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Twisted bilayered graphenes at magic angles are systems housing long ranged periodicity of Moir\'e pattern together with short ranged periodicity associated with the individual graphenes. Such materials are a fertile ground for novel states largely driven by electronic correlations. Here we find that the ubiquitous Casimir force can serve as a platform for macroscopic manifestations of the quantum effects stemming from the magic angle bilayered graphenes properties and their phases determined by electronic correlations. By utilizing comprehensive calculations for the electronic and optical response, we find that Casimir torque can probe anisotropy from the Drude conductivities in nematic states, while repulsion in the Casimir force can help identify topologically nontrivial phases in magic angle twisted bilayered graphenes., Comment: 9 pages, 6 figures (main), 7 pages, 7 figures (supplementary); provisionally accepted for publication in 2D Materials

We calculate the interactions between the Wannier functions of the 8-orbital model for twisted bilayer graphene (TBG). In this model, two orbitals per valley centered at the AA regions, the AA-p orbitals, account for the most part of the spectral weight of the flats bands. Exchange and assisted-hopping terms between these orbitals are found to be small. Therefore, the low energy properties of TBG will be determined by the density-density interactions. These interactions decay with the distance much faster than in the two orbital model, following a 1/r law in the absence of gates. The magnitude of the largest interaction in the model, the onsite term between the flat band orbitals, is controlled by the size of the AA regions and is estimated to be ~ 40 meV. To screen this interaction, the metallic gates have to be placed at a distance smaller than 5 nm. For larger distances only the long-range part of the interaction is substantially screened. The model reproduces the band deformation induced by doping found in other approaches within the Hartree approximation. Such deformation reveals the presence of other orbitals in the flat bands and is sensitive to the inclusion of the interactions involving them., Comment: 9 pages, including 6 multiple figures and one appendix

Moir\'e systems displaying flat bands have emerged as novel platforms to study correlated electron phenomena. Insulating and superconducting states appear upon doping magic angle twisted bilayer graphene (TBG), and there is evidence of correlation induced effects at the charge neutrality point (CNP) which could originate from spontaneous symmetry breaking. Our theoretical calculations show how optical conductivity measurements can distinguish different symmetry breaking states, and reveal the nature of the correlated states. In the specific case of nematic order, which breaks the discrete rotational symmetry of the lattice, we find that the Dirac cones are displaced, not only in momentum space but also in energy, inducing finite Drude weight at the CNP. We also show that the sign of the dc conductivity anisotropy induced by a nematic order depends on the degree of lattice relaxation, the doping and the nature of the symmetry breaking., Comment: 6 pages, including 4 multiple figures + Suppl. Information. with text and 3 figures

The recently observed superconductivity in twisted bilayer graphene emerges from insulating states believed to arise from electronic correlations. While there have been many proposals to explain the insulating behaviour, the commensurability at which these states appear suggests that they are Mott insulators. Here we focus on the insulating states with $\pm 2$ electrons or holes with respect to the charge neutrality point. We show that the theoretical expectations for the Mott insulating states are not compatible with the experimentally observed dependence on temperature and magnetic field if, as frequently assumed, only the correlations between electrons on the same site are included. We argue that the inclusion of non-local (inter-site) correlations in the treatment of the Hubbard model can bring the predictions for the magnetic and temperature dependencies of the Mott transition to an agreement with experiments and have consequences for the critical interactions, the size of the gap, and possible pseudogap physics. The importance of the inter-site correlations to explain the experimental observations indicates that the observed insulating gap is not the one between the Hubbard bands and that antiferromagnetic-like correlations play a key role in the Mott transition., 8 pages (including appendix), 5 figures

The theoretical understanding of the nematic state of iron-based superconductors and especially of FeSe is still a puzzling problem. Although a number of experiments call for a prominent role of local correlations and place iron superconductors at the entrance of a Hund's metal state, the effect of the electronic correlations on the nematic state has been theoretically poorly investigated. In this work we study the nematic phase of iron superconductors accounting for local correlations, including the effect of the Hund's coupling. We show that Hund's physics strongly affects the nematic properties of the system. It severely constrains the precise nature of the feasible orbital-ordered state and induces a differentiation in the effective masses of the zx/yz orbitals in the nematic phase. The latter effect leads to distinctive signatures in different experimental probes overlooked so far in the interpretation of experiments. As notable examples the splittings between zx and yz bands at Γ and M points are modified, with important consequences for angle-resolved photoemission spectroscopy measurements., E.B. acknowledges funding from Ministerio de Economía, Industria y Competitividad via Grants No. FIS2011-29689 and No. FIS2014-53218-P and from Fundación Ramón Areces. M.C. acknowledges funding from SISSA/Consiglio Nazionale delle Ricerche project “Superconductivity, Ferroelectricity and Magnetism in bad metals” (Protocollo 232/2015) and Ministero dell'Istruzione, dell'Università e della Ricerca through the PRIN 2015 program (Protocollo 2015C5SEJJ001).

Undoped iron superconductors accommodate n=6 electrons in five d orbitals. Experimental and theoretical evidence shows that the strength of correlations increases with hole doping, as the electronic filling approaches half filling with n=5 electrons. This evidence delineates a scenario in which the parent compound of iron superconductors is the half-filled system, in analogy to cuprate superconductors. In cuprates the superconductivity can be induced upon electron or hole doping. In this work we propose to search for high-Tc superconductivity and strong correlations in chromium pnictides and chalcogenides with n, Funding from Ministerio de Economía, Industria y Competitividad (Spain) via Grants No. FIS2012-33521, No. FIS2014-53218-P, No. FIS2015-64654-P, and No. MAT2015-66888-C3-1-R and from Fundación Ramón Areces is gratefully acknowledged. J.L. acknowledges the financial support of the National Natural Science Foundation of China (Grants No. 11374186 and No. 51231007) and the China Scholarship Council.

Unconventional superconductivity in iron pnictides and chalcogenides has been suggested to be controlled by the interplay of low-energy antiferromagnetic spin fluctuations and the particular topology of the Fermi surface in these materials. Based on this premise, one would also expect the large class of isostructural and isoelectronic iron germanide compounds to be good superconductors. As a matter of fact, they, however, superconduct at very low temperatures or not at all. In this work we establish that superconductivity in iron germanides is suppressed by strong ferromagnetic tendencies, which surprisingly do not originate from changes in bond angles or bond distances with respect to iron pnictides and chalcogenides, but are due to changes in the electronic structure in a wide range of energies happening upon substitution of atom species (As by Ge and the corresponding spacer cations). Our results indicate that superconductivity in iron-based materials may not always be fully understood based on d or d-p model Hamiltonians only., D. G., H. O. J., and R. V. thank the German Research Foundation (Deutsche Forschungsgemeinschaft) for financial support through grant SPP 1458. I. I. M. was supported by ONR through the NRL basic research program and by the Alexander von Humboldt Foundation. J. K. G. acknowledges the support of the NRC program at NRL. E. B. acknowledges funding from Ministerio de Economía y Competitividad vía Grant No. FIS2014-53219-P and from Fundación Ramón Areces and thanks R. Rurali and X. Cartoixa for early calculations.

[EN] High-temperature superconductivity in iron pnictides and chalcogenides emerges when a magnetic phase is suppressed. The multi-orbital character and the strength of correlations underlie this complex phenomenology, involving magnetic softness and anisotropies, with Hund's coupling playing an important role. We review here the different theoretical approaches used to describe the magnetic interactions in these systems. We show that taking into account the orbital degree of freedom allows us to unify in a single phase diagram the main mechanisms proposed to explain the (π, 0) order in iron pnictides: nesting-driven superconductivity, exchange between localised spins, and Hund-induced magnetic state with orbital differentiation. Comparison of theoretical estimates and experimental results helps locate the Fe superconductors in the phase diagram. In addition, orbital physics is crucial to address the magnetic softness, the doping-dependent properties, and the anisotropies., [FR] La supraconductivité à haute température dans les pnictures et les chalcogénures de fer émerge quand une phase magnétique est supprimée. Le caractère multi-orbital et la force des corrélations sont sous-jacents à cette phénoménologie complexe, faisant appel à la douceur magnétique et aux anisotropies, dans lesquelles le couplage de Hund joue un rôle important. Nous passons ici en revue les différentes approches théoriques utilisées pour décrire les interactions magnétiques dans ces systèmes. Nous montrons que la prise en compte du degré de liberté orbital nous permet d'unifier dans un seul diagramme de phases les principaux mécanismes proposés pour expliquer l'ordre dans les pnictures de fer : supraconductivité nesting-driven, échange entre spins localisés et état magnétique induit par couplage de Hund avec différenciation orbitale. La comparaison des estimations théoriques et des résultats expérimentaux nous permet de localiser les supraconducteurs à base de fer dans le diagramme de phases. De plus, la physique orbitale est cruciale pour approcher la douceur magnétique, les propriétés dépendant du dopage ainsi que les anisotropies., We acknowledge funding from Ministerio de Economía y Competitividad (Spain) via grants No. FIS2011-29689, No. FIS2012-33521 and No. FIS2014-53219-P and from Fundación Ramón Areces.

Oral presentation given at the 20th International Conference on Magnetism, held in Barcelona (Spain) on July 5-10th, 2015. Friday, July 10. FR.J.1_THEORY OF STRONGLY CORRELATED MATTER 09:00-10:30 (ROOM E1-E3)., A new concept has emerged in the last years in correlated electron systems: the Hund metal. This name was coined within the context of iron superconductors and refers to a strongly correlated metallic state found in multi-orbital systems with Hund¿s coupling playing a key role in setting the correlations [1]. Until very recently [2] the nature of correlations in Hund metals has been controversial and not well understood. When the atoms become spin polarized the overlap between the atomic and single particle states decreases suppressing the quasiparticle weight. Nevertheless the system seems to be far from a Mott transition as the transition is not found for moderate increase of interactions. On the other hand the strong increase of correlations as half-filling is approached has led to a description of Hund metals as doped Mott insulators. This has led to a discussion on the role of Mott physics in these systems. We have addressed the correlations in multi-orbital systems as a function of interactions, number of orbitals and electronic filling. We have clarified the nature of correlations in Hund metals and solved the controversy between Hund and Mott systems [2]. Our calculations clearly show that the suppression of coherence in Hund metals is directly connected to the Mott insulating state at half-filling. However correlations due to Hund¿s coupling are intrinsically different to those in Mott states. This is observed in the charge fluctuations, which are only weakly reduced or even enhanced in Hund metals as the quasiparticle weight is suppressed, contrary to what happens in Mott correlated systems. We have shown that the dependence of correlations, energy scales, charge and spin fluctuations can be understood by looking at the hopping processes which are suppressed or promoted by Hund's coupling.

Charge, spin, and lattice degrees of freedom are strongly entangled in iron superconductors. A neat consequence of this entanglement is the behavior of the A1g As-phonon resonance in the different polarization symmetries of Raman spectroscopy when undergoing the magnetostructural transition. In this work, we show that the observed behavior could be a direct consequence of the coupling of the phonons with the electronic excitations in the anisotropic magnetic state. We discuss this scenario within a five-orbital tight-binding model coupled to phonons via the dependence of the Slater-Koster parameters on the As position. We identify two qualitatively different channels of the electron-phonon interaction: a geometrical one related to the Fe-As-Fe angle α and another one associated with the modification upon As displacement of the Fe-As energy integrals pdσ and pdπ. While both mechanisms result in a finite B1g response, the behavior of the phonon intensity in the A1g and B1g Raman polarization geometries is qualitatively different when the coupling is driven by the angle or by the energy integral dependence. We discuss our results in view of the experimental reports. © 2013 American Physical Society., We acknowledge funding from MINECO-Spain through Grants FIS2008-00124, FIS2009-08744, FIS2011-29689, and FIS2012-33521. S.C. acknowledges support from Spanish Education Ministry programme SAB2010-0107. E.C. acknowledges support from the European FP7 Marie Curie project PIEF-GA-2009-251904 and Italian Project PRIN “GRAF” No. 20105ZZTSE.

We analyze the metallic (π,0) antiferromagnetic state of a five-orbital model for iron superconductors. We find that with increasing interactions the system does not evolve trivially from the pure itinerant to the pure localized regime. Instead we find a region with a strong orbital differentiation between xy and yz, which are half-filled gapped states at the Fermi level, and itinerant zx, 3z2−r2, and x2−y2. We argue that orbital ordering between the yz and zx orbitals arises as a consequence of the interplay of the exchange energy in the antiferromagnetic x direction and the kinetic energy gained by the itinerant orbitals along the ferromagnetic y direction with an overall dominance of the kinetic energy gain. We indicate that iron superconductors may be close to the boundary between the itinerant and the orbital differentiated regimes and that it could be possible to cross this boundary with doping., We acknowledge funding from MINECO-Spain through Grants FIS2008-00124, FIS2009-08744, and FIS2011-29689.

We discuss how to analyze the optical conductivity and Raman spectra of multiorbital systems using the velocity and the Raman vertices in a similar way Raman vertices were used to disentangle nodal and antinodal regions in cuprates. We apply this method to iron superconductors in the magnetic and nonmagnetic states, studied at the mean-field level. We find that the anisotropy in the optical conductivity at low frequencies reflects the difference between the magnetic gaps at the X and Y electron pockets. Both gaps are sampled by Raman spectroscopy. We also show that the Drude weight anisotropy in the magnetic state is sensitive to small changes in the lattice structure. © 2013 American Physical Society., We acknowledge funding from Ministerio de Economía y Competitividad through Grants No. FIS 2008-00124, No. FIS 2009-08744, No. FIS 2011-29689, and from CSIC through Grants No. PIE-200960I033 and No. PIE-200960I180.

We have analyzed the magnetic interactions of a five orbital model for iron superconductors treated both within Hartree-Fock and Heisenberg approximations. We have found that the exchange constants depend non-trivially on the Fe-As-Fe angle and on the charge and orbital filling. Within the localized picture, columnar ordering is found for intermediate Hund's coupling J_H. At smaller J_H, an unusual orbital reorganization stabilizes checkerboard ordering. Ferromagnetism appears at large J_H. Ferromagnetic correlations are enhanced with electron doping while large hole doping stabilizes checkerboard antiferromagnetism, explaining the change in magnetic interactions upon substitution of Fe by Co or Mn. For intermediate and large values of U, Hartree-Fock shows similar results as strong coupling though with a double stripe phase instead of ferromagnetism. Itinerancy enhances the stability of the columnar ordering. Comparison of the two approaches reveals a metallic region of the phase diagram where strong coupling physics is determinant., 8 pages including 7 figures. As accepted in Phys. Rev. B

We examine the magnetic phase diagram of iron pnictides using a five band model. For the intermediate values of the interaction expected to hold in the iron pnictides, we find a metallic low moment state characterized by antiparallel orbital magnetic moments. The anisotropy of the interorbital hopping amplitudes is the key to understanding this low moment state. This state accounts for the small magnetization measured in undoped iron pnictides and leads to the strong exchange anisotropy found in neutron experiments. Orbital ordering is concomitant with magnetism and produces the large zx orbital weight seen at Gamma in photoemission experiments., 4 pages, 4 eps figures. Small changes in the text. Modification of colors in Figs. Final version as accepted in PRL

We propose a five-band tight-binding model for the Fe-As layers of iron pnictides with the hopping amplitudes calculated within the Slater-Koster framework. The band structure found in DFT, including the orbital content of the bands, is well reproduced using only four fitting parameters to determine all the hopping amplitudes. The model allows to study the changes in the electronic structure caused by a modification of the angle $\alpha$ formed by the Fe-As bonds and the Fe-plane and recovers the phenomenology previously discussed in the literature. We also find that changes in $\alpha$ modify the shape and orbital content of the Fermi surface sheets., Comment: 12 pages, 6 eps figures. Figs 1 and 2 modified, minor changes in the text. A few references added

Recent experiments in underdoped hole-doped cuprates have shown the presence of two energy scales in the Raman spectrum in the superconducting state. This feature has a natural explanation in some models in which pseudogap and superconductivity compete. In electron-doped cuprates antiferromagnetic correlations are believed to survive in the superconducting state, and to produce a pseudogap above the critical temperature. Contrary to hole-doped systems, in electron-doped compounds only one energy scale appear since the pair breaking Raman intensity peaks in both B$_{1g}$ (antinodal) and B$_{2g}$ (nodal) channels at a frequency of a few meV, typical of the superconducting order parameter. In this paper we analyze the different effect in the Raman spectrum of the competition between pseudogap and superconductivity in electron and hole-doped cuprates. The difference in energy scales in both systems is explained in terms of the different truncation of the Fermi surface induced by the pseudogap. For electron-doped cuprates we also analyze the spectrum with antiferromagnetism and a non-monotonic superconducting order parameter., 7 pages, 4 postscript figures, minor changes in the text, Fig. 3 and Fig. 4 replaced to better visualize them

We study the dependence of the electronic structure of iron pnictides on the angle formed by the arsenic-iron bonds. Within a Slater-Koster tight binding model which captures the correct symmetry properties of the bands, we show that the density of states and the band structure are sensitive to the distortion of the tetrahedral environment of the iron atoms. This sensitivity is extremely strong in a two-orbital (d_xz, d_yz) model due to the formation of a flat band around the Fermi level. Inclusion of the d_xy orbital destroys the flat band while keeping a considerable angle dependence in the band structure., 5 pages, including 5 figures. Fig. 5 replaced. Minor changes in the text

We analyze and clarify the transport properties of a one-dimensional metallic nanoparticle array with interaction between charges restricted to charges placed in the same conductor. We study the threshold voltage, the I-V curves and the potential drop through the array and their dependence on the array parameters including the effect of charge and resistance disorder. We show that very close to threshold the current depends linearly on voltage with a slope independent on the array size. At intermediate bias voltages, for which a Coulomb staircase is observed we find that the average potential drop through the array oscillates with position. At higher voltages I-V curves are linear but have a finite offset voltage. We show that the slope is given by the inverse of the resistances added in series and estimate the voltage at which this linear regime is reached. We also calculate the offset voltage and relate it to the potential drop through the array., 16 pages and 8 postscript figures

Nesting in a semimetal can lead to an excitonic insulator state with spontaneous coherence between conduction and valence bands and a gap for charged excitations. In this paper we present a theory of the ferromagnetic state that occurs when the density of electrons in the conduction band and holes in the valence band differ. We find an unexpectedly rich doping-field phase diagram and an unusual collective excitation spectrum that includes two gapless collective modes. We predict regions of doping and external field in which phase-separated condensates of electrons and holes with parallel spins and opposing spins coexist., Comment: 5 pages, 3 postscript files