Scanning tunneling microscopy/spectroscopy (STM/STS) measurements were carried out on a multi-layered cuprate superconductor Ba$_2$Ca$_5$Cu$_6$O$_{12}$(O$_{1-x}$,F$_x$)$_2$. STM topography revealed random spot structures with the characteristic length $\le 0.5$ nm. The conductance spectra dI/dV(V) show the coexistence of smaller gaps $Δ_S$ and large gaps (pseudogaps) $Δ_L$. The pseudogap-related features in the superconducting state were traced with the spatial resolution of $\sim$ 0.07 nm. Here, $I$ and $V$ are the tunnel current and bias voltage, respectively. The temperature, $T$, dependence of $Δ_S$ follows the reduced Bardeen-Cooper-Schrieffer (BCS) dependence. The hallmark ratio 2$Δ_{S}(T=0)/k_B T_c$ equals to 4.9, which is smaller than those of other cuprate superconductors. Here, $T_c$ is the superconducting critical temperature and $k_B$ is the Boltzmann constant. The larger gap $Δ_L$ survives in the normal state and even increases with $T$ above $T_c$. The $T$ dependences of the spatial distributions for both relevant gaps ($Δ$ map), as well as for each gap separately ($Δ_S$ and $Δ_L$) were obtained. From the histogram of $Δ$ map, the averaged gap values were found to be $\bar Δ_S = \sim 24$ meV and $\bar Δ_L = \sim 79$ meV. The smaller gap $Δ_S$ shows a spatially homogeneous distribution while the larger gap $Δ_L$ is quite inhomogeneous, indicating that rather homogeneous superconductivity coexists with the patchy distributed pseudogap. The spatial variation length $ξ_{Δ_L}$ of $Δ_L$ correlates with the scale of the topography spot structures, being approximately 0.4 nm. This value is considerably smaller than the coherence length of this class of superconductors, suggesting that $Δ_L$ is strongly affected by the disorder of the apical O/F.
When combining the BCS expression of Tc with a shear modulus constant model, we can demonstrate that Tc oscillates depending on the number of the cuprate planes and that it reaches its first maximum for three planes. This is in good agreement with experimental data and suggests that the electron- phonon coupling is essential to the superconductivity of the cuprates.
We report that planar CuO_2 hole densities in high-T_c cuprates are consistently determined by the Cu-NMR Knight shift. In single- and bi-layered cuprates, it is demonstrated that the spin part of the Knight shift K_s(300 K) at room temperature monotonically increases with the hole density $p$ from underdoped to overdoped regions, suggesting that the relationship of K_s(300 K) vs. p is a reliable measure to determine p. The validity of this K_s(300 K)-p relationship is confirmed by the investigation of the p-dependencies of hyperfine magnetic fields and of spin susceptibility for single- and b…
We propose a mechanism for high critical temperature (T_c) in the coexistent phase of superconducting- (SC) and antiferromagnetic (AF) CuO_2 planes in multilayered cuprates. The Josephson coupling between the SC planes separated by an AF insulator (Mott insulator) is calculated perturbatively up to the fourth order in terms of the hopping integral between adjacent CuO_2 planes. It is shown that the AF exchange splitting in the AF plane suppresses the so-called pi-Josephson coupling, and the long-ranged 0-Josephson coupling leads to coexistence with a rather high value of T_c.
We study doping dependence of interlayer hoppings, t_\perp, in multilayered cuprates with four or more CuO_2 planes in a unit cell. When the double occupancy is forbidden in the plane, an effective amplitude of t_\perp in the Gutzwiller approximation is shown to be proportional to the square root of the product of doping rates in adjacent two planes, i.e., t^eff_\perp \propto t_\perp \sqrt{δ_1δ_2}, where δ_1 and δ_2 represent the doping rates of the two planes. More than three-layered cuprates have two kinds of \cuo planes, i.e., inner- and outer planes (IP and OP), resulting in two different …
Quasiparticle tunneling spectra of both hole-doped (p-type) and electron-doped (n-type) cuprates are studied using a low-temperature scanning tunneling microscope. The results reveal that neither the pairing symmetry nor the pseudogap phenomenon is universal among all cuprates, and that the response of n-type cuprates to quantum impurities is drastically different from that of the p-type cuprates. The only ubiquitous features among all cuprates appear to be the strong electronic correlation and the nearest-neighbor antiferromagnetic Cu^{2+}-Cu^{2+} coupling in the CuO_2 planes.
We report the pressure effect in Bi2Sr2Ca2Cu3O10+δ (Bi-2223) single crystal with a small amount of intergrowth of Bi2Sr2CaCu2O8+δ (Bi-2212). Their superconducting transition temperatures Tcs showed a domelike shape as a function of pressure, which showed a good agreement with the general relation between the carrier concentration and Tc. Our experimental results indicate that high pressure can induce effective carrier doping into the multilayered high-Tc cuprate superconductor
Based on a hybrid interlayer coupling mechanism, we study the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in trilayer cuprates. By introducing an interlayer magnetic scattering term, we solve the multilayer $t{-}J$ model with Josephson coupling under the framework of Gutzwiller projection. We show that both the SC and AFM orders in the multilayered system are enhanced and the range of AFM order is extended. The layer configuration of d-wave pairing gap and AFM order further plays an essential role in determining the interlayer magnetic and superconducting coupling phase …
We report on superconducting(SC) characteristics for oxygen-reduced Cu-based five-layered high-temperature superconductor (Cu,C)Ba2Ca4Cu5Oy(Cu-1245(OPT)), which includes five-fold outer planes (OP) and four-fold inner planes (IP).As a result of the reduction of the carrier density, the bulk SC for Cu-1245 (OPT) takes place at the nearly optimally-doped OP with Tc= 98 K that is different from previously-reported Cu-1245(OVD) where IP plays a primary role for the onset of SC. It gives an evidence that the carrier density of the optimally-doped layer determines its bulk Tc.Static antiferromagneti…
Low-temperature scanning electron microscopy (LTSEM) has been used to image the supercurrent distribution in ramp-type Josephson junctions between Nb and either the electron-doped cuprate Nd$_{2-x}$Ce$_x$CuO$_{4-y}$ or the hole-doped cuprate YBa$_2$Cu$_3$O$_7$. For zigzag-shaped devices in the short junction limit the critical current is strongly suppressed at zero applied magnetic field. The LTSEM images show, that this is due to the Josephson current counterflow in neighboring 0 and $π$ facets, which is induced by the $d_{x^2-y^2}$ order parameter in the cuprates. Thus, LTSEM provides imagin…
Recent advances in the development of Josephson scanning tunneling spectroscopy (JSTS) have opened a new path for the exploration of unconventional superconductors. We demonstrate that the critical current, $I_c$, measured via JSTS, images the spatial form of the superconducting order parameter in $d_{x^2-y^2}$-wave superconductors around defects and in the Fulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that $I_c$ probes the existence of phase-incoherent superconducting correlations in the pseudo-gap region of the cuprate superconductors, thus providing unprecedented insight into it…
In this work, we generalize the theory of localized surface plasmons to the case of high-Tc cuprate superconductors, spatially confined in the form of small spherical particles. At variance from ordinary metals, cuprate superconductors are characterized by a low-energy bulk excitation known as the Josephson plasma wave (JPW), arising from interlayer tunneling of the condensate along the c-axis. The effect of the JPW is revealed in a characteristic spectrum of surface excitations, which we call Josephson surface plasmons. Our results, which apply to any material with a strongly anisotropic elec…
Recent experimental studies have indicated novel superconducting proximity effects in thin-film heterostructures comprising ferromagnetic manganites and superconducting cuprates. To look for such effects microscopically, we performed scanning tunneling spectroscopy on La$_{2/3}$Ca$_{1/3}$MnO$_3$/YBa$_2$Cu$_3$O$_{7-δ}$ (LCMO/YBCO) bilayer thin films. $\emph{c}$-axis oriented films of varying thickness were grown on SrTiO$_{3}$ substrates using pulsed laser-ablated deposition. Heteroepitaxiality of the films was confirmed by cross-sectional transmission electron microscopy. Tunneling spectra wer…
We consider the problem of local tunneling into cuprate superconductors, combining model based calculations for the superconducting order parameter with wavefunction information obtained from first principles electronic structure. For some time it has been proposed that scanning tunneling microscopy (STM) spectra do not reflect the properties of the superconducting layer in the CuO$_2$ plane directly beneath the STM tip, but rather a weighted sum of spatially proximate states determined by the details of the tunneling process. These "filter" ideas have been countered with the argument that sim…
We analyze how the coherence peaks observed in Scanning Tunneling Spectroscopy (STS) of cuprate high temperature superconductors are transferred from the cuprate layer to the oxide layers adjacent to the STS microscope tip. For this purpose, we have carried out a realistic multiband calculation for the superconducting state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) assuming a short range d-wave pairing interaction confined to the nearest-neighbor Cu $d_{x^2-y^2}$ orbitals. The resulting anomalous matrix elements of the Green's function allow us to monitor how pairing is then induced not only w…
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…
The tunneling path between the CuO2-layers in cuprate superconductors and a scanning tunneling microscope tip passes through a barrier made from other oxide layers. This opens up the possibility that inelastic processes in the barrier contribute to the tunneling spectra. Such processes cause one or possibly more peaks in the second derivative current-voltage spectra displaced by phonon energies from the density of states singularity associated with superconductivity. Calculations of inelastic processes generated by apical O-phonons show good qualitative agreement with recent experiments report…
We consider a nanoscale system consisting of Manganite-ferromagnet and Cuprate-superconductor multilayers in a spin valve configuration. The magnetization of the bottom Manganite-ferromagnet is pinned by a Manganite-antiferromagnet. The magnetization of the top Manganite-ferromagnet is coupled to the bottom one via indirect exchange through the superconducting layers. We study the behavior of the critical temperature and the magnetoresistance as a function of an externally applied parallel magnetic field, when the number of Cuprate-superconductor layers are changed. There are two typical behav…
We present the first demonstration of vortices in an electron-type cuprate superconductor, the highest $T_c$ (= 43 K) electron-type cuprate $Sr_{0.9}La_{0.1}CuO_2$. Our spatially resolved quasiparticle tunneling spectra reveal a hidden low-energy pseudogap inside the vortex core and unconventional spectral evolution with temperature and magnetic field. These results cannot be easily explained by the scenario of pure superconductivity in the ground state of high-$T_c$ superconductivity.
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 report scanning tunneling spectroscopic studies of cuprate and iron-arsenic superconductors, including YBa_2Cu_3O_{7-δ} (Y-123, T_c = 93 K), Sr_{0.9}La_{0.1}CuO_2 (La-112, T_c = 43 K), and the "122" compounds Ba(Fe_{1-x}Co_x)_2As_2 (Co-122 with x = 0.06, 0.08, 0.12 for T_c = 14, 24, 20 K). For H > 0, pseudogap (Δ_{PG}) features are revealed inside the vortices, with Δ_{PG} = [(Δ_{eff})^2+(Δ_{SC})^2]^{1/2} > Δ_{SC} in Y-123 and Δ_{PG} < Δ_{SC} in La-112, suggesting that the physical origin of Δ_{PG} is a competing order coexisting with superconductivity. Additionally, Fourier transformation …
The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)$_2$Sr$_2$CuO$_{6+δ}$ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.
Fourier transform scanning tunneling microscopy on BSCCO subgap resonances has deciphered an octet of "quasi-particle" states that are consistent with the Fermi surface and energy gap observed by ARPES, but the origin of the high-intensity k-space octets and the sharply defined r-space checkerboard is unexplained. The filamentary ferroelastic nanodomain model that predicted the r-space checkerboard also explains the k-space octets and the origin of the apparent anisotropic surface d-wave gap by using strong electron-phonon interactions outside the CuO2 planes. The topological model identifies …
In two dimensions the non-interacting density of states displays a Van Hove singularity (VHS) which introduces an intrinsic electron-hole asymmetry, absent in three dimensions. We show that due to this VHS the strong-coupling analysis of tunneling spectra in high-$T_c$ superconductors must be reconsidered. Based on a microscopic model which reproduces the experimental data with great accuracy, we elucidate the peculiar role played by the VHS in shaping the tunneling spectra, and show that more conventional analyses of strong-coupling effects can lead to severe errors.
We present a model for the combined nematic and `smectic' or stripe-like orders seen in recent scanning tunneling microscopy (STM) experiments in cuprates. We model the stripe order as an electronic charge density wave with associated Peierls distortion -- a `Pomeranchuk wave'. Disorder restricts this primary order to nanoscale domains, while secondary coupling to strain generates nematic order with considerably longer range.
We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long standing puzzle. We then study quasiparticle …
We have analyzed scanning tunneling spectra of two electron-doped cuprates Pr0.88LaCe0.12CuO4 (Tc = 21 K and 24 K) and compared them with tunneling spectrum of hole-doped La1.84Sr0.16CuO4 and effective electron-boson spectral function of hole-doped La1.97Sr0.03CuO4 (extracted from angle-resolved photoemission spectrum). We have also analyzed tunneling spectra and angle-resolved photoemission spectra for hole-doped Bi2Sr2CaCu2O8. These results unambiguously rule out magnetic pairing mechanism in both electron- and hole-doped cuprates and support polaronic/bipolaronic superconductivity in hole-d…
In a recent letter [1] Pilgram, Rice and Sigrist (PRS) propose to perform oxygen isotope dependent conductivity measurements along the c-axis of the cuprate superconductor BSSCO. In Raman isotope data for vibrations along the c-axis from 1988 [2], and in site selective susceptibility experiments determining Tc, no isotope effects were observed for oxygen ions in the insulating layer [3]. Based on these earlier not by PRS quoted experiments, we argue that the suggestion made in Ref. 1 is not worth to be undertaken, and if it is carried through, no effect will be seen. From the meanwhile 12 year…
Scanning tunneling spectroscopy studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ suggest the presence of electronic inhomogeneity with a large spatial variation in gap size. Andersen {\it et al} have modelled this variation by assuming a spatially-varying pairing interaction. We show that their calculated specific heat is incompatible with the experimental data which exhibit narrow transitions. This calls into question the now-common assumption of gap and pairing inhomogeneity.
We point out the incorrect derivation of the gap equation in X.-J. Chen and H. Q. Lin [Phys. Rev. B 69 (2004) 104518; cond-mat/0306680] within the interlayer tunneling (ILT) model for multilayered cuprates. There, the local structure in k-space of the ILT effective interaction has not been taken into due account when the ILT model is generalized to the case of n layers per unit cell. This is a specific characteristic of the ILT model that, apart from giving rise to a highly nontrivial k-dependence of the gap function, is known to enhance the critical temperature Tc in a natural way. As a conse…
We present phase-sensitive evidence that the electron-doped cuprates Nd1.85Ce0.15CuO4-y (NCCO) and Pr1.85Ce0.15CuO4-y (PCCO) have d-wave pairing symmetry. This evidence was obtained by observing the half-flux quantum effect, using a scanning SQUID microscope, in c-axis oriented films of NCCO or PCCO epitaxially grown on tricrystal [100] SrTiO3 substrates designed to be frustrated for a d(x2-y2) order parameter. Samples with two other configurations, designed to b unfrustrated for a d-wave superconductor, do not show the half-flux quantum effect.
We suggest that the high temperature superconductivity in cuprate compounds may emerge due to interaction between copper-oxygen layers mediated by in-plane plasmons. The strength of the interaction is determined by the c-axis geometry and by the ab-plane optical properties. Without making reference to any particular in-plane mechanism of superconductivity, we show that the interlayer interaction favors spontaneous appearance of the superconductivity in the layers. At a qualitative level the model describes correctly the dependence of the transition temperature on the interlayer distance, and o…
Recent scanning tunneling microscopy on BSCCO 2212 has revealed a substantial spatial supermodulation of the energy gap in the superconducting state. We propose that this gap modulation is due to the superlattice modulations of the atoms in the structure, and hence the parameters in a microscopic model of the CuO2 plane. The gap modulation is estimated using renormalized mean field theory for a t-t'-J model on a superlattice. The results compare well with experiment.
The energy, momentum and temperature dependence of the quasiparticle local density of states (LDOS) of a two-dimensional $d_{x^2-y^2}$-wave superconductor with random disorder is investigated using the first-order T-matrix approximation. The results suggest that collective modes such as spin/charge density waves are relevant low-energy excitations of the cuprates that contribute to the observed LDOS modulations in recent scanning tunneling microscopy studies of $\rm Bi_2Sr_2CaCu_2O_x$.
Visualizing Chiral Edge Modes in Twisted Cuprate Superconductors via Scanning-Probe Quantum Sensing
Georgia Institute of Technology（佐治亚理工学院）；Harvard University（哈佛大学）；National Institute for Materials Science（国立材料研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Argonne National Laboratory（阿贡国家实验室）
Motivated by the recent scanning tunneling microscopy (STM) and neutron scattering experiments, we investigate various charge density wave orders coexisting with superconductivity in the cuprate superconductors. The explicit expressions of the local density of states and its Fourier component at the ordering wavevector for the weak charge modulations are derived. It is shown that the STM experiments in $Bi_2Sr_2CaCu_2O_{8+δ}$ cannot be explained by a site- or bond-centered charge modulation alone, but agree well with the presence of the dimerization hopping and transverse pairing modulations. …
The low temperature heat capacity investigations on pure(y=0) and Zn-doped La1.84Sr0.16Cu1-yZnyO4 samples have been performed in the interval of 1.8-60K by a new method of high-precision, pulsed differential calorimetry (PDC), which provides the measurements under the equilibrium conditions, in contrast to commonly used differential scanning calorimeters (DSC). For these systems a new heat capacity anomaly was observed, which is associated with Zn impurities and has the form of one wide peak. It does not show a phonon character shifts towards the higher temperatures with the increase of Zn con…
Understanding the mechanism of high transition temperature (Tc) superconductivity in cuprates has been hindered by the apparent complexity of their multilayered crystal structure. Using a cryogenic scanning tunneling microscopy, we report on layer-by-layer probing of the electronic structures of all ingredient planes (BiO, SrO, CuO2) of Bi2Sr2CaCu2O8+δ superconductor prepared by argon-ion bombardment and annealing technique. We show that the well-known pseudogap (PG) feature observed by STM is inherently a property of the BiO planes and thus irrelevant directly to Cooper pairing. The SrO plane…
Recent low-temperature scanning tunnelling spectroscopy experiments on the surface of BSCCO-2212 have revealed a strong positive correlation between the position of localized resonances at -960 meV identified with interstitial oxygen dopants and the size of the local spectral gap. We review efforts to understand these correlations within a model where the dopants modulate the pair interaction on an atomic scale. We provide further evidence for this model by comparing the correlations between the dopants and the local density of states with experimental results.
Motivated by the recent scanning tunneling microscopy (STM) experiment [J. E. Hoffman, {\it et al.}, Science {\bf 297}, 1148 (2002)], we investigate the energy-dependent modulation induced by a weak and extended defect in a d-wave superconductor. The Fourier component of the local density of states (LDOS) is calculated up to the first order in the defect parameters. Our numerically obtained image maps together with the energy-dependent charge modulation wave vectors at different dopings exhibit the essential features as those measured by the experiment. We also predict new modulation wave vect…
We present scanning tunneling spectroscopic and high-field thermodynamic studies of hole- and electron-doped (p- and n-type) cuprate superconductors. Our experimental results are consistent with the notion that the ground state of cuprates is in proximity to a quantum critical point (QCP) that separates a pure superconducting (SC) phase from a phase comprised of coexisting SC and a competing order, and the competing order is likely a spin-density wave (SDW). The effect of applied magnetic field, tunneling current, and disorder on the revelation of competing orders and on the low-energy excitat…
Scanning tunneling spectroscopy (STS) is a useful probe for studying the cuprates in the superconducting and pseudogap states. Here we present a theoretical study of the Z-map, defined as the ratio of the local density of states at positive and negative bias energies, which frequently is used to analyze STS data. We show how the evolution of the quasiparticle interference peaks in the Fourier transform Z-map can be understood by considering different types of impurity scatterers, as well as particle-hole asymmetry in the underlying bandstructure. We also explore the effects of density wave ord…
We report $^{63}$Cu- and $^{205}$Tl-NMR studies on six-layered ($n$=6) high-$T_c$ superconducting (SC) cuprate TlBa$_2$Ca$_5$Cu$_6$O$_{14+δ}$ (Tl1256) with $T_c\sim$100 K, which reveal that antiferromagnetic (AFM) order takes place below $T_{\rm N}\sim$170 K. In this compound, four underdoped inner CuO$_2$ planes ($n$(IP)=4) sandwiched by two outer planes (OPs) are responsible for the onset of AFM order, whereas the nearly optimally-doped OPs responsible for the onset of bulk SC. It is pointed out that an increase in the out-of-plane magnetic interaction within an intra-unit-cell causes $T_{\r…
To elucidate the superconductor to metal transition at the end of superconducting dome, the overdoped regime has stepped onto the center stage of cuprate research recently. Here, we use scanning tunneling microscopy to investigate the atomic-scale electronic structure of overdoped trilayer Bi-2223 and bilayer Bi-2212 cuprates. At low energies the spectroscopic maps are well described by dispersive quasiparticle interference patterns. However, as the bias increases to the superconducting coherence peak energy, a virtually non-dispersive pattern with sqrt(2)*sqrt(2) periodicity emerges. Remarkab…
The magnetization vector \vec M was measured in the reversible region of the mixed state of a high quality Tl2Ba2Ca2Cu3O10 single crystal as a function of temperature and for different magnetic field amplitudes and orientations. These measurements allowed to study the \vec M components perpendicular and parallel to the CuO2 layers (Mperp and Mpara, respectively) under arbitrary values for the corresponding components of the applied magnetic field, Hperp and Hpara. For temperatures close to Tc (in the critical fluctuation region) we observed Mperp(Hperp,Hpara) Mperp(Hperp,0) and Mpara(Hperp,Hpa…
We discuss a wealth of data from various types of experiments which together suggest that the superconducting state of optimally to overdoped BSCCO-2212 can be well-described by the BCS theory with a d-wave gap together with small-angle scattering from out-of-plane defects. These include scanning tunnelling Fourier transform spectroscopy observation of nanoscale inhomogeneity in the local gap edge position, the narrowing of the antinodal ARPES spectrum when BSCCO becomes superconducting, as well as the behavior of the microwave and thermal conductivities. We suggest that the large amount of sm…
The low-energy quasiparticle excitations in hole- and electron-type cuprate superconductors are investigated via both experimental and theoretical means. It is found that the doping and momentum dependence of the empirical low-energy quasiparticle excitations is consistent with a scenario of coexisting competing orders and superconductivity in the ground state of the cuprates. This finding, based on zero-field quasiparticle spectra, is further corrobarated by the patially resolved vortex-state scanning tunneling spectroscopy, which reveals pseudogap-like features consistent with a remaining co…
Motivated by the recent scanning tunneling microscopy (STM) experiments [J. E. Hoffman {\it et al.}, Science {\bf 297}, 1148 (2002); K. McElroy {\it et al.}, Nature (to be published)], we investigate the real space local density of states (LDOS) induced by weak disorder in a d-wave superconductor. We first present the energy dependent LDOS images around a single weak defect at several energies, and then point out that the experimentally observed checkerboard pattern in the LDOS could be understood as a result of quasiparticle interferences by randomly distributed defects. It is also shown that…
Recent scanning tunnelling microscopy (STM) studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) revealed the presence of severe inhomogeneity with length scale $L_0 \approx ξ_0$, the coherence length. Other studies have been interpreted in terms of mesoscale or nanoscale phase segregation. Here we analyze heat capacity and NMR data on Bi-2212 and (Y,Ca)Ba$_2$Cu$_3$O$_{7-δ}$ and find no evidence for phase segregation or gross inhomogeneity. For Bi-2212 the coherence scale $L_0$ increases with doping from 5 to 17$ξ_0$ and the hole density inhomogeneity decreases from 0.028 to 0.005 holes/Cu. We c…
We present the first scanning tunneling spectroscopy study on the Chevrel phase PbMo6S8, an extreme type II superconductor with a coherence length only slightly larger than in high-Tc cuprates. Tunneling spectra measured on atomically flat terraces are spatially homogeneous and show well-defined coherence peaks. The low-energy spectral weight, the zero bias conductance and the temperature dependence of the gap are incompatible with a conventional isotropic s-wave interpretation, revealing the presence of low-energy excitations in the superconducting state. We show that our data are consistent …
Scanning tunneling spectroscopy has recently discovered a positive correlation between the magnitude of the superconducting gap and positions of dopant oxygen atoms in Bi-based cuprates. We propose a microscopic mechanism that could be responsible for this effect. In particular, we demonstrate that the dopant-induced spatial variation of the atomic levels always enhances the superexchange interaction.
We show that a variety of spectral features in high-T_c cuprates can be understood from the coupling of charge carriers to some kind of dynamical order which we exemplify in terms of fluctuating charge and spin density waves. Two theoretical models are investigated which capture different aspects of such dynamical scattering. The first approach leaves the ground state in the disordered phase but couples the electrons to bosonic degrees of freedom, corresponding to the quasi singular scattering associated with the closeness to an ordered phase. The second, more phenomological approach starts fr…
We measure changes in the penetration depth $λ$ of the $T_c \approx 6$ K superconductor LaFePO. In the process scanning SQUID susceptometry is demonstrated as a technique for accurately measuring {\it local} temperature-dependent changes in $λ$, making it ideal for studying early or difficult-to-grow materials. $λ$ of LaFePO is found to vary linearly with temperature from 0.36 to $\sim$2 K, with a slope of 143$\pm$15 Å/K, suggesting line nodes in the superconducting order parameter. The linear dependence up to $\sim T_c/3$ is similar to the cuprate superconductors, indicating well-developed no…
In scanning tunneling microscopy (STM) conductance curves, the superconducting gap of cuprates is sometimes accompanied by small sub-gap structures at very low energy. This was documented early on near vortex cores and later at zero magnetic field. Using mean-field toy models of coexisting d-wave superconductivity ($d$SC), \emph{d}-form factor density wave ($d$FF-DW), and extended s-wave pair density wave ($s'$PDW), we find agreement with this phenomenon, with $s'$PDW playing a critical role. We explore the high variability of the gap structure with changes in band structure and density wave (…
The study of bosonic modes that couple to the charge carriers is a key element in understanding superconductivity. Lee et al. have used atomic-resolution scanning tunneling spectroscopy (STM) in an attempt to extract the spectrum of of these modes in the high temperature superconductor Bi2Sr2CaCu2O8+d and they found a mode whose frequency did not depend on doping but changed on 16O to 18O isotopic substitution leading them to suggest a role for lattice modes (phonons). A careful examination of their published data reveals a weaker but distinct feature that has all the characteristics of the ma…
A method is proposed to test for the nature of the pseudogap phase in cuprates using the recently developed technique of Fourier transform scanning tunneling spectroscopy. We show that the observed quasiparticle interference patterns depend critically on the quasiparticle coherence factors, making it possible to distinguish between the pseudogap dominated by superconducting fluctuations and by various particle-hole condensates.
We theoretically study the quasiparticle resonance states around a nonmagnetic impurity in cuprate superconductors based on t-t'-J-U model. The purpose of introducing the Coulomb repulsive interaction U is to partially impose the double occupancy constraint by employing the Gutzwiller projected mean-field approximation. We determine the spatial variation of the order parameter and the local density of states (LDOS) by self-consistently solving Bogoliubov-de Gennes equations. We find that in the large U limit, a zero-energy resonance peak in the LDOS indeed appears for the impurity potential in…
Conductance-voltage characteristics (CVCs) for non-symmetric tunnel junctions between $d$-wave superconductors with charge-density waves (CDWs) and normal metals were calculated. It was shown that they have a V-like form at small voltages $V$ and are asymmetric at larger $V$ owing to the presence of CDW peak in one of the $V$-branches. The spatial scatter of the dielectric (CDW) order parameter smears the CDW peak into a hump and induces a peak-dip-hump structure (PDHS) typical of CVCs observed for such junctions. At temperatures larger than the superconducting critical temperature, the PDHS e…
