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Strange metals arise in a variety of platforms for strongly correlated electrons, ranging from the cuprates, heavy fermions to flat band systems. Motivated by recent experiments in kagome metals, we study a Hubbard model on a kagome lattice whose noninteracting limit contains flat bands. A Kondo lattice description is constructed, in which the degrees of freedom are exponentially localized molecular orbitals. We identify an orbital-selective Mott transition through an extended dynamical mean field theory of the effective model. The transition describes a quantum critical point at which quasiparticles are expected to be lost and strange metallicity emerges. Our theoretical work opens up a new route for realizing beyond-Landau quantum criticality and emergent quantum phases that it nucleates., 30 pages, 8 figures

Strong correlations lead to emergent excitations at low energies. When combined with symmetry constraints, they may produce topological electronic states near the Fermi energy. Within this general framework, here we address the topological features in iron-based superconductors. We examine the effects of orbital-selective correlations on the band inversion in the iron chalcogenide FeSe$_{x}$Te$_{1-x}$ near its doping of optimal superconductivity, within a multiorbital model and using a $U(1)$ slave spin theory. The orbital selectivity of the quasiparticle spectral weight, along with its counterpart of the energy level renormalization, leads to a band inversion and Dirac node formation pinned to the immediate vicinity of the Fermi energy. Our work demonstrates both the naturalness and robustness of the topological properties in FeSe$_{x}$Te$_{1-x}$, and uncovers a new setting in which strong correlations and space-group symmetry cooperate in generating strongly correlated electronic topology., 7+3 pages, 5+4 figures

Emergent phases often appear when the electronic kinetic energy is comparable to the Coulomb interactions. One approach to seek material systems as hosts of such emergent phases is to realize localization of electronic wavefunctions due to the geometric frustration inherent in the crystal structure, resulting in flat electronic bands. Recently, such efforts have found a wide range of exotic phases in the two-dimensional kagome lattice, including magnetic order, time-reversal symmetry breaking charge order, nematicity, and superconductivity. However, the interlayer coupling of the kagome layers disrupts the destructive interference needed to completely quench the kinetic energy. Here we experimentally demonstrate that an interwoven kagome network--a pyrochlore lattice--can host a three dimensional (3D) localization of electron wavefunctions. In particular, through a combination of angle-resolved photoemission spectroscopy, fundamental lattice model and density functional theory (DFT) calculations, we present the novel electronic structure of a pyrochlore superconductor, CeRu$_2$. We find striking flat bands with bandwidths smaller than 0.03 eV in all directions--an order of magnitude smaller than that of kagome systems. We further find 3D gapless Dirac cones predicted originally by theory in the diamond lattice space group with nonsymmorphic symmetry. Our work establishes the pyrochlore structure as a promising lattice platform to realize and tune novel emergent phases intertwining topology and many-body interactions., 12 pages, 3 figures

We use resonant inelastic X-ray scattering (RIXS) at the Fe-L$_3$ edge to study the spin excitations of uniaxial-strained and unstrained FeSe$_{1-x}$S$_{x}$ ($0\leq x\leq0.21$) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range $0< x\leq0.21$ of FeSe$_{1-x}$S$_{x}$. The spin-excitation anisotropy persists to a high temperature up to $T>200$ K in $x=0.18$ and reaches a maximum around the nematic quantum critical doping ($x_c\approx0.17$). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and open the door for uniaxial strain tuning of spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity., 6 pages, 4 figures, supplemental materials uploaded

The heavy-fermion metal CeCu$_2$Si$_2$ was the first discovered unconventional, non-phonon-mediated superconductor, and for a long time was believed to exhibit single-band $d$-wave superconductivity, as inferred from various measurements hinting at a nodal gap structure. More recently however, measurements using a range of techniques at very low temperatures ($T \lessapprox 0.1$ K) provided evidence for a fully-gapped superconducting order parameter. In this Colloquium, after a brief historical overview we survey the apparently conflicting results of numerous experimental studies on this compound. We then address the different theoretical scenarios which have been applied to understand the particular gap structure, including both isotropic (sign-preserving) and anisotropic two-band $s$-wave superconductivity, as well as an effective two-band $d$-wave model, where the latter can explain the currently available experimental data on CeCu$_2$Si$_2$. The lessons from CeCu$_2$Si$_2$ are expected to help uncover the Cooper-pair states in other unconventional, fully-gapped superconductors with strongly correlated carriers, and in particular highlight the rich variety of such states enabled by orbital degrees of freedom., Comment: 33 pages, 15 figures, 2 tables; to be published as a Colloquium in Reviews of Modern Physics

The advent of iron-based superconductors in 2008 came as a complete surprise to the condensed matter community. Now 15 years later, they are beginning to impart some of their new-found wisdom on a slew of emerging superconductors that boast similar traits., Comment: Article invited by Physics Today and intended for general readers. 18 pages, 4+2 figures. Version submitted, with the number of references limited by editorial mandate. The published version has been edited

Strange metals develop near quantum critical points (QCPs) in a variety of strongly correlated systems. Some of the important issues include how the quantum critical state loses quasiparticles, how it drives superconductivity, and to what extent the strange-metal physics in different classes of correlated systems are connected with each other. In this article, we confront some of these issues from the vantage point of heavy fermion metals. We will describe the notion of Kondo destruction and how it leads to a transformation of the Fermi surface from ``large" to ``small" across the QCP, a loss of quasiparticles everywhere on the Fermi surface at the QCP, and a dynamical Planckian scaling in various properties including charge responses. We close with a brief discussion about the connections between the strange-metal physics in heavy fermion metals and its counterparts in the cuprates and other correlated materials., 33 pages, 11 figures

An overarching question in strongly correlated electron systems is how the landscape of quantum phases emerges from electron correlations. The method of extended dynamical mean field theory (EDMFT) has been developed for clean lattice models of the correlated electrons. For such models, not only onsite Hubbard-like interactions are important, but so are intersite interactions. Importantly, the EDMFT method treats the interplay between the onsite and intersite interactions dynamically. It was initially formulated for models of the two-band Anderson-lattice type with intersite interactions, as well as for the one-band Hubbard type with intersite Heisenberg-like terms that are often called Hubbard-Heisenberg models. In the case of Kondo lattice models, the EDMFT method incorporates a dynamical competition between the local Kondo and intersite Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. In these models, the EDMFT-based analyses led to the notion of Kondo destruction, which has played a central role in the understanding of quantum critical heavy fermion metals. In this article, we summarize the EDMFT method, and survey its applications, particularly for Kondo/Anderson lattice models. We also discuss the prospect for further developing the EDMFT method, as well as for applying it to address the correlation physics in a variety of new settings. Among the latter are the orbital-selective Mott physics that arises both in iron-based superconductors and in frustrated bulk systems with topological flat bands., 26 pages, 7 figures

Multiorbital models are important to both the correlation physics and topological behavior of quantum materials. LiFeAs is a prototype iron pnictide suitable for indepth investigation of this issue. Its electronic structure is strikingly different from the prediction of the noninteracting description. Here, a multiorbital Hubbard model for this compound is studied using a $U(1)$ slave spin theory. We demonstrate a new mechanism for a large change in the size of the Fermi surface, namely, orbital selectivity of the energy-level renormalization cooperating with its counterpart in the quasiparticle spectral weight. Using this effect, we show how the dominating features of the electronic structure in LiFeAs are understood in terms of the local correlations alone. Our results reveal a remarkable degree of universality out of the seemingly complex multiorbital building blocks across a broad range of strongly correlated superconductors., 6+4 pages, 4+2 figures

The heavy-fermion system $\mathrm{UTe_2}$ is a candidate for spin-triplet superconductivity, which is of considerable interest to quantum engineering. Among the outstanding issues is the nature of the pairing state. A recent surprising discovery is the observation of a resonance in the spin excitation spectrum at an antiferromagnetic wavevector [C. Duan {\it et al.}, Nature \textbf{600}, 636 (2021)], which stands in apparent contrast to the ferromagnetic nature of the interactions expected in this system. We show how the puzzle can be resolved by a multiorbital spin-triplet pairing constructed from local degrees of freedom. Because it does not commute with the kinetic part of the Hamiltonian, the pairing contains both intra- and inter-band terms in the band basis. We demonstrate that the intraband pairing component naturally yields a spin resonance at the antiferromagnetic wavevector. Our work illustrates how orbital degrees of freedom can enrich the nature and properties of spin-triplet superconductivity of strongly-correlated quantum materials., Comment: 12 pages, 7 figures

Recent experiments in quantum critical heavy fermion metals have pushed to the fore the question about whether antiferromagnetic fluctuations can promote both spin-singlet and spin-triplet superconductivity. Here we address the issue through non-perturbative calculations in antiferromagnetically correlated Kondo systems. We identify Kondo-destruction quantum critical points in both the SU(2) symmetric and Ising-anisotropic cluster Bose-Fermi Anderson models. The spin-singlet pairing correlations are significantly enhanced near the quantum critical point in the SU(2) case; however, with adequate but still realistic degree of Ising anisotropy, the spin-triplet pairing correlations are competitive. Our results demonstrate that spin-flip processes strengthen the spin-singlet pairing at the Kondo-destruction quantum critical points, and point towards a way for antiferromagnetic correlations to drive spin-triplet pairing. Further implications of our findings in the broader context of strongly correlated superconductivity are discussed., Comment: 9 pages, 5 figures

True to their unconventional nature, multi-band alkaline Fe-selenides and, more recently, the heavy-fermion CeCu$_{2}$Si$_{2}$ have shown signatures of fully-gapped but sign-changing superconductivity (SC). A two-orbital pairing state, called $s\tau_{3}$, with non-trivial matrix structure, was proposed as a candidate able to reconcile the seemingly contradictory properties of these SC's. Motivated by the non-trivial orbital structure of the proposed $s\tau_{3}$ state, which has orbital-selective pairing structure, we study prototypical Josephson junctions where at least one of the leads is in a SC state of this kind. An analysis of these junctions in the limit of two degenerate orbitals (bands) and with a simple form of junction hybridization reveals several remarkable properties. One is the emergence of gapless, purely electron- and hole-like bound states for $s\tau_{3}-N-s\tau_{3}$ junctions with arbitrary global phase difference between the leads, and likewise for $s\tau_{3}-N-I$ junctions. The other is the absence of static Josephson currents when both leads are SC's. In both of these signatures, $s\tau_{3}$ junctions are dramatically different from conventional Josephson junctions. We also find that the gapless bound states are protected by an orbital-exchange symmetry, although the protection is not topological. Junctions which break this symmetry, such as $s\tau_{3}-N-s$, have gapped Andreev bound states. In general, the Josephson effect also re-emerges once the degeneracy of the two orbitals is lifted. We support these conclusions via analytical and numerical results for the bound states, together with microscopic calculations of the Josephson current. Our results indicate that junctions involving $s\tau_{3}$ pairing in alkaline Fe-selenides's will generically have bound states with a small gap together with a greatly suppressed Josephson current., Comment: 22 pages, 11 figures

Electronic correlation is of fundamental importance to high temperature superconductivity. Iron-based superconductors are believed to possess moderate correlation strength, which combined with their multi-orbital nature makes them a fascinating platform for the emergence of exotic phenomena. A particularly striking form is the emergence of an orbital selective Mott phase, where the localization of a subset of orbitals leads to a drastically reconstructed Fermi surface. Here, we report spectroscopic evidence of the reorganization of the Fermi surface from FeSe to FeTe as Se is substituted by Te. We uncover a particularly transparent way to visualize the localization of the $d_{xy}$ electron orbital through the suppression of its hybridization with the more coherent $d$ electron orbitals, which leads to a redistribution of the orbital-dependent spectral weight near the Fermi level. These noteworthy features of the Fermi surface are accompanied by a divergent behavior of a band renormalization in the $d_{xy}$ orbital. All of our observations are further supported by our theoretical calculations to be salient spectroscopic signatures of such a non-thermal evolution from a strongly correlated metallic phase towards an orbital-selective Mott phase in FeTe$_{1-x}$Se$_x$ as Se concentration is reduced., Comment: 11 pages, 5 figures

Quantum criticality in iron pnictides involves both the nematic and antiferromagnetic degrees of freedom, but the relationship between the two types of fluctuations has yet to be clarified. Here we study this problem in the presence of a small external uniaxial potential, which breaks the $C_4$-symmetry in the B$_{1g}$ sector. We establish an identity that connects the spin excitation anisotropy, which is the difference of the dynamical spin susceptibilities at $\vec{Q}_1=\left(\pi,0\right)$ and $\vec{Q}_2=\left(0,\pi\right)$, with the dynamical magnetic susceptibility and static nematic susceptibility. Using this identity, we introduce a scaling procedure to determine the dynamical nematic susceptibility in the quantum critical regime, and illustrate the procedure for the case of the optimally Ni-doped BaFe$_2$As$_2$[Y. Song \textit{et al.}, Phys. Rev. B 92, 180504 (2015)]. The implications of our results for the overall physics of the iron-based superconductors are discussed., Comment: 8 pages, 5 figures

Motivated by growing indications for a distinct form of nematic correlations in the extremely hole doped iron pnictide compounds $A$Fe$_2$As$_2$ ($A$=K,Rb,Cs), we consider spin-driven nematic order in the general case of incommensurate magnetic fluctuations. We classify the nematic order parameters by broken mirror symmetries of the tetragonal $D_{4h}$ point group, and use this scheme to construct a general Ginzburg-Landau theory that links the nematic order to spatial pattern of magnetic fluctuations. Our analysis points to incommensurate magnetic fluctuations of wavevector $(q,q)$ as underlying a $B_{2g}$ nematic order in $A$Fe$_2$As$_2$. We substantiate this idea by microscopic calculations of the nematic order based on 3-sublattice $(2\pi/3,2\pi/3)$ spin correlations in an extended bilinear-biquadratic Heisenberg model. We summarize the existing evidence in support of the proposed mechanism, suggest ways to further test it in future experiments, and discuss the implications of our results for iron-based high temperature superconductivity., Comment: 5+6 pages, 5+3 figures, published version

The extent to which quantum criticality drives the physics of iron pnictides is a central question in the field. Earlier theoretical considerations were based on an effective field theory, and the proposed realization in P-doped iron arsenides has received extensive experimental evidence. To connect the quantum critical behavior with the underlying electronic physics, it is important to analyze it within microscopic models. Here, we do so for a multi-orbital model containing both Hubbard and Hund's interactions, by a variational Monte Carlo method based on Jastrow-Slater wave functions that allow for a non-perturbative treatment of electron correlations. We find strong evidence for the existence of a unique quantum critical point, where both nematic and $(\pi,0)$ antiferromagnetic orders develop together, in the bad-metal regime of the phase diagram. Implications of our results for the iron-based superconductivity are discussed., Comment: 7 pages, 7 figures

We used transport and inelastic neutron scattering to study the optimally phosphorus-doped BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$ superconductor ($T_c = 30$ K). In the normal state, we find that the previously reported linear temperature dependence of the resistivity below room temperature extends to $\sim$ 500 K. Our analysis of the temperature and energy ($E=\hbar��$) dependence of spin dynamical susceptibility at the antiferromagnetic (AF) ordering wave vector $��^{\prime\prime}({\bf Q}_{\rm AF},��)$ reveal an $��/ T$ scaling within $1.1, 4 figures

Electron correlations produce a rich phase diagram in the iron pnictides. Earlier theoretical studies on the correlation effect demonstrated how quantum fluctuations weaken and concurrently suppress a $C_2$-symmetric single-Q antiferromagnetic order and a nematic order. Here we examine the emergent phases near the quantum phase transition. For a $C_4$-symmetric collinear double-Q antiferromagnetic order, we show that it is accompanied by both a charge order and an enhanced nematic susceptibility. Our results provide understanding for several intriguing recent experiments in hole-doped iron arsenides, and bring out common physics that underlies the different magnetic phases of various iron-based superconductors., 5+6 pages, 2 figures; (v2) issues with cross-referencing between the main text and supplementary material are fixed

We report temperature-dependent pair distribution function measurements of Sr$_{1-x}$Na$_{x}$Fe$_2$As$_2$, an iron-based superconductor system that contains a magnetic phase with reentrant tetragonal symmetry, known as the magnetic $C_4$ phase. Quantitative refinements indicate that the instantaneous local structure in the $C_4$ phase is comprised of fluctuating orthorhombic regions with a length scale of $\sim$2 nm, despite the tetragonal symmetry of the average static structure. Additionally, local orthorhombic fluctuations exist on a similar length scale at temperatures well into the paramagnetic tetragonal phase. These results highlight the exceptionally large nematic susceptibility of iron-based superconductors and have significant implications for the magnetic $C_4$ phase and the neighboring $C_2$ and superconducting phases.

Iron chalcogenides display a rich variety of electronic orders in their phase diagram. A particularly enigmatic case is FeTe, a metal which possesses co-existing hole and electron Fermi surfaces as in the iron pnictides but has a distinct ($\pi$/2,$\pi/2$) bicollinear antiferromagnetic order in the Fe square lattice. While local-moment physics has been recognized as essential for understanding the electronic order, it has been a long-standing challenge to understand how the bicollinear antiferromagnetic ground state emerges in a proper quantum spin model. We show here that a bilinear-biquadratic spin-$1$ model on a square lattice with nonzero ring-exchange interactions exhibits the bicollinear antiferromagnetic order over an extended parameter space in its phase diagram. Our work shows that frustrated magnetism in the quantum spin model provides a unified description of the electronic orders in the iron chalcogenides and iron pnictides., Comment: 4.5 pages + supplemental material. 7 figures in total

We use inelastic neutron scattering to study the temperature and energy dependence of the spin excitation anisotropy in uniaxial-strained electron-doped iron pnictide BaFe$_{1.9}$Ni$_{0.1}$As$_2$ near optimal superconductivity ($T_c=20$ K). Our work has been motivated by the observation of in-plane resistivity anisotropy in the paramagnetic tetragonal phase of electron-underdoped iron pnictides under uniaxial pressure, which has been attributed to a spin-driven Ising-nematic state or orbital ordering. Here we show that the spin excitation anisotropy, a signature of the spin-driven Ising-nematic phase, exists for energies below $\sim$60 meV in uniaxial-strained BaFe$_{1.9}$Ni$_{0.1}$As$_2$. Since this energy scale is considerably larger than the energy splitting of the $d_{xz}$ and $d_{yz}$ bands of uniaxial-strained Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ near optimal superconductivity, spin Ising-nematic correlations is likely the driving force for the resistivity anisotropy and associated electronic nematic correlations.

Superconductors close to quantum phase transitions often exhibit a simultaneous increase of electronic correlations and superconducting transition temperatures. Typical examples are given by the recently discovered iron-based superconductors. We investigated the band-specific quasiparticle masses of AFe2As2 single crystals with A = K, Rb, and Cs and determined their pressure dependence. The evolution of electronic correlations could be tracked as a function of volume and hole doping. The results indicate that with increasing alkali-metal ion radius a quantum critical point is approached. The critical fluctuations responsible for the enhancement of the quasiparticle masses appear to suppress the superconductivity., main text: 5 pages, 4 figures; supplemental material: 6 pages, 6 figures, 3 tables

We use inelastic neutron scattering (INS) to study the spin excitations in partially detwinned NaFe$_{0.985}$Co$_{0.015}$As which has coexisting static antiferromagnetic (AF) order and superconductivity ($T_c=15$ K, $T_N=30$ K). In previous INS work on a twinned sample, spin excitations form a dispersive sharp resonance near $E_{r1}=3.25$ meV and a broad dispersionless mode at $E_{r1}=6$ meV at the AF ordering wave vector ${\bf Q}_{\rm AF}={\bf Q}_1=(1,0)$ and its twinned domain ${\bf Q}_2=(0,1)$. For partially detwinned NaFe$_{0.985}$Co$_{0.015}$As with the static AF order mostly occurring at ${\bf Q}_{\rm AF}=(1,0)$, we still find a double resonance at both wave vectors with similar intensity. Since ${\bf Q}_1=(1,0)$ characterizes the explicit breaking of the spin rotational symmetry associated with the AF order, these results indicate that the double resonance cannot be due to the static and fluctuating AF orders, but originate from the superconducting gap anisotropy., 5 pages, 5 figures; PRB, 2015 (the correct final version is now used)

We use transport and neutron scattering to study electronic, structural, and magnetic properties of the electron-doped BaFe$_{2-x}$Ni$_x$As$_2$ iron pnictides in the external stress free detwinned state. Using a specially designed in-situ mechanical detwinning device, we demonstrate that the in-plane resistivity anisotropy observed in the uniaxial strained tetragonal state of BaFe$_{2-x}$Ni$_x$As$_2$ below a temperature $T^\ast$, previously identified as a signature of the electronic nematic phase, is also present in the stress free tetragonal phase below $T^{\ast\ast}$ ($, Comment: 5 pages, 4 figures

A major puzzle about the nature of the iron-based superconductivity appears in the case of the alkaline iron selenides. Compared to the iron pnictides, these systems have only electron Fermi pockets (i.e. no hole Fermi pockets) but comparable superconducting transition temperatures. The challenge lies in reconciling the two basic experimental features of their superconducting state: a node-less gap and the existence of a resonance in the spin excitation spectrum. We propose a mechanism based on reconstructing two quasi-degenerate pairing states, one in an $s$-wave $A_{1g}$ channel that is fully gapped, and the other in a $d$-wave $B_{1g}$ channel whose pairing function changes sign across the electron Fermi pockets at the Brillouin-zone boundary. The resulting intermediate pairing state, which we call an orbital-selective $s \times \tau_3$ state, incorporates both of the above two properties. When the leading spin-singlet pairing is in the $d_{xz}, d_{yz}$ orbital subspace, this state retains the $s$-wave form factor but has a $B_{1g}$ symmetry due to an internal $\tau_3$ structure in the orbital space. Within a five-orbital $t-J_{1}-J_{2}$ model with orbital-selective exchange couplings, we show that the proposed pairing state is energetically competitive over a finite range of control parameters. We calculate the dynamical spin susceptibility in the orbital-selective $s \times \tau_3$ superconducting state and show that a spin resonance arises and has the characteristics of observed by inelastic neutron experiments in the alkaline iron selenides. More generally, the formation of the orbital-selective $s \times \tau_3$ state represents a novel means of relieving the quasi-degeneracy between $s-$ and $d-$wave pairing states, which is a hitherto unsuspected alternative to the conventional route of linearly superposing the two into a time-reversal symmetry breaking $s+id$ state.

Motivated by the studies of the superconducting pairing states in the iron-based superconductors, we analyze the effects of Brillouin zone folding procedure from a space group symmetry perspective for a general class of materials with the $P4/nmm$ space group. The Brillouin zone folding amounts to working with an effective one-Fe unit cell, instead of the crystallographic two-Fe unit cell. We show that the folding procedure can be justified by the validity of a glide reflection symmetry throughout the crystallographic Brillouin zone and by the existence of a minimal double degeneracy along the edges of the latter. We also demonstrate how the folding procedure fails when a local spin-orbit coupling is included although the latter does not break any of the space group symmetries of the bare Hamiltonian. In light of these general symmetry considerations, we further discuss the implications of the glide reflection symmetry for the superconducting pairing in an effective multi-orbital $t-J_{1}-J_{2}$ model. We find that the $P4/nmm$ space group symmetry allows only pairing states with even parity under the glide reflection and zero total momentum.

Understanding the microscopic origins of electronic phases in high-transition temperature (high-Tc) superconductors is important for elucidating the mechanism of superconductivity. In the paramagnetic tetragonal phase of BaFe2-xTxAs2 (where T is Co or Ni) iron pnictides, an in-plane resistivity anisotropy has been observed. Here we use inelastic neutron scattering to show that low-energy spin excitations in these materials change from four-fold symmetric to two-fold symmetric at temperatures corresponding to the onset of the in-plane resistivity anisotropy. Because resistivity and spin excitation anisotropies both vanish near optimal superconductivity, we conclude that they are likely intimately connected.

We use inelastic neutron scattering to show that superconductivity in electron-underdoped NaFe0.985Co0.015As induces a dispersive sharp resonance near Er1 = 3:25 meV and a broad dis- persionless mode at Er2 = 6 meV. However, similar measurements on overdoped superconducting NaFe0:955Co0:045As find only a single sharp resonance at Er = 7 meV. We connect these results with the observations of angle-resolved photoemission spectroscopy that the superconducting gaps in the electron Fermi pockets are anisotropic in the underdoped material but become isotropic in the overdoped case. Our analysis indicates that both the double neutron spin resonances and gap anisotropy originate from the orbital dependence of the superconducting pairing in the iron pnic- tides. Our discovery also shows the importance of the inelastic neutron scattering in detecting the multiorbital superconducting gap structures of iron pnictides.

Strongly correlated electron systems at the border of magnetism are of active current interest, particularly because the accompanying quantum criticality provides a route towards both strange-metal non-Fermi liquid behavior and unconventional superconductivity. Among the many important questions is whether the magnetism acts simply as a source of fluctuations in the textbook Landau framework, or instead serves as a proxy for some unexpected new physics. We put into this general context the recent developments on quantum phase transitions in antiferromagnetic heavy fermion metals. Among these are the extensive recent theoretical and experimental studies on the physics of Kondo destruction in a class of beyond-Landau quantum critical points. Also discussed are the theoretical basis for a global phase diagram of antiferromagnetic heavy fermion metals, and the recent surge of materials suitable for studying this phase diagram. Furthermore, we address the generalization of this global phase diagram to the case of Kondo insulators, and consider the future prospect to study the interplay among Kondo coherence, magnetism and topological states. Finally, we touch upon related issues beyond the antiferromagnetic settings, arising in mixed valent, ferromagnetic, quadrupolar, or spin glass f-electron systems, as well as some general issues on emergent phases near quantum critical points., 14 pages, 7 figures. Review article as part of the contributions to QCNP12. Covering quantum criticality and novel phases in the most-extensively studied case of antiferromagnetic heavy fermion metals, while extending the discussion to the less explored settings such as Kondo insulating, mixed valent, and ferromagnetic systems

We study the orbital-dependent superconducting pairing in a five-orbital t-J1-J2 model for iron pnictides. Depending on the orbital selectivity of electron correlations and the orbital characters along the Fermi surface, the superconducting gap in an A_{1g} pairing state may exhibit anisotropy. This anisotropy varies with the degree of J1-J2 magnetic frustration. We have also calculated the dynamical spin susceptibility in the superconducting state. The frequency dependence of the susceptibility at the antiferromagnetic wavevector (\pi,0) shows a resonance, whose width is enhanced by the orbital dependence of the superconducting gap; when the latter is sufficiently strong, the resonance peak may be split into two. We discuss the implications of our results on the recent angle-resolved photoemission and neutron-scattering measurements in several superconducting iron pnictides., Comment: 4.5 pages, 3 figures, with supplementary materials

In this work, we study the A$_{x}$Fe$_{2-y}$Se$_2$ (A=K, Rb) superconductors using angle-resolved photoemission spectroscopy. In the low temperature state, we observe an orbital-dependent renormalization for the bands near the Fermi level in which the dxy bands are heavily renormliazed compared to the dxz/dyz bands. Upon increasing temperature to above 150K, the system evolves into a state in which the dxy bands have diminished spectral weight while the dxz/dyz bands remain metallic. Combined with theoretical calculations, our observations can be consistently understood as a temperature induced crossover from a metallic state at low temperature to an orbital-selective Mott phase (OSMP) at high temperatures. Furthermore, the fact that the superconducting state of A$_{x}$Fe$_{2-y}$Se$_2$ is near the boundary of such an OSMP constraints the system to have sufficiently strong on-site Coulomb interactions and Hund's coupling, and hence highlight the non-trivial role of electron correlation in this family of iron superconductors.

A U(1) slave-spin representation is introduced for multi-orbital Hubbard models. As with the $Z_2$ form of L. de'Medici et al. (Phys. Rev. B 72, 205124 (2005)), this approach represents a physical electron operator as the product of a slave spin and an auxiliary fermion operator. For non-degenerate multi-orbital models, our U(1) approach is advantageous in that it captures the non-interacting limit at the mean-field level. For systems with either a single orbital or degenerate multiple orbitals, the U(1) and $Z_2$ slave-spin approachs yield the same results in the slave-spin-condensed phase. In general, the U(1) slave-spin approach contains a U(1) gauge redundancy, and properly describes a Mott insulating phase. We apply the U(1) slave-spin approach to study the metal-to-insulator transition in a five-orbital model for parent iron pnictides. We demonstrate a Mott transition as a function of the interactions in this model. The nature of the Mott insulating state is influenced by the interplay between the Hund's rule coupling and crystal field splittings. In the metallic phase, when the Hund's rule coupling is beyond a threshold, there is a crossover from a weakly correlated metal to a strongly correlated one, through which the quasiparticle speactral weight rapidly drops. The existence of such a strongly correlated metallic phase supports the incipient Mott picture of the parent iron pnictides. In the parameter regime for this phase and in the vicinity of the Mott transition, we find that an orbital selective Mott state has nearly as competitive a ground state energy., 7 pages, 2 figures

We study a multiorbital model for the alkaline iron selenides K(1-x)Fe(2-y)Se2 using a slave-spin method. With or without ordered vacancies, we identify a metal-to-Mott-insulator transition at the commensurate filling of six 3d electrons per iron ion. For Hund's couplings beyond a threshold value, this occurs via an intermediate orbital-selective Mott phase, in which the 3d xy orbital is Mott localized while the other 3d orbitals remain itinerant. This phase is still stabilized over a range of carrier dopings. Our results lead to an overall phase diagram for the alkaline iron selenides, which provides a unified framework to understand the interplay between the strength of vacancy order and carrier doping. In this phase diagram, the orbital-selective Mott phase provides a natural link between the superconducting K(1-x)Fe(2-y)Se2 and its Mott-insulating parent compound., Comment: 6 pages, 5 figures, including supplementary information

We study the finite-temperature spin dynamics of the paramagnetic phase of iron pnictides within an antiferromagnetic J_1-J_2 Heisenberg model on a square lattice with a biquadratic coupling $-K (S_i \cdot S_j)^2$ between the nearest-neighbor spins. Our focus is on the paramagnetic phase in the parameter regime of this J_1-J_2-K model where the ground state is a (\pi,0) collinear antiferromagnet. We treat the biquadratic interaction via a Hubbard-Stratonovich decomposition, and study the resulting effective quadratic-coupling model using both modified spin wave and Schwinger boson mean-field theories; the results for the spin dynamics derived from the two methods are very similar. We show that the spectral weight of dynamical structure factor S(q,\omega) is peaked at ellipses in the momentum space at low excitation energies. With increasing energy, the elliptic features expand towards the zone boundary, and gradually split into two parts, forming a pattern around (\pi,\pi). Finally, the spectral weight is anisotropic, being larger along the major axis of the ellipse than along its minor axis. These characteristics of the dynamical structure factor are consistent with the recent measurements of the inelastic neutron scattering spectra on BaFe_2As_2 and SrFe_2As_2., Comment: 13 pages, 11 figures, to be published in Phys. Rev. B

Motivated by the experimentally observed $\sqrt{5} \times \sqrt{5}$ iron vacancy order and a block spin antiferromagnetic phase with large magnetic moment in $\mathrm{K}_{0.8}\mathrm{Fe}_{1.6}\mathrm{Se}_2$, we study the magnetic phase diagram of an extended $J_1-J_2$ model on a 1/5-depleted square lattice with $\sqrt{5} \times \sqrt{5}$ vacancy order, using a classical Monte Carlo analysis. The magnetic phase diagram involves various antiferromagnetically ordered phases, and most of them have higher order commensuration. We find that the experimentally relevant block-spin state occupies a significant portion of the phase diagram, and we discuss the spin dynamics of this phase using a linear spin-wave analysis. Based on our spin wave calculations in different parameter regimes corresponding to the block spin antiferromagnetic phase, we show how spin-wave degeneracy along the high symmetry directions of the magnetic Brillouin zone can provide information regarding the underlying exchange couplings. We have also analyzed the magnetic phase diagram of a $J_1-J_2$ model on two different modulated square lattices relevant for $\mathrm{K}_y\mathrm{Fe}_{1.5}\mathrm{Se}_2$, which respectively exhibit 1/4-depleted $2\times2$ and $4\times2$ vacancy ordering., 9 pages, 8 figures, 3 tables

The degree of electron correlations remains a central issue in the iron-based superconductors. The parent iron pnictides are antiferromagnetic, and their bad-metal behavior has been interpreted in terms of proximity to a Mott transition. We study such a transition in multi-orbital models on modulated lattices containing an ordered pattern of iron vacancies, using a slave-rotor method. We show that the ordered vacancies lead to a band-narrowing, which pushes the system to the Mott insulator side. This effect is proposed to underlie the insulating behavior observed in the parent compounds of the newly discovered (K,Tl)yFexSe2 superconductors., 4 pages, 4 figures, revised version. To appear in PRL

We have studied the effect of a single nonmagnetic impurity in the recently discovered (K,Tl)Fe$_x$Se$_2$ superconductors, within both a toy two-band model and a more realistic five-band model. We have found that, out of five types of pairing symmetry under consideration, only the $d_{x^2-y^2}$-wave pairing gives rise to impurity resonance states. The intra-gap states have energies far away from the Fermi energy. The existence of these intra-gap states is robust against the presence or absence of inter-band scattering. However, the inter-band scattering does tune the relative distribution of local density of states at the resonance states. All these features can readily be accessed by STM experiments, and are proposed as a means to test pairing symmetry of the new superconductors., Comment: 4+ pages, 4 eps figures, revised version. To appear in Physical Review Letters

An optical analysis reveals that the electronic correlations in the `parent' compounds of the iron pnictide superconductors are sufficiently strong to significantly impede the mobility of the electrons., Comment: A News and Views piece; 5 pages, 1 figure

Bad metal properties have motivated a description of the parent iron pnictides as correlated metals on the verge of Mott localization. What has been unclear is whether interactions can push these and related compounds to the Mott insulating side of the phase diagram. Here we consider the iron oxychalcogenides La2O2Fe2O(Se,S)2, which contain an Fe square lattice with an expanded unit cell. We show theoretically that they contain enhanced correlation effects through band narrowing compared to LaOFeAs, and we provide experimental evidence that they are Mott insulators with moderate charge gaps. We also discuss the magnetic properties in terms of a Heisenberg model with frustrating J1-J2-J2' exchange interactions on a "doubled" checkerboard lattice., Comment: 4 pages, 5 eps figures. Version to appear in Phys. Rev. Lett

Some of the high Tc iron pnictides contain magnetic rare-earth elements, raising the question of how the existence and tunability of a d-electron antiferromagnetic order influences the heavy fermion behavior of the f-moments. With CeOFeP and CeOFeAs in mind as prototypes, we derive an extended Anderson lattice model appropriate for these quaternary systems. We show that the Kondo screening of the f-moments are efficiently suppressed by the d-electron ordering. We also argue that, inside the d-electron ordered state (as in CeOFeAs), the f-moments provide a rare realization of a quantum frustrated magnet with competing J1-J2-J3 interactions in an effective square lattice. Implications for the heavy fermion physics in broader contexts are also discussed., Comment: 4+ pages, 3 figures, final version

We use inelastic neutron scattering to explore the evolution of the low energy spin dynamics in the electron-doped cuprate Pr0.88LaCe0.12CuO4-d (PLCCO) as the system is tuned from its nonsuperconducting, as-grown antiferromagnetic (AF) state into an optimally-doped superconductor (Tc~24 K) without static AF order. The low temperature, low energy response of the spin excitations in under-doped samples is coupled to the presence of the AF phase, whereas the low-energy magnetic response for samples near optimal Tc exhibits spin fluctuations surprisingly insensitive to the sample temperature. This evolution of the low energy excitations is consistent with the influence of a quantum critical point in the phase diagram of PLCCO associated with the suppression of the static AF order. We carried out scaling analysis of the data and discuss the influence of quantum critical dynamics in the observed excitation spectrum., Comment: 11 Pages, 10 Figures. Minor changes to the text. Accepted by Phys. Rev. B and to appear in October 1st issue

Interest in the heavy fermion metals has motivated us to examine the quantum phases and their Fermi surfaces within the Kondo lattice model. We demonstrate that the model is soluble asymptotically exactly in any dimension d>1, when the Kondo coupling is small compared with the RKKY interaction and in the presence of antiferromagnetic ordering. We show that the Kondo coupling is exactly marginal in the renormalization group sense, establishing the stability of an ordered phase with a small Fermi surface, AFs. Our results have implications for the global phase diagram of the heavy fermion metals, suggesting a Lifshitz transition inside the antiferromagnetic region and providing a new perspective for a Kondo-destroying antiferromagnetic quantum critical point., 4 pages, 4 figures; (v2) corrected typos and added reference/acknowledgment; (v3) version as published in Physical Review Letters (July, 2007)

A high-energy spin resonance mode is known to exist in many high-temperature superconductors. Motivated by recent scanning tunneling microscopy (STM) experiments in superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we study the effects of this resonance mode on the local density of states (LDOS). The coupling between the electrons in a d-wave superconductor and the resonance mode produces high-energy peaks in the LDOS, which displays a two-unit-cell periodic modulation around a nonmagnetic impurity. This suggests a new means to not only detect the dynamical spin collective mode but also study its coupling to electronic excitations., Comment: 5 pages, 4 figures; typos removed; to appear in Physical Review Letters

We study the effect of spin injection into $s-$ and $d-$wave superconductors, with an emphasis on the interplay between boundary and bulk spin transport properties. The quantities of interest include the amount of non-equilibrium magnetization ($m$), as well as the induced spin-dependent current ($I_s$) and boundary voltage ($V_s$). In general, the Andreev reflection makes each of the three quantities depend on a different combination of the boundary and bulk contributions. The situation simplifies either for half-metallic ferromagnets or in the strong barrier limit, where both $V_s$ and $m$ depend solely on the bulk spin transport/relaxation properties. The implications of our results for the on-going spin injection experiments in high $T_c$ cuprates are discussed., 4 pages, REVTEX, 1 figure included; typos corrected

We study the evolution of the neutron cross-section with variable frequency $\omega$ and fixed $T$ below $T_c$ in two different cuprate families. Our calculations, which predominantly probe the role of d-wave pairing, lead to generic features, independent of Fermi surface shapes. Among our findings, reasonably consistent with experiment, are (i) for $\omega $ near the gap energy $\Delta$, both optimal {LaSrCuO} and slightly underdoped YBCO exhibit (comparably) incommensurate peaks (ii) peak sharpening below $T_c$ is seen in {LaSrCuO}, (iii) quite generically, a frequency evolution from incommensurate to commensurate and then back to incommensurate structure is found with increasing $\omega$. Due to their narrow $\omega$ regime of stability, commensurate peaks in {LaSrCuO} should be extremely difficult to observe., Comment: RevTex 5pages, 4figures; Manuscript rewritten, figures revised, and direct comparisons with experiments added