the weaker As-Fe hybridization with the longer As-Fe distance in the higher doped region. We can reproduce the spectra near the Fe-Kedge according to the Anderson impurity model with realistic valence structures using the local-density approximation (LDA) plus dynamical mean-field theory (DMFT). ForLn= Sm, the integrated-absolute difference (IAD) analysis from x-ray Fe-Kβemission spectra increases significantly. This is attributed to the enhancement of magnetic moment of Fe 3delectrons stemming from the localized picture in the higher doped region. A theoretical simulation implementing the self-consistent vertex-correction method reveals that the single dome superconducting phase forLn= Sm arises from a better nesting condition in comparison withLn= La.

Momentum dependent [Formula: see text] band splitting in LaFeAsO

The nematic phase in iron based superconductors (IBSs) has attracted attention with a notion that it may provide important clue to the superconductivity. A series of angle-resolved photoemission spectroscopy (ARPES) studies were performed to understand the origin of the nematic phase. However, there is lack of ARPES study on LaFeAsO nematic phase. Here, we report the results of ARPES studies of the nematic phase in LaFeAsO. Degeneracy breaking between the [Formula: see text] and [Formula: see text] hole bands near the [Formula: see text] and M point is observed in the nematic phase. Different temperature dependent band splitting behaviors are observed at the [Formula: see text] and M points. The energy of the band splitting near the M point decreases as the temperature decreases while it has little temperature dependence near the [Formula: see text] point. The nematic nature of the band shift near the M point is confirmed through a detwin experiment using a piezo device. Since a momentum dependent splitting behavior has been observed in other iron based superconductors, our observation confirms that the behavior is a universal one among iron based superconductors.

Raman Response in the Nematic Phase of FeSe

Raman experiments on bulk FeSe revealed that the low-frequency part of the B_{1g} Raman response R_{B1g}(Ω), which probes nematic fluctuations, rapidly decreases below the nematic transition at T_{n}∼85  K. Such behavior is expected when a gap opens up and at a first glance is inconsistent with the fact that FeSe remains a metal below T_{n}. We argue that the drop of R_{B1g}(Ω) can be ascribed to the fact that the nematic order drastically changes the orbital content of low-energy excitations near hole and electron pockets, making them nearly mono-orbital. In this situation, the B_{1g} Raman response gets reduced by the same vertex corrections that enforce charge conservation in the symmetric Raman channel. The reduction holds at low frequencies and gives rise to gaplike behavior of R_{B1g}(Ω). We also show that the enhancement of the B_{1g} Raman response near T_{n} is consistent with the sign change of the nematic order parameter between hole and electron pockets.

Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe

We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the ab plane. At low temperatures, the upper critical field μ_{0}H_{c2}^{ab} shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at μ_{0}H^{*}≈24  T well below μ_{0}H_{c2}^{ab}, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the high-field phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe.

Bulk Superconductivity and Role of Fluctuations in the Iron-Based Superconductor FeSe at High Pressures

The iron-based superconductor FeSe offers a unique possibility to study the interplay of superconductivity with purely nematic as well magnetic-nematic order by pressure (p) tuning. By measuring specific heat under p up to 2.36 GPa, we study the multiple phases in FeSe using a thermodynamic probe. We conclude that superconductivity is bulk across the entire p range and competes with magnetism. In addition, whenever magnetism is present, fluctuations exist over a wide temperature range above both the bulk superconducting and the magnetic transitions. Whereas the magnetic fluctuations are likely temporal, the superconducting fluctuations may be either temporal or spatial. These observations highlight similarities between FeSe and underdoped cuprate superconductors.

Momentum Dependence of the Nematic Order Parameter in Iron-Based Superconductors

The momentum dependence of the nematic order parameter is an important ingredient in the microscopic description of iron-based high-temperature superconductors. While recent reports on FeSe indicate that the nematic order parameter changes sign between electron and hole bands, detailed knowledge is still missing for other compounds. Combining angle-resolved photoemission spectroscopy with uniaxial strain tuning, we measure the nematic band splitting in both FeSe and BaFe_{2}As_{2} without interference from either twinning or magnetic order. We find that the nematic order parameter exhibits the same momentum dependence in both compounds with a sign change between the Brillouin center and the corner. This suggests that the same microscopic mechanism drives the nematic order in spite of the very different phase diagrams.

Anisotropic spin fluctuations in detwinned FeSe

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe, detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (±1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies, 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.6 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations.

Superconductivity in FeSe: The Role of Nematic Order

Bulk FeSe is a special iron-based material in which superconductivity emerges inside a well-developed nematic phase. We present a microscopic model for this nematic superconducting state, which takes into account the mixing between s-wave and d-wave pairing channels and the changes in the orbital spectral weight promoted by the sign-changing nematic order parameter. We show that nematicity only weakly affects T_{c}, but gives rise to cos2θ variation of the pairing gap on the hole pocket, whose magnitude and size agrees with angle resolved photoemission spectroscopy and STM data. We further show that nematicity increases the weight of the d_{xz} orbital on the hole pocket, and increases (reduces) the weight of the d_{xy} orbital on the Y (X) electron pocket.

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.

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, T _c, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.