Strong Correlations and the Normal State of the High Temperature Superconductors

We employ a five-orbital tight-binding model to develop the mean field solution for various possible spin density wave states in the iron-chalcogenides. The quasiparticle interference (QPI) technique is applied to detect signatures of these states due to scatterings arising from non-magnetic impurities. Apart from the experimentally observed double striped structure with ordering vector (pi/2,pi/2), the QPI method is investigated for the extended-stripe as well as the orthogonal double stripe phase. We discuss QPI as a possible tool to detect and classify various magnetic structures within the frame work of the Fe$_{1+y}$Te compound.

The thermomagnetic hysteresis (TH), i.e. the difference between zero field cooling (ZFC) and field cooling (FC) curves at different constant applied magnetic fields, is an important experimental method to check for the existence of pinning (or magnetic anisotropy) of different kinds of magnetic entities, like, e.g., flux lines in superconductors as well as magnetic domains in ferromagnets. Remarkable similarities in the thermomagnetic behavior of the magnetization $(M)$ of high-temperature superconducting (HTSC) La$_{2-}$Sr${_x}$CuO$_4$ below and above the bulk superconducting critical temperature $T_c$ were reported ten years ago [1]. These similarities suggest that some kind of pinned entities should exist above $T_c$ up to a temperature near the opening of the pseudo-gap phase. Whether these entities are magnetically ordered domains or stripes or superconducting vortices remain still unclear. On the other hand the thermomagnetic hysteresis is specially useful to search for the existence of superconductivity in materials where only a very small fraction of it exists, like in granular superconductors. In this work we studied the thermomagnetic hysteresis in a large field and temperature range of different Y123 powders (without and with O-vacancies) and of graphite powder samples, virgin and after n-heptane treatment [2]. A main result of our work is that the thermomagnetic hysteresis of Y123 powders with O-vacancies resembles that of n-heptane treated graphite powder in a large magnetic field and temperature region. [1] C. Panagopoulos, M. Majoros, and A. P. Petrovic, Phys. Rev. B 69, 144508 (2004). M. Majoros, C. Panagopoulos, T. Nishizaki, and H. Iwasaki, Phys. Rev. B 72, 024528 (2005). [2]Y. Kawashima, AIP Advances 3, 052132 (2013).

The magnitude and role of correlations if $\mathrm{Fe}$-based superconductors is a subject of ongoing debate. The problem has been approached either from the weak-coupling side (in the spirit of $\mathrm{Cr}$ alloys) or strong-coupling perspective (in accord with the scenario of orbital-selective Mottness). New insights have been gained since pronounced longitudinal spin excitations (LSEs) were observed [1] in parent pnictides $\mathrm{BaFe_2As_2}$ and $\mathrm{NaFeAs}$. In itinerant antiferromagnets the latter normally arise due to particle-hole (P-H) excitations between magnetically split bands, hence the data have been deemed the first direct evidence for the contribution of itinerant electrons to magnetism in these materials. I point out [2] that the above interpretation is difficult to reconcile with existing optical conductivity measurements and ARPES combined with theoretical calculations (DFT+DMFT, RPA approach to multi-orbital models) which suggest that the P-H excitations should be seen at energies notably larger than the LSEs detected experimentally. On the other hand, the LSEs in the correct energy range might arise due to multi-magnon processes which (contrary to the P-H excitations) are consistent with quasi-local-moment magnetism. Within an effective non-linear $\sigma$-model with a dissipative term, I show that the reported order of magnitude of the LSEs can be reproduced by the multi-magnon excitations if the quantum spin fluctuations are strong enough to account for the small measured ordered moments. As an element of the analysis I discuss the multi-magnon contribution to the LSEs in a microscopic two-band model of excitonic antiferromagnetism and demonstrate that itinerant electrons do not support sizable low-energy longitudinal magnetic response. \vspace{1em} [1] C. Wang \textit{et al.}, Phys. Rev. X \textbf{3}, 041036 (2013). [2] M. Fidrysiak, Eur. Phys. J. B \textbf{89}, 41 (2016).

Recent ARPES studies on ferropnictides reveal non Fermi liquid scattering rates and Lifshitz transitions near optimal doping which lead together with correlation effects to a large mass enhancement. The scattering rates do not show a huge enhancement near optimal doping as expected in a quantum critical scenario. Rather they are enhanced near a 3d5 configuration. This indicates that they are determined by local interactions and in particular by the Hunds exchange interactions. Furthermore, from the ARPES experiments we have evidence for hot and cold spots on the Fermi surface, depending on the orbital character of the bands. The cold spots determine the transport properties in th normal state. Probably the superconducting properties and the thermal properties in the normal state are determined by the hot spots. Similar results were obtained recently for the ferrochalchogenides.

Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature Tdc, the maximum of the condensation energy as a function of doping, the correlation between maximum Tdc and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state. Ref: http://www.nature.com/articles/srep22715

We investigate the strong influence of the $\Theta_{II}$-loop-current order on both unidirectional and bidirectional $d$-wave charge-density-wave/pair-density-wave (CDW/PDW) composite orders along axial momenta $(\pm Q_0,0)$ and $(0,\pm Q_0)$ that emerge in an effective hot spot model departing from the three-band Emery model relevant to the phenomenology of the cuprate superconductors. This study is motivated by the compelling evidence that the $\Theta_{II}$-loop-current order described by this model may explain groundbreaking experiments such as spin-polarized neutron scattering performed in these materials. Here, we demonstrate, within a saddle-point approximation, that the $\Theta_{II}$-loop-current order clearly coexists with bidirectional (i.e. checkerboard) $d$-wave CDW and PDW orders along axial momenta, but is visibly detrimental to the unidirectional (i.e. stripe) case. This result has potentially far-reaching implications for the physics of the cuprates and agrees well with very recent x-ray experiments on YBCO that indicate that at higher dopings the CDW order has indeed a tendency to be bidirectional.

We study the onset of spin-density wave order in itinerant electron systems via a two-dimensional lattice model amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of the model reveals a dome-shaped $d$-wave superconducting phase near the magnetic quantum phase transition. Above the critical superconducting temperature, we observe an extended fluctuation regime, which manifests itself in the opening of a gap in the electronic density of states and an enhanced diamagnetic response. While charge density wave fluctuations are moderately enhanced in the proximity of the magnetic quantum phase transition, they remain short-ranged. The striking similarity of our results to the phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.

In many unconventional superconductors a quantum critical point (QCP) of the competing charge or spin density wave (CDW/SDW) phase lies beneath the superconducting dome. In the normal state a QCP leads to non-Fermi liquid behavior and divergent quasiparticle mass due to low energy quantum fluctuations. However, whether there is a strong quasiparticle mass enhancement due to quantum fluctuations below the superconducting transition temperature is under a hot debate since there is no an evident probe to measure the effective mass in a superconducting state. BaFe$_2$(As$_{1-x}$P$_x$)$_2$ is a good system to study interplay between a QCP of SDW phase and superconductivity. Here, we investigate the effect of the SDW phase on the superconducting upper critical fields (H$_{c2}$) of high quality single crystalline BaFe$_2$(As$_{1-x}$P$_x$)$_2$ thin films. We used the H$_{c2}$ as a probe of the quasiparticle mass enhancement at $T_c$. Using high magnetic fields we probe the low temperature properties of the system close to the QCP. We have found that H$_{c2}$ has a different doping dependence on the paramagnetic and magnetic side of the phase diagram without peak-like features at the QCP. We argue that the observed behavior of the H$_{c2}$ in underdoped BaFe$_2$(As$_{1-x}$P$_x$)$_2$ is triggered by the reconstruction of the Fermi surface due to the formation of the SDW phase without noticeable mass renormalization at $T_c$ related to quantum fluctuations.

Among the iron-based superconductors FeSe with $T_c$~9K is a special case since it undergoes a structural tetragonal to orthorhombic transition at $T_s$~87K, but does not order magnetically at any temperature. This material attracted a lot of attention due to the strong increase of $T_c$ up to 37K under high pressure [1] and existence of the high-Tc intercalates [2]. The most intriguing results came from a monolayer of FeSe grown on $SrTiO_3$ where it has been reported increase of superconducting transition temperature up to 100K [3]. In our work using high resolution ARPES we have explored the evolution of the electronic structure of the of FeSe single crystals through $T_s$. We demonstrate that while the hole pocket at $\Gamma$-point undergoes a significant symmetry breaking distortion below $T_s$, the electron pockets distortions at M-points do not involve significant fourfold symmetry breaking or any resolvable lifting of $d_{xz}-d_{yz}$ band degeneracy. These new results demonstrate that the nature of the "nematic" state of FeSe cannot be explained by ferro-orbital ordering but might be described by a stripe antiferro-orbital order. REFERENCES 1. S. Medvedev, T. M. McQueen, I. A. Troyan, T. Palasyuk, M. I. Eremets, R. J. Cava, S. Naghavi, F. Casper, V. Ksenofontov, G. Wortmann, and C. Felser, Nat. Mater. 8, 630 (2009). 2. M. Burrard-Lucas, D. G. Free, S. J. Sedlmaier, J. D. Wright, S. J. Cassidy, Y. Hara, A. J. Corkett, T. Lancaster, P. J. Baker, S. J. Blundell, and S. J. Clarke, Nat. Mater. 12, 15 (2013). 3. J.-F. Ge, Z.-L. Liu, C. Liu, C.-L. Gao, D. Qian, Q.-K. Xue, Y. Liu, and J.-F. Jia, Nat. Mater. 14, 285, (2015).

Complex electronic order in pnictide superconductors studied by nuclear probe spectroscopy The interplay of itinerant magnetism and unconventional superconductivity in Fe based superconductors and other intermetallic systems with complex Fermi surfaces is a fascinating topic in contemporary correlated electron physics. In my talk I will discuss Mössbauer spectroscopy and muon spin relaxation experiments on hole doped 122 pnictides like Ba$_{1-x}$K$_x$Fe$_2$As$_2$ [1]. I will present data on Ca$_{1-x}$Na$_x$Fe$_2$As$_2$ (x = 0.35, 0.50 and 0.67)[2]. The parent compound CaFe$_2$As$_2$ shows a spin density wave order below T$_N$ = 165 K. With increasing Na-substitution level, the magnetic order parameter as well as the magneto-structural phase transition is suppressed. For x = 0.50 we find a microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature Tc. A systematic comparison with other 122 pnictides reveals a linear correlation between the magnetic order parameter reduction and the ratio of the transition temperatures, T$_C$/T$_N$, which can be understood in the framework of a Landau-theory. I will also discuss multigap superconductivity with broken time reversal symmetry in locally non-centrosymmetric SrPtAs. µSR experiments prove the development of a small static spontaneous internal field just below TC, evidencing the time reversal symmetry (TRS) breaking SrPtAs [3]. 75As-NMR and -NQR investigations clearly reveal a two step behaviour in the spin-lattice relaxation rate evidencing multigap superconductivity with very weak inter-band coupling and constraints for the possible pairing symmetries. Unconventional chiral d-wave or f -wave order parameters are consistent with our data [4]. [1] E. Wiesenmayer et al., Phys. Rev. Lett. 107, 237001 (2011). [2] Ph. Materne. et al., Phys. Rev. B 92, 134511 (2015). [3] P.K. Biswas et al., Phys. Rev. B 87, 180503 (2013). [4] F. Brückner et al., Phys. Rev. B 90, 220503 (2014).

FeSe is the simplest representative of iron-based superconducting family and can be considered as a model system to study mechanism of superconductivity in this class of materials. We report out-of-plane resistivity measurements for high quality superconducting FeSe single crystals in magnetic fields up to 9 Tesla. This superconductor proved to be slightly anisotropic in terms of upper critical field H_{c2} measured by in-plane resistivity [1]. Our goal was to study temperature and angular behavior of upper critical field in the H \parallel ab geometry by performing of out-of-plane resistivity measurements. For careful studies of c-axis resistivity we used direct R_c measurement technique that does not demand any additional mathematical models [2]. Temperature dependence of H_{c2} \parallel c is in consistency with literature [1]. Derivative dH_{c2}/dT is – 5.74 T/K and estimation of H_{c2}(0) (WHH theory [3]) gives 35.9 T. We studied superconducting transitions R(B) in different in-plane field orientations (the measuring current was always perpendicular to magnetic field). H_{c2} obtained from magnetoresistance data exhibits an anisotropic behavior. References: [1] S.I. Vedeneev et.al. PRB 75, 064512 (2007). [2] S.I. Vedeneev, et.al. PRB 87, 134512 (2013). [3] N.R. Werthamer, E. Helfand, and P.C. Hohenberg, Phys. Rev. 147, 295 (1966). Authors: D.A. Knyazev^{1,2}, T.A. Romanova^1, A.V. Sadakov^1, D.A. Chareev^3 Affiliations: 1) 119991, Moscow, Leninsky prospect, 53 (Lebedev Physical Institute of Russian Academy of Sciences) 2) 253-421, Wroclaw, Gajowicka str., 95 (International Laboratory of High Magnetic Fields and Low Temperatures, Poland) 3) 142432, Moscow District, Chernogolovka, (Institute of Experimental Mineralogy, Russian Academy of Sciences)

The discovery of a new class of materials 3D topological insulators (TIs) and topological superconductors (TSs) has generated a lot of excitement in condensed matter physics. Bi2Se3 has attracted particular attention due to the intercalating copper between fivefold layers that induces superconducting transition below \sim 4 K in such system. Surface electron modes of a TI form a single Dirac cone - the linear dispersion that describes massless particles. Due to circulating of electron arount Dirac point, the electron wave function acquires a Berry phase. The Berry phase can be experimentally estimated from Landau-level fan diagram of the Shubnikov–de Haas (SdH) oscillations of longitudinal resistivity: \Delta \rho_{xx} \sim \cos[2\pi(F/B_N - 1/2 + \beta)], where F is the frequency of oscillations, B_N are positions of extremums and \beta is Berry phase. Careful study of the Berry phase can verify the Dirac nature of quasiparticles in TIs. Question about the Berry phase value in TIs is still opened, and its robust experimental value is unknown. Our experiments aim at determining of the Berry phase value in TIs using magnetotransport measurements of high-quality single crystals of Bi_{2-x}Cu_xSe_3 in high magnetic fields up to 20 T and at temperatures down to 0.3 K. The 2D nature of the SdH oscillations in our samples was confirmed by sample rotation in magnetic field. From analysis of our data we assume that 2D SdH oscillations originate from several parallel 2D conducting channels in a Bi_{2-x}Cu_xSe_3 single crystal. Our experiments show the presence of "3D quantum Hall effect" in such a system when the effective thickness of the 2D conducting layer is commensurable with fivefold layer in Bi_{2-x}Cu_xSe_3 crystal structure. The intercalation of Cu between between fivefold layers in Bi_{2-x}Cu_xSe_3 single crystals gives rise to superconductivity in this 3D TI that is well described by the extended Tinkham model for conventional thin-film superconductor. Authors: D.A. Knyazev^{1,2}, T.A. Romanova^1, A.V. Sadakov^1 Affiliations: 1) 119991, Moscow, Leninsky prospect, 53 (Lebedev Physical Institute of Russian Academy of Sciences) 2) 253-421, Wroclaw, Gajowicka str., 95 (International Laboratory of High Magnetic Fields and Low Temperatures, Poland)

We propose an effective spin-fermion (SF) model that takes into account strong electron correlations. These correlations bring us naturally to the SF model at infinitely strong coupling with a simultaneously renormalized hopping amplitude. This theory is difficult to implement analytically, since there is still no machinery available with the proper technical tools. However, it is just this effective model that is appropriate to address the cuprates at very low doping, rather than its weak-coupling SF version. The latter leaves out the effects produced by the no double occupancy constraint -- the essence of the physics of strongly correlated electrons.

We connect between the problem of thermodynamics of localized magnetic moments in a Dirac semimetal, the interaction with relativistic electrons leading to the effective ferromagnetic exchange between the moments, and the existing theories dealing with long--range exchange interaction. We point out that the results of high--temperature expansion for the free energy of a dilute ensemble of magnetic impurities in the semimetal performed by V. Cheianov et al. (Phys. Rev. B 86, 054424 (2012)) give an indication to the existence of a new disordered fixed point in such model.

The pseudogap is a partial gap in the electronic density of states that opens in the normal (non-superconducting) state of cuprate superconductors and whose origin is a long-standing puzzle. Its connection to the Mott insulator phase at low doping remains ambiguous and its relation to the charge order that reconstructs the Fermi surface at intermediate doping is still unclear. We have used measurements of the Hall coefficient in magnetic fields up to 88 tesla to show that Fermi-surface reconstruction by charge order in the cuprate YBCO ends sharply at a critical doping p = 0.16 that is distinctly lower than the pseudogap critical point p* = 0.19. This shows that the pseudogap and charge order are separate phenomena. We find that the change in carrier density from "1 + p" in the conventional metal at high doping to "p" at low doping starts at the pseudogap critical point. This shows that the pseudogap and the antiferromagnetic Mott insulator are linked.

Starting with a minimal model with the on-site Hilbert space reduced to only three effective valence centers [CuO$_4$]$^{7-,6-,5-}$ (nominally Cu$^{1+;2+;3+}$) we present an unified approach to the description of the variety of the local intra-unit-cell (IUC) order parameters determining a low-energy physics in cuprates. To describe the diagonal and off-diagonal, or quantum local charge order we develop an S=1 pseudospin model with a non-Heisenberg effective Hamiltonian that provides a physically clear description of different phases from a bare parent antiferromagnetic insulating phase to a Fermi liquid in overdoped cuprates. We show that the superconductivity and spin magnetism are nonsymbiotic phenomena with competing order parameters. Furthermore we argue that instead of a well-isolated Zhang-Rice (ZR) singlet the ground state of the hole Cu$^{3+}$ center in cuprates should be described by a complex multiplet, formed by a competition of conventional hybrid Cu 3d-O 2p $b_{1g}(\sigma )$ state and purely oxygen nonbonding O 2p$\pi$ states with $a_{2g}(\pi)$ and $e_{ux,y}(\pi)$ symmetry. In contrast with inactive ZR singlet we arrive at several novel competing IUC orbital and spin-orbital order parameters, e.g., electric dipole and quadrupole moments, Ising-like net orbital magnetic moment, orbital toroidal moment, intra-plaquette's staggered order of Ising-like oxygen orbital magnetic moments. As a most impressive validation of the non-ZR model we explain fascinating results of recent neutron scattering measurements that revealed novel type of the IUC magnetic ordering in pseudogap phase of several hole-doped cuprates. The research was supported by the Government of the Russian Federation, Program 02.A03.21.0006 and by the Ministry of Education and Science of the Russian Federation, projects Nos. 1437 and 2725.

We made use of a special algorithm for CUDA architecture for NVIDIA graphics cards, a nonlinear conjugate-gradient method to minimize energy functional, and Monte-Carlo technique to directly observe the forming of the ground state configuration for the 2D hard-core bosons with lowering the temperature and its evolution with deviation away from half filling. The technique allowed us to examine earlier implications and uncover novel features of the phase transitions, in particular, look upon the nucleation of the odd domain structure, emergence of filamentary superfluidity nucleated at the antiphase domain walls of the charge ordered phase, and nucleation and evolution of different topological structures. The research was supported by the Government of the Russian Federation, Program 02.A03.21.0006 and by the Ministry of Education and Science of the Russian Federation, projects Nos. 1437 and 2725.

The underdoped cuprate superconductor $YBa_{2}Cu_{3}O_{(7-y)}$ (YBCO) is known to exhibit an electronic nematic phase in proximity to antiferromagnetism (see e.g. Refs.[1, 2]). While nematicity sets in at large temperatures of T = 150 K, static spin density wave order only emerges at much lower temperatures of T = 2K. The magnetic response shows a strong in-plane anisotropy: it displays incommensurate Bragg peaks along one of the two crystal directions and a commensurate peak along the other one. Both anistropy and incommensurability remain even in the absence of long-range magnetic order at higher temperatures. Interestingly, the onset of incommensurate spin fluctuations coincides with the nematic transition. We theoretically approach this scenario using a strong-coupling method in the spirit of the tJ-model, and show that it can naturally account for the emergence of nematicity (and incommensurability), even in close proximity to a Neel ordered antiferromagnet. References 1. V. Hinkov et al., Science 319, 597 (2008). 2. D. Haug et al., New J. Phys. 12, 105006 (2010).

Iron Selenide (FeSe) is the simplest member of the Iron-based superconductors, with a varying Tc between 8 K and 109 K. In order to understand this unconventional mechanism of superconductivity, we must first understand the high temperature electronic structure. At 90 K there is a spontaneous electronic ordering that breaks the rotational symmetry of the lattice whilst preserving its translational symmetry, that has been dubbed “the nematic phase”. This phase is thought to be directly linked with the mechanism of high-temperature superconductivity. Using the latest experimental ARPES data, a 10-orbital tight binding model has been optimised to quantitatively agree with the fermi surface and band structure both above and below the nematic phase transition of FeSe.

The structurally simplest Fe-based superconductor FeSe with a critical temperature $T_{c}\approx$ 8.5~K displays a breaking of the four-fold rotational symmetry at a temperature $T_{s}\approx 87~$K. We investigated the electronic properties of FeSe using scanning tunneling microscopy/spectroscopy (STM/S), magnetization, and electrical transport measurements. The results indicated two new energy scales (i) $T^{*} \approx$ 75~K denoted by an onset of electron-hole asymmetry in STS, enhanced spin fluctuations, and increased positive magnetoresistance; (ii) $T^{**} \approx$ 22 - 30~K, marked by opening up of a partial gap of about 8 meV in STS and a recovery of Kohler's rule. Our results reveal onset of an incipient ordering mode at $T^{*}$ and its nucleation below $T^{**}$. The ordering mode observed here, both in spin as well as charge channels, suggests a coupling between the spins with charge/orbital/pocket degrees of freedom.

The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic metal is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to 24 × 24 sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP.

Starting with a pedagogical introduction to the Bloch-Boltzmann theory and its failure we will introduce the memory function formalism. After giving the general introduction we will consider our recent specific work. We have considered non-equilibrium relaxation of electrons due to their coupling with phonons. In our model electrons are living at a higher temperature than that of the phonon bath, mimicking a non-equilibrium steady state situation. We study the relaxation of such hot electrons by proposing a suitable generalization of the memory function formalism formulated by Goetze and Woelfle. We derive analytical expressions for both dc and optical scattering rates in various temperature and frequency regimes. Limiting cases are in accord with the previous studies.

We study particle-hole instabilities in the framework of the spin-fermion (SF) model. In contrast to previous studies, we assume that adjacent hot spots can overlap due to a shallow dispersion of the electron spectrum in the antinodal region. In addition, we take into account effects of a remnant low energy and momentum Coulomb interaction. We demonstrate that at sufficiently small values $|\varepsilon(\pi,0)-E_F|\lesssim\Gamma$, where $E_F$ is the Fermi energy, $\varepsilon(\pi,0)$ is the energy in the middle of the Brillouin zone edge, and $\Gamma$ is a characteristic energy of the fermion-fermion interaction due to the antiferromagnetic fluctuations, the leading particle-hole instability is a d-form factor Fermi surface deformation (the Pomeranchuk instability) rather than the charge modulation along the Brillouin zone diagonals predicted within the standard SF model previously. At lower temperatures, we find that the deformed Fermi surface is further unstable to formation of a d-form factor charge density wave (CDW) with a wave vector along the Cu-O-Cu bonds (axes of the Brillouin zone). We show that the remnant Coulomb interaction enhances the d-form-factor symmetry of the CDW. These findings can explain the robustness of this order in the cuprates. The approximations made in the paper are justified by a small parameter that allows one to implement an Eliashberg-like treatment. Comparison with experiments suggests that in many cuprate compounds the prerequisites for the proposed scenario are indeed fulfilled and the results obtained may explain important features of the charge modulations observed recently.

Recent applications of Quantum Monte Carlo (QMC) technique to Fe-based superconductorsopened a way to directly verify the applicability of the itinerant scenario for these systems. Fe-based superconductors undergo various instabilities upon lowering temperature (magnetism, superconductivity, nematicity/orbital order), and one can check whether the hierarchy of instabilities obtained within the itinerant approach is the same as in unbiased QMC simulations. In a recent paper[arXiv:1512:08523] the authors considered the simplest two-band model with interaction tailored to favor orbital order. The type of the orbital order found in QMC is different from the one found in earlier itinerant analysis. We used itinerant approach and argued that it is applicable because critical coupling for orbital and superconducting instabilities is parameterically smaller than the bandwidth. We found that the leading instability in the orbital channel is towards antiferro-orbital order and the one in the pairing channel is towards s++ superconductivity. Our calculations show that they are in perfect agreement with QMC. We view the agreement with unbiased QMC as the indication that orbital and superconducting orders in FeSCs can be properly accounted for within the itinerant scenario.

We report NMR results in iron-pnictide superconductors BaFe$_{2-x}$Ni$_x$As$_2$ (Ref.1), NaFe$_{1-x}$Co$_x$As (Ref.2) and LaFeAsO$_{1-x}$F$_x$ (Ref.3-4), and address the issues including spin and orbital nematicity, quantum critical phenomena, and coexistence of superconductivity and magnetism. NaFeAs is a system where strucual transition temperature $T_s$ = 54 K is well separated from Neel temperature $T_N$ = 42 K. We report NMR measurements on NaFe$_{1-x}$Co$_x$As that revealed orbital and spin nematicity occurring at a temperature $T^\ast$ far above $T_s$ in the tetragonal phase. We show that the NMR spectra splitting and its evolution can be explained by an incommensurate orbital order that sets in below $T^\ast$ and becomes commensurate below $T_s$, which brings about the observed spin nematicity. In LaFeAsO$_{1-x}$F$_x$ synthesized at high presure, we find a new dome with $T_c$ peaked at $x_{opt}$=0.55 where the electrical resistivity shows a $T$-linear behavior but without magnetic fluctuations. By NMR and transmission electron microscopy, we show that a C4 rotation symmetry-breaking structural transition takes place for large $x$ which terminates at $x_{opt}$. Our results point to a new paradigm of high temperature superconductivity. Ref: 1. R. Zhou et al, Nature Commun. 4, 2265 (2013) 2. R. Zhou et al, Phys. Rev. B 93, 060502(R) (2016). 3. T. Oka et al, Phys. Rev. Lett. 108, 047001 (2012) 4. J. Yang et al, Chin. Phys. Lett. 32, 107401 (2015).

We report on the observation of an asymmetric broadening of the $^(17)$O NMR lines in the field-induced charge-ordered state of YBa$_2$Cu$_3$O$_y$. We argue that this effect is more likely due to a non-gaussian distribution of Knight shifts rather than to an unresolved line splitting produced by charge order. Such a Knight shift distribution is a typical signature of quasiparticle bound states that are known to form near various interfaces between superconducting and normal metallic regions or, under some circumstances, around point-defects in metals and superconductors. We argue that these bound states arise here from scattering off, yet unidentified, defects rather than from vortex cores or from pair-density-wave type superconductivity.