Impurity states and interlayer tunneling in high temperature superconductors

Atomic manipulation of the gap in Bi2Sr2CaCu2O8+x

Single-atom manipulation within doped correlated electron systems could help disentangle the influence of dopants, structural defects, and crystallographic characteristics on local electronic states. Unfortunately, the high diffusion barrier in these materials prevents conventional manipulation techniques. Here, we demonstrate the possibility to reversibly manipulate select sites in the optimally doped high-temperature superconductor Bi₂Sr₂CaCu₂O_8+x using the local electric field of the tip of a scanning tunneling microscope. We show that upon shifting individual Bi atoms at the surface, the spectral gap associated with superconductivity is seen to reversibly change by as much as 15 milli-electron volts (on average ~5% of the total gap size). Our toy model, which captures all observed characteristics, suggests that the electric field induces lateral movement of local pairing potentials in the CuO₂ plane.

Noisy defects in the high-Tc superconductor Bi2Sr2CaCu2O8+x

Dopants and impurities are crucial in shaping the ground state of host materials: semiconducting technology is based on their ability to donate or trap electrons, and they can even be used to transform insulators into high temperature superconductors. Due to limited time resolution, most atomic-scale studies of the latter materials focussed on the effect of dopants on the electronic properties averaged over time. Here, by using atomic-scale current-noise measurements in optimally doped Bi₂Sr₂CaCu₂O_8+x, we visualize sub-nanometre sized objects where the tunnelling current-noise is enhanced by at least an order of magnitude. We show that these objects are previously undetected oxygen dopants whose ionization and local environment leads to unconventional charge dynamics resulting in correlated tunnelling events. The ionization of these dopants opens up new routes to dynamically control doping at the atomic scale, enabling the direct visualization of local charging on e.g. high-T_c superconductivity.

The effects of dopants in high-temperature superconductors on the surrounding electronic structure give insights into their unconventional microscopic behaviour. Here the authors find a new class of defects that they identify as oxygen dopants whose ionization and local environment induce unusual atomic-scale charge dynamics.

Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates

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 interference phenomena induced by out-of-plane weak potential scatterers, and show how patterns long observed in cuprates can be understood in terms of the interference of Wannier functions above the surface. Our results show excellent agreement with experiment and enable a better understanding of novel phenomena in the cuprates via STM imaging.

The physics of Kondo impurities in graphene

This article summarizes our understanding of the Kondo effect in graphene, primarily from a theoretical perspective. We shall describe different ways to create magnetic moments in graphene, either by adatom deposition or via defects. For dilute moments, the theoretical description is in terms of effective Anderson or Kondo impurity models coupled to graphene's Dirac electrons. We shall discuss in detail the physics of these models, including their quantum phase transitions and the effect of carrier doping, and confront this with existing experimental data. Finally, we will point out connections to other quantum impurity problems, e.g., in unconventional superconductors, topological insulators, and quantum spin liquids.

Reaffirming the d(x2-y2) superconducting gap using the autocorrelation angle-resolved photoemission spectroscopy of Bi1.5Pb0.55Sr1.6La0.4CuO(6+δ)

Knowledge of the gap function is important to understand the pairing mechanism for high-temperature (T(c)) superconductivity. However, Fourier transform scanning tunneling spectroscopy (FT STS) and angle-resolved photoemission spectroscopy (ARPES) in the cuprates have reported contradictory gap functions, with FT-STS results deviating strongly from a canonical d(x2-y2) form. By applying an "octet model" analysis to autocorrelation ARPES, we reveal that a contradiction occurs because the octet model does not consider the effects of matrix elements and the pseudogap. This reaffirms the canonical d(x2-y2) superconducting gap around the node, which can be directly determined from ARPES. Further, our study suggests that the FT-STS reported fluctuating superconductivity around the node at far above T(c) is not necessary to explain the existence of the quasiparticle interference at low energy.

Origin of the electron-hole asymmetry in the scanning tunneling spectrum of the high-temperature Bi2Sr2CaCu2O8+delta superconductor

We have developed a material specific theoretical framework for modeling scanning tunneling spectroscopy (STS) of high-temperature superconducting materials in the normal as well as the superconducting state. Results for Bi2Sr2CaCu2O8+delta (Bi2212) show clearly that the tunneling process strongly modifies the STS spectrum from the local density of states of the dx2-y2 orbital of Cu. The dominant tunneling channel to the surface Bi involves the dx2-y2 orbitals of the four neighboring Cu atoms. In accord with experimental observations, the computed spectrum displays a remarkable asymmetry between the processes of electron injection and extraction, which arises from contributions of Cu dz2 and other orbitals to the tunneling current.

Rotational symmetry breaking in the ground state of sodium-doped cuprate superconductors

We use an extended t-J model to study a single hole bound to a Na+ acceptor in Ca2-xNaxCuO2Cl2. For parameters suitable to cuprates, the ground state has a twofold degeneracy, corresponding to even (odd) reflection symmetry around the x (y) axes. The conductance pattern of the broken symmetry state is anisotropic as the tip of a tunneling microscope scans above the Cu-O-Cu bonds along the x (y) axes. This anisotropy is pronounced at lower voltages but reduced at higher voltages. Our theory agrees qualitatively with recent data of scanning tunneling microscopy showing broken local rotational symmetry.

Andreev states near short-ranged pairing potential impurities

We study Andreev states near atomic scale modulations in the pairing potential in both s- and d-wave superconductors with short coherence lengths. For a moderate reduction of the local gap, the states exist only close to the gap edge. If one allows for local sign changes of the order parameter, however, resonances can occur at energies close to the Fermi level. The local density of states (LDOS) around such pairing potential defects strongly resembles the patterns observed by tunneling measurements around Zn impurities in Bi2Sr2CaCu2O8+x (BSCCO). We discuss how this phase impurity model of the Zn LDOS pattern can be distinguished from other proposals experimentally.

Elastic scattering susceptibility of the high temperature superconductor Bi2Sr2CaCu2O(8+delta): a comparison between real and momentum space photoemission spectroscopies

The joint density of states of Bi2Sr2CaCu2O(8+delta) is calculated by evaluating the autocorrelation of the single particle spectral function A(k, omega) measured from angle resolved photoemission spectroscopy (ARPES). These results are compared with Fourier transformed (FT) conductance modulations measured by scanning tunneling microscopy (STM). Good agreement between the two experimental probes is found for two different doping values examined. In addition, by comparing the FT-STM results to the autocorrelated ARPES spectra with different photon polarization, new insight on the form of the STM matrix elements is obtained. This shines new light on unsolved mysteries in the tunneling data.

Effects of a collective spin resonance mode on the scanning tunneling microscopy spectra of d-wave superconductors

A high-energy spin resonance mode is known to exist in many high-temperature superconductors. Motivated by recent scanning tunneling microscopy experiments in superconducting Bi(2)Sr(2)CaCu(2)O(8+delta), we study the effects of this resonance mode on the local density of states (LDOS). The coupling between the electrons in a d-wave superconductor and the resonance mode produces high-energy peaks in the LDOS, which displays a two-unit-cell periodic modulation around a nonmagnetic impurity. This suggests a new means to not only detect the dynamical spin collective mode but also study its coupling to electronic excitations.

Impurities and quantum interference in the chains of YBa2Cu3O6+x

Motivated by recent experiments, we study the electronic structure near impurities in the chains of YBa2Cu3O6+x. Using a model of proximity induced chain superconductivity, we show that a resonance state in the chain density of states is induced only by a magnetic impurity. The spatial form of the resonance reflects the particle-hole nature of chain superconductivity and therefore distinguishes it from other broken symmetry phases. Because of quantum interference effects between impurities, the chains can undergo a quantum phase transition into a polarized state.

Impurity bound states in disordered d-wave superconductors

Recent STM experiments on Bi2Sr2Ca2Cu3O10 observed sharp bound states associated with Zn and Ni impurities, as previously predicted theoretically. Here we extend the theory to the case of a finite concentration of impurities. Using the nonlocal coherent potential approximation, we show that the resonance peak both broadens and shifts as a function of impurity concentration.

Atomic scale imaging and spectroscopy of a CuO(2) plane at the surface of Bi(2)Sr(2)CaCu(2)O(8+delta)

We have used a scanning tunneling microscope to demonstrate that a single CuO2 plane can form a stable and atomically ordered layer at the surface of Bi(2)Sr(2)CaCu(2)O(8+delta). In contrast to previous studies on high-T(c) surfaces, the CuO2-terminated surface exhibits a strongly suppressed tunneling conductance at low voltages. We consider a number of different explanations for this phenomena and propose that it may be caused by how the orbital symmetry of the CuO2 plane's electronic states affects the tunneling process.