Showing papers on "Pseudogap published in 2015"

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy

Abstract: The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order-parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.

Charge ordering in the electron-doped superconductor Nd2–xCexCuO4

Abstract: In cuprate high-temperature superconductors, an antiferromagnetic Mott insulating state can be destabilized toward unconventional superconductivity by either hole or electron doping. In hole-doped (p-type) cuprates, a charge ordering (CO) instability competes with superconductivity inside the pseudogap state. We report resonant x-ray scattering measurements that demonstrate the presence of charge ordering in the n-type cuprate Nd 2– x Ce x CuO 4 near optimal doping. We find that the CO in Nd 2– x Ce x CuO 4 occurs with similar periodicity, and along the same direction, as in p-type cuprates. However, in contrast to the latter, the CO onset in Nd 2– x Ce x CuO 4 is higher than the pseudogap temperature, and is in the temperature range where antiferromagnetic fluctuations are first detected. Our discovery opens a parallel path to the study of CO and its relationship to antiferromagnetism and superconductivity.

Topological surface states and Fermi arcs of the noncentrosymmetric Weyl semimetals TaAs, TaP, NbAs, and NbP

Abstract: Very recently the topological Weyl semimetal (WSM) state was predicted in the noncentrosymmetric compounds NbP, NbAs, TaP, and TaAs and soon led to photoemission and transport experiments to verify the presumed topological properties such as Fermi arcs (unclosed Fermi surfaces) and the chiral anomaly. In this work we have performed fully ab initio calculations of the surface band structures of these four WSM materials and revealed the Fermi arcs with spin-momentum-locked spin texture. On the (001) polar surface, the shape of the Fermi surface depends sensitively on the surface terminations (cations or anions), although they exhibit the same topology with arcs. The anion (P or As) terminated surfaces are found to fit recent photoemission measurements well. Such surface potential dependence indicates that the shape of the Fermi surface can be sensitively manipulated by depositing guest species (such as K atoms), as we demonstrate. On the polar surface of a WSM without inversion symmetry, Rashba-type spin polarization naturally exists in the surface states and leads to strong spin texture. By tracing the spin polarization of the Fermi surface, one can distinguish Fermi arcs from trivial Fermi circles. The four compounds NbP, NbAs, TaP, and TaAs present an increasing amplitude of spin-orbit coupling (SOC) in band structures. By comparing their surface states, we reveal the evolution of topological Fermi arcs from the spin-degenerate Fermi circle to spin-split arcs when the SOC increases from zero to a finite value. Our work presents a comprehensive understanding of the topological surface states of WSMs, which will especially be helpful for future spin-revolved photoemission and transport experiments.

Collapse of the Mott Gap and Emergence of a Nodal Liquid in Lightly Doped Sr 2 IrO 4

Abstract: We report angle resolved photoemission experiments on the electron doped Heisenberg antiferromagnet (Sr(1-x)La(x))(2)IrO(4). For a doping level of x=0.05, we find an unusual metallic state with coherent nodal excitations and an antinodal pseudogap bearing strong similarities with underdoped cuprates. This state emerges from a rapid collapse of the Mott gap with doping resulting in a large underlying Fermi surface that is backfolded by a (π,π) reciprocal lattice vector which we attribute to the intrinsic structural distortion of Sr(2)IrO(4).

Emergence of coherence in the charge-density wave state of 2H-NbSe2.

Abstract: A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T(cdw). Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at T(cdw) marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in 'pseudogap' states.

Pseudogap from ARPES experiment: three gaps in cuprates and topological superconductivity

Abstract: A term first coined by Mott back in 1968 a `pseudogap' is the depletion of the electronic density of states at the Fermi level, and pseudogaps have been observed in many systems. However, since the discovery of the high temperature superconductors (HTSC) in 1986, the central role attributed to the pseudogap in these systems has meant that by many researchers now associate the term pseudogap exclusively with the HTSC phenomenon. Recently, the problem has got a lot of new attention with the rediscovery of two distinct energy scales (`two-gap scenario') and charge density waves patterns in the cuprates. Despite many excellent reviews on the pseudogap phenomenon in HTSC, published from its very discovery up to now, the mechanism of the pseudogap and its relation to superconductivity are still open questions. The present review represents a contribution dealing with the pseudogap, focusing on results from angle resolved photoemission spectroscopy (ARPES) and ends up with the conclusion that the pseudogap in cuprates is a complex phenomenon which includes at least three different `intertwined' orders: spin and charge density waves and preformed pairs, which appears in different parts of the phase diagram. The density waves in cuprates are competing to superconductivity for the electronic states but, on the other hand, should drive the electronic structure to vicinity of Lifshitz transition, that could be a key similarity between the superconducting cuprates and iron based superconductors. One may also note that since the pseudogap in cuprates has multiple origins there is no need to recoin the term suggested by Mott.

Mott physics and spin fluctuations: A unified framework

Abstract: We present a formalism for strongly correlated electron systems which consists in a local approximation of the dynamical three-leg interaction vertex. This vertex is self-consistently computed using a quantum impurity model with dynamical interactions in the charge and spin channels, similar to dynamical mean field theory approaches. The electronic self-energy and the polarization are both frequency and momentum dependent. The method interpolates between the spin-fluctuation or GW approximations at weak coupling and the atomic limit at strong coupling. We apply the formalism to the Hubbard model on a two-dimensional square lattice and show that as interactions are increased towards the Mott insulating state, the local vertex acquires a strong frequency dependence, driving the system to a Mott transition, while at low enough temperatures the momentum dependence of the self-energy is enhanced due to large spin fluctuations. Upon doping, we find a Fermi arc in the one-particle spectral function, which is one signature of the pseudogap state.

Pseudogap from ARPES experiment: Three gaps in cuprates and topological superconductivity (Review Article)

Abstract: A term first coined by Mott back in 1968 a “pseudogap” is the depletion of the electronic density of states at the Fermi level, and pseudogaps have been observed in many systems. However, since the discovery of the high-temperature superconductors (HTSC) in 1986, the central role attributed to the pseudogap in these systems has meant that by many researchers now associate the term pseudogap exclusively with the HTSC phenomenon. Recently, the problem has got a lot of new attention with the rediscovery of two distinct energy scales (“two-gap scenario”) and charge density waves patterns in the cuprates. Despite many excellent reviews on the pseudogap phenomenon in HTSC, published from its very discovery up to now, the mechanism of the pseudogap and its relation to superconductivity are still open questions. The present review represents a contribution dealing with the pseudogap, focusing on results from angle resolved photoemission spectroscopy (ARPES) and ends up with the conclusion that the pseudogap in cuprates is a complex phenomenon which includes at least three different “intertwined” orders: spin and charge density waves and preformed pairs, which appears in different parts of the phase diagram. The density waves in cuprates are competing to superconductivity for the electronic states but, on the other hand, should drive the electronic structure to vicinity of Lifshitz transition, that could be a key similarity between the superconducting cuprates and iron-based superconductors. One may also note that since the pseudogap in cuprates has multiple origins there is no need to recoin the term suggested by Mott.

Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics

Abstract: We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin, and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why d-wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength.

Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi2Sr2CaCu2O8+δ

Abstract: In the high-temperature (T(c)) cuprate superconductors, a growing body of evidence suggests that the pseudogap phase, existing below the pseudogap temperature T*, is characterized by some broken electronic symmetries distinct from those associated with superconductivity. In particular, recent scattering experiments have suggested that charge ordering competes with superconductivity. However, no direct link of an interplay between the two phases has been identified from the important low-energy excitations. Here, we report an antagonistic singularity at T(c) in the spectral weight of Bi2Sr2CaCu2O(8+δ) as compelling evidence for phase competition, which persists up to a high hole concentration p ~ 0.22. Comparison with theoretical calculations confirms that the singularity is a signature of competition between the order parameters for the pseudogap and superconductivity. The observation of the spectroscopic singularity at finite temperatures over a wide doping range provides new insights into the nature of the competitive interplay between the two orders and the complex phase diagram near the pseudogap critical point.

Quantum dimer model for the pseudogap metal

Abstract: We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S = 1 / 2 S=1/2, charge + e +e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8 × 8 8×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

Collapse of the normal-state pseudogap at a Lifshitz transition in the Bi(2)Sr(2)CaCu(2)O(8+δ) cuprate superconductor.

Abstract: We report a fine tuned doping study of strongly overdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal-state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active holelike Fermi surface becomes electronlike. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side.

Two types of nematicity in the phase diagram of the cuprate superconductor YBa 2 Cu 3 O y

Abstract: Nematicity has emerged as a key feature of cuprate superconductors, but its link to other fundamental properties such as superconductivity, charge order, and the pseudogap remains unclear Here we use measurements of transport anisotropy in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ to distinguish two types of nematicity The first is associated with short-range charge-density-wave modulations in a doping region near $p=012$ It is detected in the Nernst coefficient, but not in the resistivity The second type prevails at lower doping, where there are spin modulations but no charge modulations In this case, the onset of in-plane anisotropy---detected in both the Nernst coefficient and the resistivity---follows a line in the temperature-doping phase diagram that tracks the pseudogap energy We discuss two possible scenarios for the latter nematicity

Electron scattering, charge order, and pseudogap physics in La1.6-xNd0.4SrxCuO4 : An angle-resolved photoemission spectroscopy study

Abstract: We report an angle-resolved photoemission study of the charge stripe ordered La1.6-xNd0.4SrxCuO4 (Nd-LSCO) system. A comparative and quantitative line-shape analysis is presented as the system evolves from the overdoped regime into the charge ordered phase. On the overdoped side (x = 0.20), a normal-state antinodal spectral gap opens upon cooling below 80 K. In this process, spectral weight is preserved but redistributed to larger energies. A correlation between this spectral gap and electron scattering is found. A different line shape is observed in the antinodal region of charge ordered Nd-LSCO x = 1/8. Significant low-energy spectral weight appears to be lost. These observations are discussed in terms of spectral-weight redistribution and gapping originating from charge stripe ordering.

Superconductivity in an electron band just above the Fermi level: possible route to BCS-BEC superconductivity

Abstract: Conventional superconductivity follows Bardeen-Cooper-Schrieffer(BCS) theory of electrons-pairing in momentum-space, while superfluidity is the Bose-Einstein condensation(BEC) of atoms paired in real-space. These properties of solid metals and ultra-cold gases, respectively, are connected by the BCS-BEC crossover. Here we investigate the band dispersions in FeTe(0.6)Se(0.4)(Tc = 14.5 K ~ 1.2 meV) in an accessible range below and above the Fermi level(EF) using ultra-high resolution laser angle-resolved photoemission spectroscopy. We uncover an electron band lying just 0.7 meV (~8 K) above EF at the Γ-point, which shows a sharp superconducting coherence peak with gap formation below Tc. The estimated superconducting gap Δ and Fermi energy [Symbol: see text]F indicate composite superconductivity in an iron-based superconductor, consisting of strong-coupling BEC in the electron band and weak-coupling BCS-like superconductivity in the hole band. The study identifies the possible route to BCS-BEC superconductivity.

Quasiparticle spectra of 2 H -NbSe 2 : Two-band superconductivity and the role of tunneling selectivity

Abstract: We have studied the superconducting state of 2H−NbSe2 by scanning tunneling spectroscopy along two different crystal orientations, the c and the a/b axes. Along the c axis a large gap is dominant in the spectra, while a smaller gap is measured along the a/b axis. We show that these spectra are accurately described by the McMillan model where the small gap is induced through the coupling to the band associated with the large gap. In order to assign the small and large gaps to specific parts of the 2H−NbSe2 Fermi surface, the electronic structure was studied using first-principles calculations. While we cannot exclude the possibility of intrinsic anisotropy of the gaps, we propose that the large gap opens in the Fermi surface cylinders located around the corner K points while the sheets located around Γ are associated with the small gap. An additional component of the Fermi surface, a selenium based pocket, plays an essential role in the tunneling process. The role of the charge density wave occurring in this material is also discussed. Finally, we are able to give a coherent description of the observed characteristics of the tunneling spectra of 2H−NbSe2 as well as the differences with 2H−NbS2 where no charge density wave state is present. Further experimental work, such as high-resolution ARPES, would be very useful to confirm our interpretation. The approach and modeling developed here could also be relevant for other compounds of the dichalcogenide family.

Charge order in the pseudogap phase of cuprate superconductors

Abstract: Charge ordering instabilities are studied in a multiorbital model of cuprate superconductors. A known, key feature of this model is that the large local Coulomb interaction in the Cu orbitals generates local moments with short range antiferromagnetic (AF) correlations. The strong simplifying ansatz that these moments are static and ordered allows us to explore a regime not generally accessible to weak-coupling approaches. The AF correlations lead to a pseudogap-like reconstruction of the Fermi surface. We find that the leading charge instability within this pseudogap-like state is to a phase with a spatially modulated transfer of charge between neighbouring oxygen px and py orbitals accompanied by weak modulations of the charge density on the Cu orbitals. As a prime result of the AF Fermi-surface reconstruction, the wavevectors of the charge modulations are oriented along the crystalline axes with a periodicity that agrees quantitatively with experiments. This suggests a resolution to a discrepancy between experiments, which find axial order, and previous theoretical calculations, which find modulation wavevectors along the Brillouin zone diagonal. The axial order is stabilized by hopping processes via the Cu4s orbital, which is commonly not included in model analyses of cuprate superconductors. The main implication of our results is that charge order emerges from the pseudogap state, and is not the primary source of the pseudogap.

Pressure, compressibility, and contact of the two-dimensional attractive fermi gas.

Abstract: Using ab initio lattice methods, we calculate the finite temperature thermodynamics of homogeneous two-dimensional spin-1/2 fermions with attractive short-range interactions. We present results for the density, pressure, compressibility, and quantum anomaly (i.e., Tan's contact) for a wide range of temperatures (mostly above the superfluid phase, including the pseudogap regime) and coupling strengths, focusing on the unpolarized case. Within our statistical and systematic uncertainties, our prediction for the density equation of state differs quantitatively from the prediction by Luttinger-Ward theory in the strongly coupled region of parameter space, but otherwise agrees well with it. We also compare our calculations with the second- and third-order virial expansion, with which they are in excellent agreement in the low-fugacity regime.

Chiral Mott insulators, Meissner effect, and Laughlin states in quantum ladders

Abstract: We introduce generic bosonic models exemplifying that chiral Meissner currents can persist in insulating phases of matter. We first consider interacting bosons on a two-leg ladder. The total density sector can be gapped in a bosonic Mott insulator at odd-integer filling, while the relative density sector remains superfluid due to interchain hopping. Coupling the relative density to gauge fields yields a pseudospin Meissner effect. We show that the same phase arises if the bosons are replaced by spinful fermions confined in Cooper pairs, and find a dual fermionic Mott insulator with spinon currents. We prove that, by tuning the mean density, the Mott insulator with Meissner currents turns into a low-dimensional bosonic $\ensuremath{ u}=\frac{1}{2}$ Laughlin state for strong enough repulsive interactions across the ladder rungs. We finally discuss extensions to multileg ladders and bilayers in which spinon superfluids with Meissner currents become possible. We propose two experimental realizations, one with ultracold atoms in the setup of Atala et al. [Nat. Phys. 10, 588 (2014)] and another with Josephson junction arrays. We also address a Bose-Fermi mixture subject to a magnetic field in connection with the pseudogap phase of high-${T}_{c}$ cuprates.

Ultraviolet/infrared mixing in non-Fermi liquids

Abstract: We study low-energy effective-field theories for non-Fermi liquids with Fermi surfaces of general dimensions and codimensions. When the dimension of the Fermi surface is greater than one, low-energy particle-hole excitations remain strongly coupled with each other across the entire Fermi surface. In this case, even the observables that are local in the momentum space (such as the Green's functions) become dependent on the size of the Fermi surface in singular ways, resulting in a ultraviolet/infrared (UV/IR) mixing. By tuning the dimension and codimension of the Fermi surface independently, we find perturbative non-Fermi-liquid fixed points controlled by both UV/IR mixing and interactions.

Kinetic-energy-driven superconductivity in cuprate superconductors

Abstract: Superconductivity in cuprate superconductors occurs upon charge-carrier doping Mott insulators, where a central question is what mechanism causes the loss of electrical resistance below the superconducting (SC) transition temperature? In this paper, we attempt to summarize the basic idea of the kinetic-energy-driven SC mechanism in the description of superconductivity in cuprate superconductors. The mechanism of the kinetic-energy-driven superconductivity is purely electronic without phonons, where the charge-carrier pairing interaction in the particle–particle channel arises directly from the kinetic energy by the exchange of spin excitations in the higher powers of the doping concentration. This kinetic-energy-driven d-wave SC-state is controlled by both the SC gap and quasiparticle coherence, which leads to that the maximal SC transition temperature occurs around the optimal doping, and then decreases in both the underdoped and overdoped regimes. In particular, the same charge-carrier interaction mediated by spin excitations that induces the SC-state in the particle–particle channel also generates the normal-state pseudogap state in the particle–hole channel. The normal-state pseudogap crossover temperature is much larger than the SC transition temperature in the underdoped and optimally doped regimes, and then monotonically decreases upon the increase of doping, eventually disappearing together with superconductivity at the end of the SC dome. This kinetic-energy-driven SC mechanism also indicates that the strong electron correlation favors superconductivity, since the main ingredient is identified into a charge-carrier pairing mechanism not from the external degree of freedom such as the phonon but rather solely from the internal spin degree of freedom of the electron. The typical properties of cuprate superconductors discussed within the framework of the kinetic-energy-driven SC mechanism are also reviewed.

Interaction-induced singular Fermi surface in a high-temperature oxypnictide superconductor

Abstract: In the family of iron-based superconductors, LaFeAsO-type materials possess the simplest electronic structure due to their pronounced two-dimensionality. And yet they host superconductivity with the highest transition temperature Tc ≈ 55K. Early theoretical predictions of their electronic structure revealed multiple large circular portions of the Fermi surface with a very good geometrical overlap (nesting), believed to enhance the pairing interaction and thus superconductivity. The prevalence of such large circular features in the Fermi surface has since been associated with many other iron-based compounds and has grown to be generally accepted in the field. In this work we show that a prototypical compound of the 1111-type, SmFe0.92Co0.08AsO , is at odds with this description and possesses a distinctly different Fermi surface, which consists of two singular constructs formed by the edges of several bands, pulled to the Fermi level from the depths of the theoretically predicted band structure by strong electronic interactions. Such singularities dramatically affect the low-energy electronic properties of the material, including superconductivity. We further argue that occurrence of these singularities correlates with the maximum superconducting transition temperature attainable in each material class over the entire family of iron-based superconductors.

Emergent loop current order from pair density wave superconductivity

Abstract: There is evidence that the pseudogap phase in the cuprates breaks time-reversal symmetry. Here we show that pair density wave (PDW) states give rise to a translational invariant nonsuperconducting order parameter that breaks time-reversal and parity symmetries, but preserves their product. This secondary order parameter has a different origin, but shares the same symmetry properties as a magnetoelectric loop current order that has been proposed earlier in the context of the cuprates to explain the appearance of intracell magnetic order. We further show that, due to fluctuations, this secondary loop current order, which breaks only discrete symmetries, can preempt PDW order, which breaks both continuous and discrete symmetries. In such a phase, the emergent loop current order coexists with spatial short-range superconducting order and possibly short-range charge density wave (CDW) order. Finally, we propose a PDW phase that accounts for intracell magnetic order and the Kerr effect, has CDW order consistent with x-ray scattering and nuclear magnetic resonance observations, and quasiparticle properties consistent with angle-resolved photoemission scattering.

Hall effect and Fermi surface reconstruction via electron pockets in the high-$T_c$ cuprates

Abstract: The mechanism by which the Fermi surface of high-$T_c$ cuprates undergoes a dramatic change from a large hole-like barrel to small arcs or pockets on entering the pseudogap phase remains a question of fundamental importance. Here we calculate the normal-state Hall coefficient from the resonating-valence-bond spin-liquid model developed by Yang, Rice and Zhang. In this model, reconstruction of the Fermi surface occurs via an intermediate regime where the Fermi surface consists of both hole- and electron-like pockets. We find that the doping $(x)$ dependence of the Hall number transitions from $1+x$ to $x$ over this narrow doping range. At low temperatures, a switch from a downturn to an upturn in the Hall coefficient signals the departure of the electron-like pockets from the Fermi surface.

Pairing effects in the normal phase of a two-dimensional Fermi gas

Abstract: In a recent experiment [M. Feld et al., Nature 480, 75 (2011); B. Froehlich et al., Phys. Rev. Lett. 109,130403 (2012)], a pairing gap was detected in a two-dimensional (2D) Fermi gas with attractive interaction at temperatures where superfluidity does not occur. The question remains open as to whether this gap is a pseudogap phenomenon or is due to a molecular state. In this paper, by using a t-matrix approach, we reproduce quite well the experimental data for a 2D Fermi gas, and set the boundary between the pseudogap and molecular regimes. We also show that pseudogap phenomena occurring in 2D and 3D can be related through a variable spanning the BCS-BEC crossover in a universal way.

Checkerboard order in vortex cores from pair-density-wave superconductivity

Abstract: We consider competing pair-density-wave (PDW) and $d$-wave superconducting states in a magnetic field. We show that PDW order appears in the cores of $d$-wave vortices, driving checkerboard charge-density-wave (CDW) order in the vortex cores, which is consistent with experimental observations. Furthermore, we find an additional CDW order that appears on a ring outside the vortex cores. This CDW order varies with a period that is twice that of the checkerboard CDW and it only appears where both PDW and $d$-wave order coexist. The observation of this additional CDW order would provide strong evidence for PDW order in the pseudogap phase of the cuprates. We further argue that the CDW seen by nuclear magnetic resonance at high fields is due to a PDW state that emerges when a magnetic field is applied.

The form and origin of orbital ordering in the electronic nematic phase of iron-based superconductors

Abstract: We investigated the form of orbital ordering in the electronic nematic phase of iron-based superconductors by applying a group theoretical analysis on a realistic five-band model. We find the orbital order can be either of the inter-orbital s-wave form or intra-orbital d-wave form. From the comparison with existing ARPES measurements of band splitting, we find the orbital ordering in the 122 system is dominated by an intra-orbital d-wave component, while that of the 111 system is dominated by an inter-orbital s-wave component. We find both forms of orbital order are strongly entangled with the nematicity in the spin correlation of the system. The condensation energy of the magnetic ordered phase is found to be significantly improved (by more than 20%) when the degeneracy between the (π, 0) and (0, π) ordering pattern is lifted by the orbital order. We argue there should be a large difference in both the scattering rate and the size of the possible pseudogap on the electron pocket around the X = (π, 0) and Y = (0, π) point in the electronic nematic phase. We propose this as a possible origin for the observed nematicity in resistivity measurements.