Intra-unit-cell electronic nematicity of the high-T(c) copper-oxide pseudogap states

A universal explanation of tunneling conductance in exotic superconductors

A longstanding mystery in understanding cuprate superconductors is the inconsistency between the experimental data measured by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES). In particular, the gap between prominent side peaks observed in STS is much bigger than the superconducting gap observed by ARPES measurements. Here, we reconcile the two experimental techniques by generalising a theory which was previously applied to zero-dimensional mesoscopic Kondo systems to strongly correlated two-dimensional (2D) exotic superconductors. We show that the side peaks observed in tunneling conductance measurements in all these materials have a universal origin: They are formed by coherence-mediated tunneling under bias and do not directly reflect the underlying density of states (DOS) of the sample. We obtain theoretical predictions of the tunneling conductance and the density of states of the sample simultaneously and show that for cuprate and pnictide superconductors, the extracted sample DOS is consistent with the superconducting gap measured by ARPES.

Phonon dispersions and Fermi surfaces nesting explaining the variety of charge ordering in titanium-oxypnictides superconductors

There has been a puzzle between experiments and theoretical predictions on the charge ordering of layered titanium-oxypnictides superconductors. Unconventional mechanisms to explain this discrepancy have been argued so far, even affecting the understanding of superconductivity on the compound. We provide a new theoretical prediction, by which the discrepancy itself is resolved without any complicated unconventional explanation. Phonon dispersions and changes of nesting vectors in Fermi surfaces are clarified to lead to the variety of superlattice structures even for the common crystal structures when without CDW, including orthorhombic 2 × 2 × 1 one for BaTi₂As₂O, which has not yet been explained successfully so far, being different from tetragonal for BaTi₂Sb₂O and BaTi₂Bi₂O. The electronic structure analysis can naturally explain experimental observations about CDW including most latest ones without any cramped unconventional mechanisms.

Orbital symmetry of charge-density-wave order in La1.875Ba0.125CuO4 and YBa2Cu3O6.67

Recent theories of charge-density-wave (CDW) order in high-temperature superconductors have predicted a primarily d CDW orbital symmetry. Here, we report on the orbital symmetry of CDW order in the canonical cuprate superconductors La1.875Ba0.125CuO4 (LBCO) and YBa2Cu3O6.67 (YBCO), using resonant soft X-ray scattering and a model mapped to the CDW orbital symmetry. From measurements sensitive to the O sublattice, we conclude that LBCO has predominantly s' CDW orbital symmetry, in contrast to the d orbital symmetry recently reported in other cuprates. Furthermore, we show for YBCO that the CDW orbital symmetry differs along the a and b crystal axes and that these both differ from LBCO. This work highlights CDW orbital symmetry as an additional key property that distinguishes the different cuprate families. We discuss how the CDW symmetry may be related to the '1/8-anomaly' and to static spin ordering.

Bipartite electronic superstructures in the vortex core of Bi2Sr2CaCu2O8+δ

The central issue in the physics of cuprate superconductivity is the mutual relationship among superconductivity, pseudogap and broken-spatial-symmetry states. A magnetic field B suppresses superconductivity, providing an opportunity to investigate the competition among these states. Although various B-induced electronic superstructures have been reported, their energy, spatial and momentum-space structures are unclear. Here, we show using spectroscopic-imaging scanning tunnelling microscopy on Bi₂Sr₂CaCu₂O_8+δ that there are two distinct B-induced electronic superstructures, both being localized in the vortex core but appearing at different energies. In the low-energy range where the nodal Bogoliubov quasiparticles are well-defined, we observe the so-called vortex checkerboard that we identify as the B-enhanced quasiparticle interference pattern. By contrast, in the high-energy region where the pseudogap develops, the broken-spatial-symmetry patterns that pre-exist at B=0 T is locally enhanced in the vortex core. This evidences the competition between superconductivity and the broken-spatial-symmetry state that is associated with the pseudogap.

Field-induced electronic structures with spatial, momentum and energy resolution reveal the nature of interaction among multiple phases in correlated materials. Here, Machida et al. report two magnetic field-induced electronic superstructures in Bi₂Se₂CaCu₂O_8+δ, evidencing competition between superconductivity and emerging states.

Revisiting the vortex-core tunnelling spectroscopy in YBa2Cu3O7-δ

The observation by scanning tunnelling spectroscopy of Abrikosov vortex cores in the high-temperature superconductor YBa2Cu3O7-δ (Y123) has revealed a robust pair of electron-hole symmetric states at finite subgap energy. Their interpretation remains an open question because theory predicts a different signature in the vortex cores, characterized by a strong zero-bias conductance peak. Here, we present scanning tunnelling spectroscopy data on very homogeneous Y123 at 0.4 K revealing that the subgap features do not belong to vortices: they are actually observed everywhere along the surface with high spatial and energy reproducibility, even in the absence of magnetic field. Detailed analysis and modelling show that these states remain unpaired in the superconducting phase and belong to an incoherent channel, which contributes to the tunnelling signal in parallel with the superconducting density of states.

Short range smectic order driving long range nematic order: example of cuprates

We present a model for describing the combined presence of nematic and 'smectic' or stripe-like orders seen in recent scanning tunneling microscopy (STM) experiments on cuprates. The smectic order is treated as an electronic charge density wave with an associated Peierls distortion or a 'Pomeranchuk wave'. This primary order is restricted to nanoscale domains by disorder effects, while the secondary coupling to strain generates the nematic order with a considerably longer range. A variety of experimental results are shown to be consistent with our theoretical predictions.

Defects, Disorder, and Strong Electron Correlations in Orbital Degenerate, Doped Mott Insulators

We elucidate the effects of defect disorder and e-e interaction on the spectral density of the defect states emerging in the Mott-Hubbard gap of doped transition-metal oxides, such as Y(1-x)Ca(x)VO(3). A soft gap of kinetic origin develops in the defect band and survives defect disorder for e-e interaction strengths comparable to the defect potential and hopping integral values above a doping dependent threshold; otherwise only a pseudogap persists. These two regimes naturally emerge in the statistical distribution of gaps among different defect realizations, which turns out to be of Weibull type. Its shape parameter k determines the exponent of the power-law dependence of the density of states at the chemical potential (k-1) and hence distinguishes between the soft gap (k≥2) and the pseudogap (k<2) regimes. Both k and the effective gap scale with the hopping integral and the e-e interaction in a wide doping range. The motion of doped holes is confined by the closest defect potential and the overall spin-orbital structure. Such a generic behavior leads to complex nonhydrogenlike defect states that tend to preserve the underlying C-type spin and G-type orbital order and can be detected and analyzed via scanning tunneling microscopy.

Strain engineering Dirac surface states in heteroepitaxial topological crystalline insulator thin films

The unique crystalline protection of the surface states in topological crystalline insulators has led to a series of predictions of strain-generated phenomena, from the appearance of pseudo-magnetic fields and helical flat bands to the tunability of Dirac surface states by strain that may be used to construct 'straintronic' nanoswitches. However, the practical realization of this exotic phenomenology via strain engineering is experimentally challenging and is yet to be achieved. Here, we have designed an experiment to not only generate and measure strain locally, but also to directly measure the resulting effects on Dirac surface states. We grew heteroepitaxial thin films of topological crystalline insulator SnTe in situ and measured them using high-resolution scanning tunnelling microscopy to determine picoscale changes in the atomic positions, which reveal regions of both tensile and compressive strain. Simultaneous Fourier-transform scanning tunnelling spectroscopy was then used to determine the effects of strain on the Dirac electrons. We find that strain continuously tunes the momentum space position of the Dirac points, consistent with theoretical predictions. Our work demonstrates the fundamental mechanism necessary for using topological crystalline insulators in strain-based applications.

Evidence for orbital order and its relation to superconductivity in FeSe0.4Te0.6

The emergence of nematic electronic states accompanied by a structural phase transition is a recurring theme in many correlated electron materials, including the high-temperature copper oxide- and iron-based superconductors. We provide evidence for nematic electronic states in the iron-chalcogenide superconductor FeSe0.4Te0.6 from quasi-particle scattering detected in spectroscopic maps. The symmetry-breaking states persist above T c into the normal state. We interpret the scattering patterns by comparison with quasi-particle interference patterns obtained from a tight-binding model, accounting for orbital ordering. The relation to superconductivity and the influence on the coherence length are discussed.

Symmetry of charge order in cuprates

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.

Revealing the Empty-State Electronic Structure of Single-Unit-Cell FeSe/SrTiO3

We use scanning tunneling spectroscopy to investigate the filled and empty electronic states of superconducting single-unit-cell FeSe deposited on SrTiO3(001). We map the momentum-space band structure by combining quasiparticle interference imaging with decay length spectroscopy. In addition to quantifying the filled-state bands, we discover a Γ-centered electron pocket 75 meV above the Fermi energy. Our density functional theory calculations show the orbital nature of empty states at Γ and explain how the Se height is a key tuning parameter of their energies, with broad implications for electronic properties.

Electronic Properties of BaFe2As2 upon Doping and Pressure: The Prominent Role of the As p Orbitals

Using high-resolution, lifetime removed, x-ray absorption spectroscopy at the As K edge, we evidence the strong sensitivity of the As electronic structure upon electron doping with Co or pressure change in BaFe2As2, at room temperature. Our results unravel the prominent role played by As-4p orbitals in the electronic properties of the Fe pnictide superconductors. We propose a unique picture to describe the overall effect of both external parameter doping and pressure, resolving the apparent contradiction between angle-resolved photoemission spectroscopy, transport, and absorption results, with the As-p states as a key ingredient.

Phase diagram of cuprate high-temperature superconductors described by a field theory based on anharmonic oxygen degrees of freedom

In high temperature superconductors, although some phenomena such as the Mott transition (MT) at low doping are clearly driven by electron correlations, recent experimental data imply that anharmonic oxygen degrees of freedom-characteristic of perovskite materials-are playing a significant role. A key test of the role of anharmonic oxygen is to reproduce the complex cuprate phase diagram from a simple model. Here, we show that a field theory based on nonlinear coupling to anharmonic oxygens, parametrized from ab initio calculations, quantitatively reproduces the cuprate phase diagram for dopings above the MT. Pairing is mediated by renormalized oxygen vibrations transmuted into excitations of the pseudogap. The observed strong dependence of gap to transition temperature ratio on Tc also emerges from this field theory. This work suggests that including vibrational degrees of freedom is key to developing a complete understanding of the cuprates.

Enhancement of superconductivity near a nematic quantum critical point

We consider a low T_{c} metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that (1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP, (2) the symmetry of the superconducting state (d wave, s wave, p wave) is typically determined by the noncritical interactions, but T_{c} is enhanced by the nematic fluctuations in all channels, and (3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks down, but in 3D, the enhancement is much weaker.

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb1-xSnxSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons-a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Finally, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.

From quantum matter to high-temperature superconductivity in copper oxides

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi2Sr2CaCu2O(8+δ)

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.

Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates

The nature of the pseudogap regime of cuprate superconductors at low hole density remains unresolved. It has a number of seemingly distinct experimental signatures: a suppression of the paramagnetic spin susceptibility at high temperatures, low-energy electronic excitations that extend over arcs in the Brillouin zone, X-ray detection of charge-density wave order at intermediate temperatures and quantum oscillations at high magnetic fields and low temperatures. Here we show that a model of competing charge-density wave and superconducting orders provides a unified description of the intermediate and low-temperature regimes. We treat quantum oscillations at high field beyond semiclassical approximations, and find clear and robust signatures of an electron pocket compatible with existing observations; we also predict oscillations due to additional hole pockets. In the zero-field and intermediate temperature regime, we compute the electronic spectrum in the presence of thermally fluctuating charge-density and superconducting orders. Our results are compatible with experimental trends.

Nanoscale interplay of strain and doping in a high-temperature superconductor

The highest-temperature superconductors are electronically inhomogeneous at the nanoscale, suggesting the existence of a local variable that could be harnessed to enhance the superconducting pairing. Here we report the relationship between local doping and local strain in the cuprate superconductor Bi(2)Sr(2)CaCu(2)O(8+x). We use scanning tunneling microscopy to discover that the crucial oxygen dopants are periodically distributed in correlation with local strain. Our picoscale investigation of the intraunit-cell positions of all oxygen dopants provides essential structural input for a complete microscopic theory.

Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors

Understanding the role played by broken-symmetry states such as charge, spin and orbital orders in the mechanism of emergent properties, such as high-temperature superconductivity, is a major current topic in materials research. That the order may be within one unit cell, such as nematic, was only recently considered theoretically, but its observation in the iron-pnictide and doped cuprate superconductors places it at the forefront of current research. Here, we show that the recently discovered BaTi2Sb2O superconductor and its parent compound BaTi2As2O form a symmetry-breaking nematic ground state that can be naturally explained as an intra-unit-cell nematic charge order with d-wave symmetry, pointing to the ubiquity of the phenomenon. These findings, together with the key structural features in these materials being intermediate between the cuprate and iron-pnictide high-temperature superconducting materials, render the titanium oxypnictides an important new material system to understand the nature of nematic order and its relationship to superconductivity.

Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates

The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO2 unit cell, segregating the results into three separate electronic structure images containing only the Cu sites [Cu(r)] and only the x/y axis O sites [Ox(r) and O(y)(r)]. Phase-resolved Fourier analysis reveals directly that the modulations in the O(x)(r) and O(y)(r) sublattice images consistently exhibit a relative phase of π. We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials-specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intraunit-cell states that exhibit a predominantly d-symmetry form factor.

Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking

The existence of electronic symmetry breaking in the underdoped cuprates and its disappearance with increased hole density p are now widely reported. However, the relation between this transition and the momentum-space (k-space) electronic structure underpinning the superconductivity has not yet been established. Here, we visualize the Q = 0 (intra-unit-cell) and Q ≠ 0 (density-wave) broken-symmetry states, simultaneously with the coherent k-space topology, for Bi₂Sr₂CaCu₂O(8+δ) samples spanning the phase diagram 0.06 ≤ p ≤ 0.23. We show that the electronic symmetry-breaking tendencies weaken with increasing p and disappear close to a critical doping p(c) = 0.19. Concomitantly, the coherent k-space topology undergoes an abrupt transition, from arcs to closed contours, at the same p(c). These data reveal that the k-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.

Quenched disorder and vestigial nematicity in the pseudogap regime of the cuprates

The cuprate high-temperature superconductors have been the focus of unprecedentedly intense and sustained study not only because of their high superconducting transition temperatures, but also because they represent the most exquisitely investigated examples of highly correlated electronic materials. In particular, the pseudogap regime of the phase diagram exhibits a variety of mysterious emergent behaviors. In the last few years, evidence from NMR and scanning tunneling microscopy (STM) studies, as well as from a new generation of X-ray scattering experiments, has accumulated, indicating that a general tendency to short-range-correlated incommensurate charge density wave (CDW) order is "intertwined" with the superconductivity in this regime. Additionally, transport, STM, neutron-scattering, and optical experiments have produced evidence--not yet entirely understood--of the existence of an associated pattern of long-range-ordered point-group symmetry breaking with an electron-nematic character. We have carried out a theoretical analysis of the Landau-Ginzburg-Wilson effective field theory of a classical incommensurate CDW in the presence of weak quenched disorder. Although the possibilities of a sharp phase transition and long-range CDW order are precluded in such systems, we show that any discrete symmetry-breaking aspect of the charge order--nematicity in the case of the unidirectional (stripe) CDW we consider explicitly--generically survives up to a nonzero critical disorder strength. Such "vestigial order," which is subject to unambiguous macroscopic detection, can serve as an avatar of what would be CDW order in the ideal, zero disorder limit. Various recent experiments in the pseudogap regime of the hole-doped cuprates are readily interpreted in light of these results.

Cu(Ir₁ - xCrx)₂S₄: a model system for studying nanoscale phase coexistence at the metal-insulator transition

Increasingly, nanoscale phase coexistence and hidden broken symmetry states are being found in the vicinity of metal-insulator transitions (MIT), for example, in high temperature superconductors, heavy fermion and colossal magnetoresistive materials, but their importance and possible role in the MIT and related emergent behaviors is not understood. Despite their ubiquity, they are hard to study because they produce weak diffuse signals in most measurements. Here we propose Cu(Ir_{1 − x}Cr_x)₂S₄ as a model system, where robust local structural signals lead to key new insights. We demonstrate a hitherto unobserved coexistence of an Ir⁴⁺ charge-localized dimer phase and Cr-ferromagnetism. The resulting phase diagram that takes into account the short range dimer order is highly reminiscent of a generic MIT phase diagram similar to the cuprates. We suggest that the presence of quenched strain from dopant ions acts as an arbiter deciding between the competing ground states.

Charge order driven by Fermi-arc instability in Bi2Sr(2-x)La(x)CuO(6+δ)

The understanding of the origin of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. We combined resonant x-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, and in momentum and real space within one cuprate family, Bi2Sr(2-x)La(x)CuO(6+δ). The observed wave vectors rule out simple antinodal nesting in the single-particle limit but match well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations of electronic order in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates and uncover its intimate connection to the pseudogap regime.

Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O(8+x). Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.

Nematic phase in stripe-forming systems within the self-consistent screening approximation

We show that in order to describe the isotropic-nematic transition in stripe-forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of a two-point correlation function characteristic of a nematic phase.

Scanning probe image wizard: a toolbox for automated scanning probe microscopy data analysis

We describe SPIW (scanning probe image wizard), a new image processing toolbox for SPM (scanning probe microscope) images. SPIW can be used to automate many aspects of SPM data analysis, even for images with surface contamination and step edges present. Specialised routines are available for images with atomic or molecular resolution to improve image visualisation and generate statistical data on surface structure.

Concepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivity

Unconventional superconductivity (SC) is said to occur when Cooper pair formation is dominated by repulsive electron-electron interactions, so that the symmetry of the pair wave function is other than an isotropic s-wave. The strong, on-site, repulsive electron-electron interactions that are the proximate cause of such SC are more typically drivers of commensurate magnetism. Indeed, it is the suppression of commensurate antiferromagnetism (AF) that usually allows this type of unconventional superconductivity to emerge. Importantly, however, intervening between these AF and SC phases, intertwined electronic ordered phases (IP) of an unexpected nature are frequently discovered. For this reason, it has been extremely difficult to distinguish the microscopic essence of the correlated superconductivity from the often spectacular phenomenology of the IPs. Here we introduce a model conceptual framework within which to understand the relationship between AF electron-electron interactions, IPs, and correlated SC. We demonstrate its effectiveness in simultaneously explaining the consequences of AF interactions for the copper-based, iron-based, and heavy-fermion superconductors, as well as for their quite distinct IPs.

Evidence for short-range-ordered charge stripes far above the charge-ordering transition in La1.67Sr0.33NiO4

The temperature evolution of structural effects associated with charge order (CO) and spin order in La1.67Sr0.33NiO4 has been investigated using neutron powder diffraction. We report an anomalous shrinking of the c/a lattice parameter ratio that correlates with T(CO). The sign of this change can be explained by the change in interlayer Coulomb energy between the static-stripe-ordered state and the fluctuating-stripe-ordered state or the charge-disordered state. In addition, we identify a contribution to the mean-square displacements of Ni and in-plane O atoms whose width correlates quite well with the size of the pseudogap extracted from the reported optical conductivity, with a non-Debye-like component that persists below and well above T(CO). We infer that dynamic charge-stripe correlations survive to T∼2T(CO).

The k-space origins of scattering in Bi2Sr2CaCu2O8+x

We demonstrate a general, computer automated procedure that inverts the reciprocal space scattering data (q-space) that are measured by spectroscopic imaging scanning tunnelling microscopy (SI-STM) in order to determine the momentum space (k-space) scattering structure. This allows a detailed examination of the k-space origins of the quasiparticle interference (QPI) pattern in Bi2Sr2CaCu2O8+x within the theoretical constraints of the joint density of states (JDOS). Our new method allows measurement of the differences between the positive and negative energy dispersions, the gap structure and an energy dependent scattering length scale. Furthermore, it resolves the transition between the dispersive QPI and the checkerboard ([Formula: see text] excitation). We have measured the k-space scattering structure over a wide range of doping (p ∼ 0.22-0.08), including regions where the octet model is not applicable. Our technique allows the complete mapping of the k-space scattering origins of the spatial excitations in Bi2Sr2CaCu2O8+x, which allows for better comparisons between SI-STM and other experimental probes of the band structure. By applying our new technique to such a heavily studied compound, we can validate our new general approach for determining the k-space scattering origins from SI-STM data.

Bond order in two-dimensional metals with antiferromagnetic exchange interactions

We present an unrestricted Hartree-Fock computation of charge-ordering instabilities of two-dimensional metals with antiferromagnetic exchange interactions, allowing for arbitrary ordering wave vectors and internal wave functions of the particle-hole pair condensate. We find that the ordering has a dominant d symmetry of rotations about lattice points for a range of ordering wave vectors, including those observed in recent experiments at low temperatures on YBa2Cu3O(y). This d symmetry implies the charge ordering is primarily on the bonds of the Cu lattice, and we propose incommensurate bond order parameters for the underdoped cuprates. The field theory for the onset of Néel order in a metal has an emergent pseudospin symmetry which "rotates" d-wave Cooper pairs to particle-hole pairs [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)]; our results show that this symmetry has consequences even when the spin correlations are short ranged and incommensurate.

Surface-enhanced charge-density-wave instability in underdoped Bi2Sr(2-x)La(x)CuO(6+δ)

Neutron and X-ray scattering experiments have provided mounting evidence for spin and charge ordering phenomena in underdoped cuprates. These range from early work on stripe correlations in Nd-LSCO to the latest discovery of charge-density-waves in YBa2Cu3O(6+x). Both phenomena are characterized by a pronounced dependence on doping, temperature and an externally applied magnetic field. Here, we show that these electron-lattice instabilities exhibit also a previously unrecognized bulk-surface dichotomy. Surface-sensitive electronic and structural probes uncover a temperature-dependent evolution of the CuO2 plane band dispersion and apparent Fermi pockets in underdoped Bi2 Sr(2-x) La(x) CuO(6+δ) (Bi2201), which is directly associated with an hitherto-undetected strong temperature dependence of the incommensurate superstructure periodicity below 130 K. In stark contrast, the structural modulation revealed by bulk-sensitive probes is temperature-independent. These findings point to a surface-enhanced incipient charge-density-wave instability, driven by Fermi surface nesting. This discovery is of critical importance in the interpretation of single-particle spectroscopy data, and establishes the surface of cuprates and other complex oxides as a rich playground for the study of electronically soft phases.

Glassy behavior of two-dimensional stripe-forming systems

We study two-dimensional frustrated but nondisordered systems applying a replica approach to a stripe-forming model with competing interactions. The phenomenology of the model is representative of several well-known systems, like high-Tc superconductors and ultrathin ferromagnetic films, which have been the subject of intense research. We establish the existence of a glass transition to a nonergodic regime accompanied by an exponential number of long-lived metastable states, responsible for slow dynamics and nonequilibrium effects.

Transport signatures of electronic-nematic stripe phases

Electronic-nematic phases are broadly characterized by spontaneously broken rotational symmetry. Although they have been widely recognized in the context of high temperature cuprates, bilayer ruthenates, and iron-based superconductors, the focus so far has been exclusively on the uniform nematic phase. Recently, however, it was proposed that on a square lattice a nematic instability in the d-wave charge channel could lead to a spatially modulated nematic state, where the modulation vector q is determined by the relative location of the Fermi level to the van Hove singularity. Interestingly, this finite-q nematic (nematic stripe) phase has also been identified as an additional leading instability that is as strong as the superconducting instability near the onset of spin density wave order. Here, we study the electrical conductivity tensor in the modulated nematic phase for a general modulation vector. Our results can be used to identify nematic stripe phases in correlated materials.

Local electronic nematicity in the two-dimensional one-band Hubbard model

Nematicity is a well-known property of liquid crystals and has been recently discussed in the context of strongly interacting electrons. An electronic nematic phase has been seen in many experiments in certain strongly correlated materials, in particular, in the pseudogap phase generic to many hole-doped cuprate superconductors. Recent measurements in high Tc superconductors have shown that even if the lattice is perfectly rotationally symmetric, the ground state can still have strongly nematic local properties. Our study of the two-dimensional one-band Hubbard model provides strong support for the recent experimental results on local rotational C4 symmetry breaking. The variational cluster approach is used here to show the possibility of an electronic nematic state and the proximity of the underlying symmetry-breaking ground state within the Hubbard model. We identify this nematic phase in the overdoped region and show that the local nematicity decreases with increasing electron filling. Our results also indicate that strong Coulomb interaction may drive the nematic phase into a phase similar to the stripe structure. The calculated spin (magnetic) correlation function in momentum space shows the effects resulting from real-space nematicity.

Pseudogap temperature as a Widom line in doped Mott insulators

The pseudogap refers to an enigmatic state of matter with unusual physical properties found below a characteristic temperature T* in hole-doped high-temperature superconductors. Determining T* is critical for understanding this state. Here we study the simplest model of correlated electron systems, the Hubbard model, with cluster dynamical mean-field theory to find out whether the pseudogap can occur solely because of strong coupling physics and short nonlocal correlations. We find that the pseudogap characteristic temperature T* is a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. The Widom line emanating from the critical endpoint of a first-order transition is thus the organizing principle for the pseudogap phase diagram of the cuprates. No additional broken symmetry is necessary to explain the phenomenon. Broken symmetry states appear in the pseudogap and not the other way around.

Infrared measurement of the pseudogap of P-doped and Co-doped high-temperature BaFe2As2 superconductors

We report on infrared studies of charge dynamics in a prototypical pnictide system: the BaFe2As2 family. Our experiments have identified hallmarks of the pseudogap state in the BaFe2As2 system that mirror the spectroscopic manifestations of the pseudogap in the cuprates. The magnitude of the infrared pseudogap is in accord with that of the spin-density-wave gap of the parent compound. By monitoring the superconducting gap of both P- and Co-doped compounds, we find that the infrared pseudogap is unrelated to superconductivity. The appearance of the pseudogap is found to correlate with the evolution of the antiferromagnetic fluctuations associated with the spin-density-wave instability. The strong-coupling analysis of infrared data further reveals the interdependence between the magnetism and the pseudogap in the iron pnictides.

Susceptibility anisotropy in an iron arsenide superconductor revealed by x-ray diffraction in pulsed magnetic fields

In addition to unconventional high-T(c) superconductivity, the iron arsenides exhibit strong magnetoelastic coupling and a notable electronic anisotropy within the a-b plane. We relate these properties by studying underdoped Ba(Fe(1-x)Co(x))2As2 by x-ray diffraction in pulsed magnetic fields up to 27.5 T. We exploit magnetic detwinning effects to demonstrate anisotropy in the in-plane susceptibility, which develops at the structural phase transition despite the absence of magnetic order. The degree of detwinning increases smoothly with decreasing temperature, and a single-domain condition is realized over a range of field and temperature. At low temperatures we observe an activated behavior, with a large hysteretic remnant effect. Detwinning was not observed within the superconducting phase for accessible magnetic fields.

Electronic nematicity above the structural and superconducting transition in BaFe2(As(1-x)P(x))2

Electronic nematicity, a unidirectional self-organized state that breaks the rotational symmetry of the underlying lattice, has been observed in the iron pnictide and copper oxide high-temperature superconductors. Whether nematicity plays an equally important role in these two systems is highly controversial. In iron pnictides, the nematicity has usually been associated with the tetragonal-to-orthorhombic structural transition at temperature T(s). Although recent experiments have provided hints of nematicity, they were performed either in the low-temperature orthorhombic phase or in the tetragonal phase under uniaxial strain, both of which break the 90° rotational C(4) symmetry. Therefore, the question remains open whether the nematicity can exist above T(s) without an external driving force. Here we report magnetic torque measurements of the isovalent-doping system BaFe(2)(As(1-x)P(x))(2), showing that the nematicity develops well above T(s) and, moreover, persists to the non-magnetic superconducting regime, resulting in a phase diagram similar to the pseudogap phase diagram of the copper oxides. By combining these results with synchrotron X-ray measurements, we identify two distinct temperatures-one at T*, signifying a true nematic transition, and the other at T(s) (<T*), which we show not to be a true phase transition, but rather what we refer to as a 'meta-nematic transition', in analogy to the well-known meta-magnetic transition in the theory of magnetism.

Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors

A complicating factor in unravelling the theory of high-temperature (high-T(c)) superconductivity is the presence of a 'pseudogap' in the density of states, the origin of which has been debated since its discovery. Some believe the pseudogap is a broken symmetry state distinct from superconductivity, whereas others believe it arises from short-range correlations without symmetry breaking. A number of broken symmetries have been imaged and identified with the pseudogap state, but it remains crucial to disentangle any electronic symmetry breaking from the pre-existing structural symmetry of the crystal. We use scanning tunnelling microscopy to observe an orthorhombic structural distortion across the cuprate superconducting Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4+x) (BSCCO) family tree, which breaks two-dimensional inversion symmetry in the surface BiO layer. Although this inversion-symmetry-breaking structure can impact electronic measurements, we show from its insensitivity to temperature, magnetic field and doping, that it cannot be the long-sought pseudogap state. To detect this picometre-scale variation in lattice structure, we have implemented a new algorithm that will serve as a powerful tool in the search for broken symmetry electronic states in cuprates, as well as in other materials.

Electronic confinement and ordering instabilities in colossal magnetoresistive bilayer manganites

We present angle-resolved photoemission studies of (La{1-z}Pr{z}){2-2x}Sr{1+2x}Mn{2}O{7} with x=0.4 and z=0.1, 0.2, and 0.4 along with density functional theory calculations and x-ray scattering data. Our results show that the bilayer splitting in the ferromagnetic metallic phase of these materials is small, if not completely absent. The charge carriers are therefore confined to a single MnO{2} layer, which in turn results in a strongly nested Fermi surface. In addition to this, the spectral function also displays clear signatures of an electronic ordering instability well below the Fermi level. The increase of the corresponding interaction strength with z and its magnitude of ∼400  meV make the coupling to a bare phonon highly unlikely. Instead we conclude that fluctuating order, involving electronic and lattice degrees of freedom, causes the observed renormalization of the spectral features.