Electronic Structure of the Cuprate Superconducting and Pseudogap Phases from Spectroscopic Imaging STM

We survey the use of spectroscopic imaging STM to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E=Delta0. We find that the Bogoliubov quasiparticle interference signatures of delocalized Cooper pairing are restricted to a k-space arc which terminates near the lines connecting k=\pm(pi/a0,0) to k=\pm(pi/a0). This arc shrinks continuously with decreasing hole density such that Luttinger's theorem could be satisfied if it represents the front side of a hole-pocket which is bounded behind by the lines between k=\pm(pi/a0,0) and k=\pm(0,pi/a0). In both phases the only broken symmetries detected for the |E|<Delta0 states are those of a d-wave superconductor. The second class of states occurs proximate to the pseudogap energy scale E=Delta1. Here the non-dispersive electronic structure breaks the expected 90o-rotational symmetry of electronic structure within each unit cell, at least down to 180o-rotational symmetry. This Q=0 electronic symmetry breaking was first detected as an electronic inequivalence at the two oxygen sites within each unit cell by using a measure of nematic (C2) symmetry. Incommensurate non-dispersive conductance modulations, locally breaking both rotational and translational symmetries, coexist with this intra-unit-cell electronic symmetry breaking at E=Delta1. Their characteristic wavevector Q is determined by the k-space points where Bogoliubov quasiparticle interference terminates and therefore changes continuously with doping. The distinct broken electronic symmetry states (Q=0 and finite Q) coexisting at E~Delta1 are found to be indistinguishable in the dSC and PG phases.Comment: 32 pages with 10 figure

How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+d

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the enigmatic 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles -- the excitations resulting from the breaking of Cooper pairs -- should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi2Sr2CaCu2O8+d in r-space and k-space simultaneously. We find that although the low energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy independent fashion. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.Comment: This is author's version. See the Nature website for the published versio

Picometer registration of zinc impurity states in Bi2Sr2CaCu2O8+delta for phase determination in intra-unit-cell Fourier transform STM

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). By studying the Bragg peaks in Fourier transforms of electronic structure images and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit-cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such a Bragg-peak Fourier analysis. Exemplary of this challenge is the high-temperature superconductor Bi2Sr2CaCu2O8+delta for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a similar to 2%(2 pi) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unit-cell rotational symmetry breaking at the CuO2 plane (Lawler et al 2010 Nature 466 347-51, Schmidt et al 2011 New J. Phys. 13 065014, Fujita K et al 2012 J. Phys. Soc. Japan 81 011005). Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for the Bragg-peak Fourier analysis of intra-unit-cell symmetry.Publisher PDFPeer reviewe