Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O(8+delta)

From a single-band metal to a high-temperature superconductor via two thermal phase transitions

The nature of the pseudogap phase of cuprate high-temperature superconductors is a major unsolved problem in condensed matter physics. We studied the commencement of the pseudogap state at temperature T* using three different techniques (angle-resolved photoemission spectroscopy, polar Kerr effect, and time-resolved reflectivity) on the same optimally doped Bi2201 crystals. We observed the coincident, abrupt onset at T* of a particle-hole asymmetric antinodal gap in the electronic spectrum, a Kerr rotation in the reflected light polarization, and a change in the ultrafast relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (T(c)), entangled in an energy-momentum-dependent manner with the preexisting pseudogap features, ushering in a ground state with coexisting orders.

Fluctuating stripes at the onset of the pseudogap in the high-T(c) superconductor Bi(2)Sr(2)CaCu(2)O(8+x)

Doped Mott insulators have a strong propensity to form patterns of holes and spins often referred to as stripes. In copper oxides, doping also gives rise to the pseudogap state, which can be transformed into a high-temperature superconducting state with sufficient doping or by reducing the temperature. A long-standing issue has been the interplay between the pseudogap, which is generic to all hole-doped copper oxide superconductors, and stripes, whose static form occurs in only one family of copper oxides over a narrow range of the phase diagram. Here we report observations of the spatial reorganization of electronic states with the onset of the pseudogap state in the high-temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+x), using spectroscopic mapping with a scanning tunnelling microscope. We find that the onset of the pseudogap phase coincides with the appearance of electronic patterns that have the predicted characteristics of fluctuating stripes. As expected, the stripe patterns are strongest when the hole concentration in the CuO(2) planes is close to 1/8 (per copper atom). Although they demonstrate that the fluctuating stripes emerge with the onset of the pseudogap state and occur over a large part of the phase diagram, our experiments indicate that the stripes are a consequence of pseudogap behaviour rather than its cause.

Mesoscopic percolating resistance network in a strained manganite thin film

Many unusual behaviors in complex oxides are deeply associated with the spontaneous emergence of microscopic phase separation. Depending on the underlying mechanism, the competing phases can form ordered or random patterns at vastly different length scales. By using a microwave impedance microscope, we observed an orientation-ordered percolating network in strained Nd(1/2)Sr(1/2)MnO3 thin films with a large period of 100 nanometers. The filamentary metallic domains align preferentially along certain crystal axes of the substrate, suggesting the anisotropic elastic strain as the key interaction in this system. The local impedance maps provide microscopic electrical information of the hysteretic behavior in strained thin film manganites, suggesting close connection between the glassy order and the colossal magnetoresistance effects at low temperatures.

Model of quasiparticles coupled to a frequency-dependent charge-density-wave order parameter in cuprate superconductors

We investigate a model where superconducting electrons are coupled to a frequency dependent charge-density wave order parameter Delta_{r}(omega). Our approach can reconcile the simultaneous existence of low-energy Bogoljubov quasiparticles and high energy electronic order as observed in scanning tunneling microscopy (STM) experiments. The theory accounts for the contrast reversal in the STM spectra between positive and negative bias observed above the pairing gap. An intrinsic relation between scattering rate and inhomogeneities follows naturally.

Impurity-induced frustration in correlated oxides

Using the example of Zn-doped La2CuO4, we demonstrate that a spinless impurity doped into a nonfrustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The proposed mechanism should be common to other correlated oxides.

Visualizing pair formation on the atomic scale and the search for the mechanism of superconductivity in high-T(c) cuprates

We have developed several new experimental techniques, based on the scanning tunneling microscope, to visualize the process of pair formation on the atomic scale and to probe with high precision what controls the strength of pairing in high-T(c) cuprate superconductor compounds. These new experiments provide evidence that pairing in these exotic superconductors occurs above the bulk transition temperature and in nanoscale regions with sizes of 1-3 nm. The high temperature nucleation and proliferation of these nanoscale puddles have a strong connection to the temperature-doping phase diagram of these superconductors. On average we have found that the pairing gap Δ and the temperature at which they first nucleate T(p) follow the simple relation: 2Δ/k(B)T(p)∼8. Moreover, the variations of the pairing strength on the nanoscale can be examined to find microscopic clues to the mechanism of pairing. Specifically, we have found evidence that suggests that strong electronic correlation, as opposed to coupling of electrons to bosons, is responsible for the pairing mechanism in the cuprates. Surprisingly, we have found that nanoscale measurements of electronic correlations in the normal state (at temperatures as high as twice T(c)) can be used to predict the strength of the local pairing interaction at low temperatures.

Valence bond glass theory of electronic disorder and the pseudogap state of high-temperature cuprate superconductors

We show that the low-energy fluctuations of the valence bond due to the superexchange are pinned by the electronic disorder from off-stoichiometric dopants, leading to a valence bond glass (VBG) pseudogap phase in underdoped high-T_{c} cuprates. The antinodal Fermi surface sections are gapped out, giving rise to a normal state Fermi arc whose length shrinks with underdoping. Below T_{c}, the superexchange interaction induces a d-wave superconducting gap that coexists with the VBG pseudogap. The evolution of the local and momentum-space spectroscopy with doping and temperature captures the salient properties of the pseudogap phenomena and the electronic disorder.

Coexistence of competing orders with two energy gaps in real and momentum space in the high temperature superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}

Through a combined scanning tunneling microscopy and angle-resolved photoemission spectroscopy study, we report the observation of two distinct gaps (a small and a large gap) that coexist both in real space and in the antinodal region of momentum space, below the superconducting transition temperature (T_{c}) of Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}. We show that the small gap is associated with superconductivity. The large-gap persists above T_{c}, and seems linked to observed charge ordering. We find a strong correlation between the large and small gaps suggesting that they are affected by similar physical processes.

Disorder-induced stabilization of the pseudogap in strongly correlated systems

The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two nonperturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and quantum Monte Carlo simulations. We find distinctive evidence for a zero-energy anomaly which is robust upon variation of doping, disorder, and interaction strength. Its similarities to, and differences from, pseudogap formation in other contexts, including perturbative treatments of interactions and disorder, classical theories of localized charges, and in the clean Hubbard model, are discussed.

Local density of states of one-dimensional Mott insulators and charge-density wave states with a boundary

We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.

Scanning Josephson tunneling microscopy of single-crystal Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} with a conventional superconducting tip

We have performed both Josephson and quasiparticle tunneling in vacuum tunnel junctions formed between a conventional superconducting scanning tunneling microscope tip and overdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} single crystals. A Josephson current is observed with a peak centered at a small finite voltage due to the thermal-fluctuation-dominated superconducting phase dynamics. Josephson measurements at different surface locations yield local values for the Josephson I_{C}R_{N} product. Corresponding energy gap measurements were also performed and a surprising inverse correlation was observed between the local I_{C}R_{N} product and the local energy gap.

Band-structure engineering of gold atomic wires on silicon by controlled doping

We report on the systematic tuning of the electronic band structure of atomic wires by controlling the density of impurity atoms. The atomic wires are self-assembled on Si(111) by substitutional gold adsorbates and extra silicon atoms are deposited as the impurity dopants. The one-dimensional electronic band of gold atomic wires, measured by angle-resolved photoemission, changes from a fully metallic to semiconducting one with its band gap increasing above 0.3 eV along with an energy shift as a linear function of the Si dopant density. The gap opening mechanism is suggested to be related to the ordering of the impurities.

Effect of a single localized impurity on the local density of States in monolayer and bilayer graphene

We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in monolayer and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.

Proposed design of a Josephson diode

We propose a new type of Josephson junction formed by two superconductors close to the superconductor-Mott-insulator transition, one of which is doped with holes and the other is doped with electrons. A self-organized Mott-insulating depletion region is formed at the interface between two superconductors, giving rise to an asymmetric response of current to the external voltage. The collective excitations of the depletion region result in a novel phase dynamics that can be measured experimentally in the noise spectrum of the Josephson current.

Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+δ

Pairing of electrons in conventional superconductors occurs at the superconducting transition temperature T(c), creating an energy gap Delta in the electronic density of states (DOS). In the high-T(c) superconductors, a partial gap in the DOS exists for a range of temperatures above T(c) (ref. 2). A key question is whether the gap in the DOS above T(c) is associated with pairing, and what determines the temperature at which incoherent pairs form. Here we report the first spatially resolved measurements of gap formation in a high-T(c) superconductor, measured on Bi2Sr2CaCu2O8+delta samples with different T(c) values (hole concentration of 0.12 to 0.22) using scanning tunnelling microscopy. Over a wide range of doping from 0.16 to 0.22 we find that pairing gaps nucleate in nanoscale regions above T(c). These regions proliferate as the temperature is lowered, resulting in a spatial distribution of gap sizes in the superconducting state. Despite the inhomogeneity, we find that every pairing gap develops locally at a temperature T(p), following the relation 2Delta/k(B)T(p) = 7.9 +/- 0.5. At very low doping (< or =0.14), systematic changes in the DOS indicate the presence of another phenomenon, which is unrelated and perhaps competes with electron pairing. Our observation of nanometre-sized pairing regions provides the missing microscopic basis for understanding recent reports of fluctuating superconducting response above T(c) in hole-doped high-T(c) copper oxide superconductors.

The Ground State of the Pseudogap in Cuprate Superconductors

We present studies of the electronic structure of La(2-x)BaxCuO4, a system where the superconductivity is strongly suppressed as static spin and charge orders or "stripes" develop near the doping level of x = (1/8). Using angle-resolved photoemission and scanning tunneling microscopy, we detect an energy gap at the Fermi surface with magnitude consistent with d-wave symmetry and with linear density of states, vanishing only at four nodal points, even when superconductivity disappears at x = (1/8). Thus, the nonsuperconducting, striped state at x = (1/8) is consistent with a phase-incoherent d-wave superconductor whose Cooper pairs form spin-charge-ordered structures instead of becoming superconducting.

Quantum control mechanism analysis through field based Hamiltonian encoding

Optimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding (HE) has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlled system. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schrodinger's equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment.

Interface controlled electronic charge inhomogeneities in correlated heterostructures

For heterostructures of ultrathin, strongly correlated copper-oxide films and dielectric perovskite layers, we predict inhomogeneous electronic interface states. Our study is based on an extended Hubbard model for the cuprate film. The interface is implemented by a coupling to the electron and phonon degrees of freedom of the dielectric oxide layer. We find that electronic ordering in the film is associated with a strongly inhomogeneous polaron effect. We propose to consider the interfacial tuning as a powerful mechanism to control the charge ordering in correlated electronic systems.

Spin excitations in fluctuating stripe phases of doped cuprate superconductors

Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.

Local atomic structure and discommensurations in the charge density wave of CeTe3

The local structure of in the incommensurate charge density wave (IC-CDW) state has been obtained using atomic pair distribution function analysis of x-ray diffraction data. Local atomic distortions in the Te nets due to the CDW are larger than observed crystallographically, resulting in distinct short and long Te-Te bonds. Observation of different distortion amplitudes in the local and average structures is explained by the discommensurated nature of the CDW, since the pair distribution function is sensitive to the local displacements within the commensurate regions, whereas the crystallographic result averages over many discommensurated domains. The result is supported by STM data. This is the first quantitative local structural study within the commensurate domains in an IC-CDW system.

Nondispersive fermi arcs and the absence of charge ordering in the pseudogap phase of Bi2Sr2CaCu2O8+delta

The autocorrelation of angle resolved photoemission data from the high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta) shows distinct peaks in momentum space which disperse with binding energy in the superconducting state, but not in the pseudogap phase. Although it is tempting to attribute a nondispersive behavior in momentum space to charge ordering, a deconstruction of the autocorrelation reveals that the nondispersive peaks arise from the tips of the Fermi arcs, which themselves do not change with binding energy.

Structural matters in HTSC: the origin and form of stripe organization and checkerboarding

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 2-q 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 looked at, in particular p = 0.1836 or 9/49, which is associated with the maximization of the superconducting condensation energy and the termination of the pseudogap regime. The stripe models are dictated by real space organization of the holes, whereas the dispersionless checkerboarding is interpreted in terms of correlation driven collapse of normal Fermi surface behaviour and response functions. The incommensurate spin diffraction below the 'resonance energy' is seen as in no way expressing spin-wave physics or Fermi surface nesting, but is driven by charge and strain (Jahn-Teller) considerations, and it stands virtually without dispersion. The apparent dispersion comes from the downward dispersion of the resonance peak, and the growth of a further incoherent commensurate peak pursuant upon the falling level of charge stripe organization under excitation.

Laser based angle-resolved photoemission, the sudden approximation, and quasiparticle-like spectral peaks in Bi2Sr2CaCu2O(8+delta)

A new low photon energy regime of angle-resolved photoemission spectroscopy is accessed with lasers and used to study the high T(C) superconductor Bi2Sr2CaCu2O(8+delta). The low energy increases bulk sensitivity, reduces background, and improves resolution. With this we observe spectral peaks which are sharp on the scale of their binding energy--the clearest evidence yet for quasiparticles in the normal state. Crucial aspects of the data such as the dispersion, superconducting gaps, and the bosonic coupling kink are found to be robust to a possible breakdown of the sudden approximation.

Nuclear-magnetic-resonance evidence for charge inhomogeneity in stripe ordered La(1.8-x)Eu0.2Sr(x)CuO4

We report 17O nuclear-magnetic-resonance (NMR) results in the stripe ordered La(1.8-x)Eu0.2Sr(x)CuO4 system. Below a temperature T(q) approximately 80 K, the local electric field gradient and the absolute intensity of the NMR signal of the planar O site exhibit a dramatic decrease. We interpret these results as microscopic evidence for a spatially inhomogeneous charge distribution, where the NMR signal from O sites in the domain walls of the spin density modulation are wiped out due to large hyperfine fields, and the remaining signal arises from the intervening Mott insulating regions.

Gap-inhomogeneity-induced electronic states in superconducting Bi2Sr2CaCu2O(8+delta)

In this Letter, we analyze, using scanning tunneling spectroscopy, the density of electronic states in nearly optimally doped Bi2Sr2CaCu2O(8+delta) in zero magnetic field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a 2xi0 x 2xi0 patch with an enhanced or suppressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.

Electronic inhomogeneity and breakdown of the universal thermal conductivity of cuprate superconductors

We report systematic, high-precision measurements of the low-T (down to 70 mK) thermal conductivity kappa of YBa2Cu3O(y), La(2-x)Sr(x)CuO4, and Bi2Sr2CaCu2O(8+delta). Careful examinations of the Zn- and hole-doping dependences of the residual thermal conductivity kappa0/T, as well as the in-plane anisotropy of kappa0/T in Bi2Sr2CaCu2O(8+delta), indicate a breakdown of the universal thermal conductivity, a notable theoretical prediction for d-wave superconductors. Our results point to an important role of electronic inhomogeneities, which are not considered in the standard perturbation theory for thermal conductivity, in the underdoped to optimally doped regime.

Fourfold structure of vortex-core states in Bi2Sr2CaCu2O8+delta

We present a detailed study of vortex-core spectroscopy in slightly overdoped Bi2Sr2CaCu2O8+delta using a low-temperature scanning tunneling microscope. Inside the vortex core, we observe a fourfold symmetric modulation of the local density of states with an energy-independent period of (4.3 +/- 0.3)a0. Furthermore, we demonstrate that this square modulation is related to the vortex-core states which are located at +/-6 meV. Since the core-state energy is proportional to the superconducting gap magnitude , our results strongly suggest the existence of a direct relation between the superconducting state and the local electronic modulations in the vortex core.

Visualization of localized holes in manganite thin films with atomic resolution

The magnetic and transport behaviors of manganites are critically related to the spatial distribution and correlation of doped holes. Using in situ scanning tunneling microscopy, we have imaged both occupied and unoccupied states simultaneously in a hole-doped (La(5/8-0.3)Pr0.3)Ca(3/8)MnO3 epitaxial thin film grown by laser molecular beam epitaxy. Doped holes localized on Mn4+ ion sites were directly observed with atomic resolution in the paramagnetic state at room temperature. In contrast to a random distribution, these doped holes show strong short-range correlation and clear preference of forming nanoscale CE-type charge-order-like clusters. The results provide direct visualization of the nature of intriguing electronic inhomogeneity in transition metal oxides.

Doped Mott insulators are insulators: hole localization in the cuprates

We demonstrate that a Mott insulator lightly doped with holes is still an insulator at low temperature even without disorder. Hole localization obtains because the chemical potential lies in a pseudogap which has a vanishing density of states at zero temperature. The energy scale for the pseudogap is set by the nearest-neighbor singlet-triplet splitting. As this energy scale vanishes if transitions, virtual or otherwise, to the upper Hubbard band are not permitted, the fundamental length scale in the pseudogap regime is the average distance between doubly occupied sites. Consequently, the pseudogap is tied to the noncommutativity of the two limits U-->infinity (U the on-site Coulomb repulsion) and L -->infinity (the system size).

Synthesis, structure, and magnetic properties of the layered copper(II) oxide Na2Cu2TeO6

A new quaternary layered transition-metal oxide, Na2Cu2TeO6, has been synthesized under air using stoichiometric (with respect to the cationic elements) mixtures of Na2CO3, CuO, and TeO2. Na2Cu2TeO6 crystallizes in the monoclinic space group C2/m with a = 5.7059(6) A, b = 8.6751(9) A, c = 5.9380(6) A, beta = 113.740(2) degrees, V = 269.05(5) A3, and Z = 2, as determined by single-crystal X-ray diffraction. The structure is composed of infinity(2)[Cu2TeO6] layers with the Na atoms located in the octahedral voids between the layers. Na2Cu2TeO6 is a green nonmetallic compound, in agreement with the electronic structure calculation and electrical resistance measurement. The magnetic susceptibility shows Curie-Weiss behavior between 300 and 600 K with an effective moment of 1.85(2) muB/Cu(II) and theta(c) = -87(6) K. A broad maximum at 160 K is interpreted as arising from short-range one-dimensional antiferromagnetic correlations. With the aid of the technique of magnetic dimers, the short-range order was analyzed in terms of an alternating chain model, with the surprising result that the stronger intrachain coupling involves a super-superexchange pathway with a Cu-Cu separation of >5 A. The J2/J1 ratio within the alternating chain refined to 0.10(1), and the spin gap is estimated to be 127 K.

Charge-fluctuation contribution to the Raman response in superconducting cuprates

We calculate the Raman response contribution due to soft collective modes, finding a strong dependence on the photon polarizations and on the characteristic wave vectors of the modes. We compare our results with recent Raman spectroscopy experiments in underdoped cuprates, La2-xSrxCuO4 and (Y1.97Ca0.3)Ba2CuO6.05, where anomalous low-energy peaks are observed, which soften upon lowering the temperature. We show that the specific dependence on doping and on photon polarizations of these peaks can naturally arise from charge collective excitations at finite wavelength.

Dynamical properties of charged stripes in La2-xSrxCuO4

Inelastic light-scattering spectra of underdoped La2-xSrxCuO4 single crystals are presented which provide direct evidence of the formation of quasi-one-dimensional charged structures in the two-dimensional CuO2 planes. The stripes manifest themselves in a Drude-like peak at low energies and temperatures. The selection rules allow us to determine the orientation to be along the diagonals at x=0.02 and along the principal axes at x=0.10. The electron-lattice interaction determines the correlation length which turns out to be larger in compound classes with lower superconducting transition temperatures. Temperature is the only scale of the response at different doping levels demonstrating the importance of quantum critical behavior.

Complexity in Strongly Correlated Electronic Systems

A wide variety of experimental results and theoretical investigations in recent years have convincingly demonstrated that several transition metal oxides and other materials have dominant states that are not spatially homogeneous. This occurs in cases in which several physical interactions-spin, charge, lattice, and/or orbital-are simultaneously active. This phenomenon causes interesting effects, such as colossal magnetoresistance, and it also appears crucial to understand the high-temperature superconductors. The spontaneous emergence of electronic nanometer-scale structures in transition metal oxides, and the existence of many competing states, are properties often associated with complex matter where nonlinearities dominate, such as soft materials and biological systems. This electronic complexity could have potential consequences for applications of correlated electronic materials, because not only charge (semiconducting electronic), or charge and spin (spintronics) are of relevance, but in addition the lattice and orbital degrees of freedom are active, leading to giant responses to small perturbations. Moreover, several metallic and insulating phases compete, increasing the potential for novel behavior.

Magic doping fractions for high-temperature superconductors

We report hole-doping dependence of the in-plane resistivity rho(ab) in a cuprate superconductor La(2-x)Sr(x)CuO4, carefully examined using a series of high-quality single crystals. Our detailed measurements find a tendency towards charge ordering at particular rational hole-doping fractions of 1/16, 3/32, 1/8, and 3/16. This observation appears to suggest a specific form of charge order and is most consistent with the recent theoretical prediction of the checkerboard-type ordering of the Cooper pairs at rational doping fractions x = (2m+1)/2n, with integers m and n.

Coincidence of checkerboard charge order and antinodal state decoherence in strongly underdoped superconducting Bi2Sr2CaCu2O8 + delta)

The doping dependence of nanoscale electronic structure in superconducting Bi(2)Sr(2)CaCu(2)O(8 + delta) is studied by scanning tunneling microscopy. At all dopings, the low energy density-of-states modulations are analyzed according to a simple model of quasiparticle interference and found to be consistent with Fermi-arc superconductivity. The superconducting coherence peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping and a new spectral type appears. Exclusively in regions exhibiting this new spectrum, we find local "checkerboard" charge ordering of high energy states, with a wave vector of Q = (+/- 2pi/4.5a(0),0); (0, +/- 2pi/4.5a(0)) +/- 15%. Surprisingly, this spatial ordering of high energy states coexists harmoniously with the low energy Bogoliubov quasiparticle states.

Nodal quasiparticles and antinodal charge ordering in Ca2-xNaxCuO2Cl2

Understanding the role of competing states in the cuprates is essential for developing a theory for high-temperature superconductivity. We report angle-resolved photoemission spectroscopy experiments which probe the 4a0 x 4a0 charge-ordered state discovered by scanning tunneling microscopy in the lightly doped cuprate superconductor Ca2-xNaxCuO2Cl2. Our measurements reveal a marked dichotomy between the real- and momentum-space probes, for which charge ordering is emphasized in the tunneling measurements and photoemission is most sensitive to excitations near the node of the d-wave superconducting gap. These results emphasize the importance of momentum anisotropy in determining the complex electronic properties of the cuprates and places strong constraints on theoretical models of the charge-ordered state.

Charge modulation, spin response, and dual Hofstadter butterfly in high-Tc cuprates

The modulated density of states observed in recent STM experiments in underdoped cuprates is argued to be a manifestation of the charge-density wave of Cooper pairs (CPCDW). CPCDW formation is due to superconducting phase fluctuations enhanced by Mott-Hubbard correlations near half-filling. The physics behind the CPCDW is related to a Hofstadter problem in a dual superconductor. It is shown that CPCDW does not impact nodal fermions at the leading order. An experiment is proposed to probe coupling of the CPCDW to the spin carried by nodal quasiparticles.

Role of spin in quasiparticle interference

Quasiparticle interference patterns measured by scanning tunneling microscopy can be used to study the local electronic structure of metal surfaces and high-temperature superconductors. Here, we show that even in nonmagnetic systems the spin of the quasiparticles can have a profound effect on the interference patterns. On Bi(110), where the surface state bands are not spin degenerate, the patterns are not related to the dispersion of the electronic states in a simple way. In fact, the features which are expected for the spin-independent situation are absent and the observed interference patterns can be interpreted only by taking spin-conserving scattering events into account.

Pair density wave in the pseudogap state of high temperature superconductors

Recent scanning tunneling microscopy experiments of Bi(2)Sr(2)CaCu(2)O(8+delta) have shown evidence of real-space organization of electronic states at low energies in the pseudogap state [Science 303, 1995 (2004)]]. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper pairs without global phase coherence. We show that scanning tunneling microscopy measurements can distinguish a pair density wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an on site periodic potential.

Electronic transport in underdoped YBa2Cu3O7-delta nanowires: evidence for fluctuating domain structures

We have measured the transport properties of a series of underdoped YBa(2)Cu(3)O(7-delta) nanowires fabricated with widths of 100-250 nm. We observe large telegraphlike fluctuations in the resistance between the pseudogap temperature T* and the superconducting transition temperature T(c), consistent with the formation and dynamics of a domain structure. We also find anomalous hysteretic steps in the current-voltage characteristics well below T(c).

A ‘checkerboard’ electronic crystal state in lightly hole-doped Ca2-xNaxCuO2Cl2

The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the 'pseudogap' regime. This regime is rich in peculiar electronic phenomena, prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca2-xNaxCuO2Cl2. Tunnelling spectroscopy (at energies |E| > 100 meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for |E| < 100 meV, the spectrum exhibits a V-shaped energy gap centred on E = 0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO2-unit-cell square 'checkerboard', independent of energy. Intricate atomic-scale electronic structure variations also exist within the checkerboard. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca2-xNaxCuO2Cl2.