One of the main challenges in understanding high TC superconductivity is to disentangle the rich variety of states of matter that may coexist, cooperate, or compete with d-wave superconductivity. At center stage is the pseudogap phase, which occupies a large portion of the cuprate phase diagram surrounding the superconducting dome [1]. Using scanning tunneling microscopy, we find that a static, non-dispersive, "checkerboard"-like electronic modulation exists in a broad regime of the cuprate phase diagram and exhibits strong doping dependence. The continuous increase of checkerboard periodicity with hole density strongly suggests that the checkerboard originates from charge density wave formation in the anti-nodal region of the cuprate Fermi surface. These results reveal a coherent picture for static electronic orderings in the cuprates and shed important new light on the nature of the pseudogap phase.
Checkerboard patterns have been proposed in order to explain STM experiments on the cuprates BSCCO and Na-CCOC. However the presence of these patterns has not been confirmed by a bulk probe such as neutron scattering. In particular, simple checkerboard patterns are inconsistent with neutron scattering data, in that they have low energy incommsensurate (IC) spin peaks rotated 45 degrees from the direction of the charge IC peaks. However, it is unclear whether other checkerboard patterns can solve the problem. In this paper, we have studied more complicated checkerboard patterns ("modulated chec…
The checkerboard pattern in the differential conductance maps on underdoped cuprates appears when the STM is placed above the O-sites in the outermost CuO$_{\text{2}}$-plane. In this position the interference between tunneling paths through the apical ions above the neighboring Cu-sites leads to an asymmetric weighting of final states in the two antinodal regions of ${\boldsymbol{k}}$-space. The form of the asymmetry in the differential conductance spectra in the checkerboard pattern favors asymmetry in the localization length rather than a nematic displacement as the underlying origin.
We systematically investigate charge-ordering phases by means of a restricted and unrestricted Gutzwiller approximation to the single-band Hubbard model with nearest ($t$) and next-nearest neighbor hopping ($t'$). When $|t'/t|$ is small, as appropriate for ${\rm La_{2-x}Sr_xCuO_4}$, stripes are found, whereas in compounds with larger $|t'/t|$ (such as ${\rm Ca_{2-x}Na_x CuO_2Cl_2}$ and ${\rm Bi_2Sr_2CaCu_2O_{8+δ}}$) checkerboard structures are favored. In contrast to the linear doping dependence found for stripes the charge periodicity of checkerboard textures is locked to 4 unit cells over a …
We consider the scenario where a 4-lattice constant, rotationally symmetric charge density wave (CDW) is present in the underdoped cuprates. We prove a theorem that puts strong constraint on the possible form factor of such a CDW. We demonstrate, within mean-field theory, that a particular form factor within the allowed class describes the angle-resolved photoemission and scan tunneling spectroscopy well. We conjecture that the ``large pseudogap'' in cuprates is the consequence of this type of charge density wave.
We discuss the magnetic excitations of well-ordered stripe and checkerboard phases, including the high energy magnetic excitations of recent interest and possible connections to the "resonance peak" in cuprate superconductors. Using a suitably parametrized Heisenberg model and spin wave theory, we study a variety of magnetically ordered configurations, including vertical and diagonal site- and bond-centered stripes and simple checkerboards. We calculate the expected neutron scattering intensities as a function of energy and momentum. At zero frequency, the satellite peaks of even square-wave s…
We study a periodic polaronic system, which exhibits a nanoscale superlattice structure, as a model for hole-doped cuprates with checkerboard-like heterogeneity, as has been observed recently by scanning tunneling microscopy (STM). Within this model, the electronic and phononic excitations are investigated by applying an unrestricted Hartree-Fock and a random phase approximation (RPA) to a multiband Peierls-Hubbard Hamiltonian in two dimensions.
We investigate the strong influence of the $Θ_{II}$-loop-current order on both unidirectional and bidirectional d-wave charge-density-wave/pair-density-wave (CDW/PDW) composite orders along axial momenta $(\pm Q_0,0)$ and $(0,\pm Q_0)$ that emerge in an effective hot spot model departing from the three-band Emery model relevant to the phenomenology of the cuprate superconductors. This study is motivated by the compelling evidence that the $Θ_{II}$-loop-current order described by this model may explain groundbreaking experiments such as spin-polarized neutron scattering performed in these mater…
The seminal work by Bardeen, Cooper and Schrieffer taken further by Eliashberg to the intermediate coupling solved the problem of conventional superconductors about half a century ago. The Froehlich and Jahn-Teller electron-phonon interactions were identified as an essential piece of physics in all novel superconductors. The BCS theory provides a qualitatively correct description of some of them like magnesium diborade and doped fullerenes (if the polaron formation is taken into account). However, cuprates remain a problem. Here I show that the bipolaron extension of the BCS theory to the stro…
A simple model is proposed as a possible explanation for the checkerboard pattern of modulations in the hole density observed in recent tunneling experiments on underdoped cuprates. Two assumptions are made; first, an enhanced hole density near the acceptor dopants and secondly short range correlations in the positions of these dopants caused by their electrostatic and anisotropic elastic interactions. Together these can lead to a structure factor in qualitative agreement with experiment.
Magneto-oscillations in kinetic and magnetic response functions of a few underdoped cuprates are perhaps one of the most striking observations since many probes of underdoped cuprates clearly point to a non Fermi-liquid normal state. Their observation in the vortex state well below the upper critical field raises a doubt concerning their normal state origin. Here I propose an explanation of the magneto-oscillations as emerging from the quantum interference of the vortex lattice and checkerboard modulations of the electron density of states revealed by STM with atomic resolution in some cuprate…
We investigate the dimensionality of inhomogeneous spin modulation patterns in the cuprate family of high-temperature superconductors with particular focus on 1/8-doped lanthanum cuprates. We compare one-dimensional stripe modulation pattern with two-dimensional checkerboard of spin vortices in the context of nuclear quadrupole resonance(NQR) and muon spin rotation(muSR) experiments. In addition, we also consider the third pattern, a two-dimensional superposition of spin spirals. Overall, we have found that none of the above patterns leads to a consistent interpretation of the two types of exp…
The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that there is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or glob…
In the pseudogap state the spectrum of the autocorrelation of angle resolved photoemission (AC-ARPES) data of Bi2212 presents non-dispersive peaks in momentum space which compare well with those responsible of the checkerboard pattern found in the density of states by Scanning Tunneling Microscopy. This similarity suggests that the checkerboard pattern originates from peaks in the joint density of states, as the dispersive peaks found in the superconducting state do. Here we show that the experimental AC-ARPES spectrum can be reproduced within a model for the pseudogap with no charge-ordering …
The Bogoliubov-de Gennes (BdG) equations are solved in the strong-coupling limit, where real-space (preformed) pairs bose-condense with finite center-of-mass momenta. There are two energy scales in this regime, a temperature independent incoherent gap $Δ_p$ and a temperature dependent coherent gap $Δ_c (T)$, modulated in real space. The single-particle density of states (DOS) reveals checkerboard modulations similar to the tunnelling DOS in cuprates.
Lanthanum family of high-temperature cuprate superconductors is known to exhibit both spin and charge electronic modulations around doping level 1/8. We assume that these modulations have the character of two-dimensional spin-vortex checkerboard and investigate whether this assumption is consistent with the Fermi surface and the pseudogap measured by angle-resolved photo-emission spectroscopy. We also explore the possibility of observing quantum oscillations of transport coefficients in such a background. These investigations are based on a model of non-interacting spin-1/2 fermions hopping on…
We discuss recent elastic neutron scattering and scanning tunneling experiments on high-T_c cuprates exposed to an applied magnetic field. In particular we show that a physical picture consisting of antiferromagnetic vortex cores operating as pinning centers for surrounding stripes is qualitatively consistent with the neutron data provided the stripes have the usual antiphase modulation. Further, we calculate the electronic structure in such a region using a T-matrix method, and find a checkerboard interference pattern consistent with recent scanning tunneling experiments.
Within a Green's function formalism we calculate the electronic structure around static extended magnetic and non-magnetic perturbations in a d-wave superconductor. In partucular, we discuss recent elastic neutron scattering and scanning tunneling experiments on High-T_c cuprates exposed to an applied magnetic field. A physical picture consisting of antiferromagnetic vortex cores operating as pinning centers for surrounding stripes is qualitatively consistent with the neutron data provided the stripes have the usual antiphase modulation. The low energy electronic structure in such a region rev…
In two dimensions, quenched disorder always rounds transitions involving the breaking of spatial symmetries so, in practice, it can often be difficult to infer what form the symmetry breaking would take in the ``ideal,'' zero disorder limit. We discuss methods of data analysis which can be useful for making such inferences, and apply them to the problem of determining whether the preferred order in the cuprates is ``stripes'' or ``checkerboards.'' In many cases we show that the experiments clearly indicate stripe order, while in others (where the observed correlation length is short), the answ…
We study charge ordered d-wave resonating valence bond states (dRVB) in the doped cuprates, and estimate the energies of these states in a generalized $t-J $ model by using a renormalized mean field theory. The long range Coulomb potential tends to modulate the charge density in favor of the charge ordered RVB state. The possible relevance to the recently observed $4 \times 4$ checkerboard patterns in tunnelling conductance in high $T_c$ cuprates is discussed.
In this paper, we show that the theory of high $T_c$ superconductivity based on a microscopic model with $d$-density wave (DDW) scenario in the pseudogap phase is able to reproduce some of the most important features of the recent experimentally discovered hidden charge order in several families of Cuprates. In particular, by computing and comparing energies of charge orders of different modulation directions derived from a full microscopic theory with $d$-density wave scenario, the axial charge order $ϕ_{X(Y)}$ with wavevector $\mathbf{Q}=(Q_0,0)((0,Q_0))$ is shown to be unambiguously energet…
Motivated by recent neutron scattering and scanning tunneling microscopy (STM) experiments on cuprate superconductors, we discuss charge-ordered states, in particular with two-dimensional charge modulation patterns, co-existing with superconductivity. We extend previous studies of a large-N mean-field formulation of the t-J model. In addition to bond-centered superconducting stripe states at low doping, we find checkerboard-modulated superconducting states which are favorable in an intermediate doping interval. We also analyze the energy dependence of the Fourier component of the local density…
Based on the newly developed real-space spin-parallel pairing and superconducting theory, we explore a simple explanation for the observed checkerboard patterns in hole-doped Ca{2-x}Na{x}CuO{2}Cl{2} cuprate superconductor. At a hole concentration x=1/8=0.125, the analytical results show that there exists a phase competition between non-superconducting 4a*4b (a=b) checkerboard phase and 8a*2c superconducting vortex phase, where a, b and c are the lattice constants of the superconductor. At a lower hole concentration x=1/16=0.0625, it is revealed that the metastable 4\sqrt{2}a*4\sqrt{2}a checker…
We study inhomogeneous states in the t-J model using an unrestricted Gutzwiller approximation. We find that $pa\times pa$ checkerboard order, where $p$ is a doping dependent number, emerges from Fermi surface instabilities of both the staggered flux phase and the Fermi liquid state with realistic band parameters. In both cases, the checkerboard order develops at wave vectors $(\pm 2π/pa,0)$, $(0,\pm2π/pa)$ that are tied to the peaks of the wave-vector dependent susceptibility, and is of the Lomer-Rice-Scott type. The properties of such periodic, inhomogeneous states are discussed in connection…
Strong electron-phonon interactions in cuprates and other high-temperature superconductors have gathered support over the last decade in a large number of experiments. Here I briefly introduce the Froehlich-Coulomb multi-polaron model of high-temperature superconductivity, which includes strong on-site repulsive correlations and the long-range Coulomb and electron-phonon (e-ph) interactions. Our extension of the BCS theory to the strong-coupling regime with the long-range \emph{unscreened} electron-phonon interaction could naturally explain the isotope effects, unconventional thermomagnetic tr…
Spatial 4a x 4a modulations, with a the lattice constant of CuO_2 planes, or the so called checkerboards can arise from double-Q spin density wave (SDW) with Q_1 = (pm pi/a, pm 3 pi/4a) and Q_2 = (pm 3 pi/4a, pm pi/a). When multi-Q pair density wave, that is, the condensation of d gamma-wave Cooper pairs with zero total momenta, pm 2Q_1, pm 2Q_2, pm 4Q_1, pm 4Q_2, and so on is induced by the SDW, gaps can have fine structures similar to those of the so called zero-temperature pseudogaps.
We discuss the effects of quenched disorder on a model of charge density wave (CDW) ordering on the square lattice. Our model may be applicable to the cuprate superconductors, where a random electrostatic potential exists in the CuO2 planes as a result of the presence of charged dopants. We argue that the presence of a random potential can affect the unidirectionality of the CDW order, characterized by an Ising order parameter. Coupling to a unidirectional CDW, the random potential can lead to the formation of domains with 90 degree relative orientation, thus tending to restore the rotational …
A central question in the high temperature cuprate superconductors is the fate of the parent Mott insulator upon charge doping. Here we use scanning tunneling microscopy to investigate the local electronic structure of lightly doped cuprate in the antiferromagnetic insulating regime. We show that the doped charge induces a spectral weight transfer from the high energy Hubbard bands to the low energy in-gap states. With increasing doping, a V-shaped density of state suppression occurs at the Fermi level, which is accompanied by the emergence of checkerboard charge order. The new STM perspective…
We present a phenomenological model that describes the low energy electronic structure of the cuprate high temperature superconductor Bi2Sr2CaCu2O8+x as observed by Spectroscopic Imagining Scanning Tunneling Microscopy (SI-STM). Our model is based on observations from Quasiparticle Interference (QPI) measurements and Local Density of States (LDOS) measurements that span a range of hole densities from critical doping, p~0.19, to extremely underdoped, p~0.06. The model presented below unifies the spectral density of states observed in QPI studies with that of the LDOS. In unifying these two sepa…
We propose that the inhomogeneous patterns seen by STM in some underdoped superconducting cuprates could be related to a bond-order-wave instability of the staggered flux state, one of the most studied "normal" state proposed to compete with the d-wave RVB superconductor. A checkerboard pattern is obtained by a Gutzwiller renormalized mean-field theory of the t-J model for doping around 1/8. It is found that the charge modulation is always an order of magnitude smaller than the bond-order modulations. This is confirmed by an exact optimization of the wavefunction by a variational Monte Carlo s…
A d-wave superconductor, subject to strong phase fluctuations, is known to suffer an antiferromagnetic instability closely related to the chiral symmetry breaking in (2+1)-dimensional quantum electrodynamics (QED3). On the basis of this idea we formulate a "QED3 in a box" theory of local instabilities of a d-wave superconductor in the vicinity of a single pinned vortex undergoing quantum fluctuations around its equilibrium position. As a generic outcome we find an incommensurate 2D spin density wave forming in the neighborhood of a vortex with a concomitant "checkerboard" pattern in the local …
It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice using the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest in both strong and weak coupling regimes. At a given doping, the size of the d-wave order parameter manifests itself directly in the heigh…
The correlation between the condensation energy and the critical temperature is studied within a charge ordered superlattice bilayer model in which pairing is supported by inter-layer Coulomb energy gain (potential energy driven superconductivity).The 2D pair-condensate can be characterized by a charge ordered state with a "checkerboard" like pattern seen by scanning tunneling microscopy.The drop of the c-axis dielectric screening can be the primary source of the condensation energy at optimal doping.We find that Coulomb energy gain occurs along the c-axis, which is proportional to the measure…
One of the key challenges in the field of high-temperature superconductivity is understanding the nature of fermionic quasiparticles. Experiments consistently demonstrate the existence of a second energy scale, distinct from the d-wave superconducting gap, that persists above the transition temperature into the "pseudogap" phase. One common class of models relates this energy scale to the quasiparticle gap due to a competing order, such as the incommensurate "checkerboard" order observed in scanning tunneling microscopy (STM) and resonant elastic X-ray scattering (REXS). In this paper we show …
We analyze the superconducting state and c-axis charge dynamics of cuprates at optimal doping using a charge ordered bilayer superlattice model in which pairing is supported by inter-layer Coulomb energy gain (potential energy driven superconductivity).The 2D pair-condensate can be characterized by a charge ordered state with a "checkerboard" like pattern seen by scanning tunneling microscopy.The pair condensation might lead to the sharp decrease of the normal state c-axis anisotropy of the hole content and hence to the decrease of inter-layer dielectric screening.The decrease of the c-axis di…
We analyze the interplay between charge-density-wave (CDW) and pair-density-wave (PDW) orders within the spin-fermion model for the cuprates. We specifically consider CDW order with transferred momenta $(\pm Q,0)$/$(0,\pm Q)$, and PDW order with total momenta $(0,\pm Q)/(\pm Q,0)$. We show that both emerge in the spin-fermion model near the onset of antiferromagnetism. We further argue that the two orders are nearly degenerate due to an approximate SU(2) particle-hole symmetry of the model. The ${\rm SU}(2)$ symmetry becomes exact if one neglects the curvature of the Fermi surface in hot regio…
We present a theoretical model to show that the transition from an antiferromagnetic (AFM) phase to the $d_{x^2-y^2}$-wave superconductivity occurs through a robust companion of a finite momentum pairing between $({\bf k},\uparrow)$ and $(-{\bf k}-{\bf Q},\downarrow)$ electrons, namely pair-density wave (PDW) state, where ${\bf Q}=(π,π)$ is the AFM wavevector. Interestingly, the spatial structure of the PDW is constrained to be a $p+ip$-wave symmetry, which follows $p_{\bf k}=p_{-{\bf k}-{\bf Q}}$ under fermions exchange in cuprates, dictating a spin-singlet pairing. Furthermore, the PDW state…
A major obstacle in understanding the mechanism of Cooper pairing in the cuprates is the existence of various intertwined orders associated with spin, charge, and Cooper pairs. Of particular importance is the ubiquitous charge order features that have been observed in a variety of cuprates, especially in the underdoped regime of the phase diagram. To explain the origin of the charge order and its implication to the superconducting phase, many theoretical models have been proposed, such as charge stripes, electronic nematicity, and Fermi surface instability. A highly appealing physical picture …
One of the central issues concerning the mechanism of high temperature superconductivity in cuprates is the nature of the ubiquitous charge order and its implications to superconductivity. Here we use scanning tunneling microscopy to investigate the evolution of charge order from the optimally doped to strongly overdoped Bi2Sr2CuO6+δ cuprates. We find that with increasing hole concentration, the long-range checkerboard order gradually evolves into short-range glassy patterns consisting of diluted charge puddles. Each charge puddle has a unidirectional nematic internal structure, and exhibits c…
The hypothesis that holes doped into high-Tc cuprate superconductors organize themselves in two-dimensional (2D) array of diagonal stripes is discussed, and, on the basis of this hypothesis, a new microscopic model of superconductivity is proposed and solved. The model describes two kinds of hole states localized either inside the stripes or in the antiferromagnetic domains between the stripes. The characteristic energy difference between these two kinds of states is identified with the pseudogap. The superconducting (SC) order parameter predicted by the model has two components, whose phases …
Following the early discovery of stripe-like order in La-based copper-oxide superconductors, charge ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between uni- (stripes) and bi-directional (checkerboard) charge order in Y- and Bi-based materials. Here we use resonant x-ray scattering (RXS) to measure the two-dimensional structure factor in YBCO, in reciprocal space. Our data reveal the presence of charge stripe order, i.e. locally unidirectional density waves, suggesting it as the true microscopic nature of charge modulations in cu…
Charge carriers in low-doped semiconductors may distort the atomic lattice and trap themselves forming so-called small polarons. High carrier concentrations can lead to short range ordered polarons (large polarons) and even to long range charge and orbital order. Both systems should be insulating with a large electrical resistivity, which decreases with increasing temperature. However, photoemission measurements recently found a polaronic pseudogap, in a metallic phase of La2-2xSr1+2xMn2O7. This layered manganite is famous for colossal magnetoresistance (CMR) associated with a phase transition…
We introduce and study an XY-type model of thermal and quantum phase fluctuations in a two-dimensional correlated lattice d-wave superconductor based on the QED3 effective theory of high temperature superconductors. General features of and selected results obtained within this model were reported earlier in an abbreviated format (Z. Tesanovic, cond-mat/0405235). The model is geared toward describing not only the long distance but also the intermediate lengthscale physics of underdoped cuprates. In particular, we elucidate the dynamical origin and investigate specific features of the Cooper pai…
We study the timely issue of charge order checkerboard patterns observed in a variety of cuprate superconductors. We suggest a minimal model in which strong quantum fluctuations in the vicinity of a single antiferromagnetic quantum critical point generate the complexity seen in the phase diagram of cuprates superconductors and, in particular, the evidenced charge order. The Fermi surface is found to fractionalize into hotspots and antinodal regions, where physically different gaps are formed. In the phase diagram, this is reflected by three transition temperatures for the formation of pseudoga…
Even though the rare-earth tritellurides are tetragonal materials with a quasi two dimensional (2D) band structure, they have a "hidden" 1D character. The resultant near-perfect nesting of the Fermi surface leads to the formation of a charge density wave (CDW) state. We show that for this band structure, there are two possible ordered phases: A bidirectional "checkerboard" state would occur if the CDW transition temperature were sufficiently low, whereas a unidirectional "striped" state, consistent with what is observed in experiment, is favored when the transition temperature is higher. This …
One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ord…
We find unknown $s$- and $d$-wave amplitudes of the recently discovered charge density wave (CDW) in underdoped cuprates. To do so we perform a combined analysis of experimental data for ortho-II YBa$_2$Cu$_3$O$_{y}$. The analysis includes data on nuclear magnetic resonance, resonant inelastic X-ray scattering, and hard X-ray diffraction. The amplitude of doping modulation found in our analysis is $3.5\cdot 10^{-3}$ in a low magnetic field and $T=60$K, the amplitude is $6.5\cdot 10^{-3}$ in a magnetic field of 30T and $T=1.3$K. The values are in units of elementary charge per unit cell of a Cu…
Intrinsic translational symmetry-breaking charge stripes in underdoped iron pnictides
Tsinghua University（清华大学）；Southern University of Science and Technology（南方科技大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）
Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing which can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here we use SJTM to visualize the interplay of PDW and DSC states in Bi2Sr2CaCu2O8+x at a carrier …
The CuO$_2$ antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E|<$Δ^*$, where $Δ^*$ is the pseudogap energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite Q density-wave (DW) state and a Q=0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these d…
Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we st…
The paper deals with the controversial charge and spin self-organization phenomena in the HTSC cuprates, of which neutron, X-ray, STM and ARPES experiments give complementary, sometimes apparently contradictory glimpses. The examination has been set in the context of the boson-fermion, negative-U understanding of HTSC advocated over many years by the author. Stripe models are developed which are 2q in nature and diagonal in form. For such a geometry to be compatible with the data rests upon both the spin and charge arrays being face-centred. Various special doping concentrations are closely lo…
We investigate the double layered Sr$_{3}$(Ru$_{1-x}$Mn$_{x}$)$_{2}$O$_{7}$ and its doping-induced quantum phase transition (QPT) from a metal to an antiferromagnetic (AFM) Mott insulator. Using spectroscopic imaging with the scanning tunneling microscope (STM), we visualize the evolution of the electronic states in real- and momentum-space. We find a partial-gap in the tunneling density of states at the Fermi energy (E$_{F}$) that develops with doping to form a weak Mott insulating (Δ ~ 100meV) state. Near the QPT, we discover a spatial electronic reorganization into a commensurate checkerboa…
The path from a Mott insulating phase to high temperature superconductivity encounters a rich set of unconventional phenomena involving the insulator-to-metal transition (IMT) such as emergent electronic orders and pseudogaps that ultimately affect the condensation of Cooper pairs. A huge hindrance to understanding the origin of these phenomena in the curates is the difficulty in accessing doping levels near the parent state. Recently, the J$_{eff}$=1/2 Mott state of the perovskite strontium iridates has revealed intriguing parallels to the cuprates, with the advantage that it provides unique …
