Research Article

Atomic-Scale Sources and Mechanism of Nanoscale Electronic Disorder in Bi2Sr2CaCu2O8+δ

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Science  12 Aug 2005:
Vol. 309, Issue 5737, pp. 1048-1052
DOI: 10.1126/science.1113095

Abstract

The randomness of dopant atom distributions in cuprate high–critical temperature superconductors has long been suspected to cause nanoscale electronic disorder. In the superconductor Bi2Sr2CaCu2O8+δ, we identified populations of atomic-scale impurity states whose spatial densities follow closely those of the oxygen dopant atoms. We found that the impurity-state locations are strongly correlated with all manifestations of the nanoscale electronic disorder. This disorder occurs via an unanticipated mechanism exhibiting high-energy spectral weight shifts, with associated strong superconducting coherence peak suppression but very weak scattering of low-energy quasi-particles.

Important new electronic materials have been created by chemically doping their inert parent compounds with charge carriers. Examples include organic conductors, cuprate high-temperature superconductors, manganites that display colossal magnetoresistance, cobaltates that display large thermoelectric powers, and magnetic semiconductors. In such chemical doping schemes, a critical challenge is to generate the desired electronic properties without also creating destructive electronic disorder due to the random distribution of dopant atoms.

Cuprate high-Tc superconductivity (HTSC) is one of the most remarkable examples of this situation. In hole-doped cuprates (those with the highest critical temperature Tc), superconductivity appears when electron acceptor atoms are introduced into the parent insulators (1). This process almost always creates random distributions of differently charged dopant atoms near the critical CuO2 crystal planes. These are potential sources of electronic and crystalline disorder (2) and Tc suppression (3, 4). Indeed, dopant atoms may have two diametrically opposite influences on HTSC, being destructive at the atomic scale but supportive globally (via enhanced carrier densities). Thus, a key challenge in cuprate studies has been to determine directly how dopant atoms influence the superconducting electronic structure at the atomic scale.

Spectroscopic imaging scanning tunneling microscopy (SI-STM) studies reveal nanoscale electronic disorder in many cuprates. For example, YBa2Cu3O6–δ exhibits local density of states (LDOS) modulations at the CuO plane (5). In NaxCa2–xCuO2Cl2, topographic imaging shows both random nanoscale electronic disorder (6) and disorder related to the 4 × 4 electronic “checkerboard” of nondispersive LDOS modulations (7). Bi2Sr2CaCu2O8+δ (Bi-2212) exhibits several signatures of electronic disorder, including subgap dispersive LDOS modulations (8), disordered regions (diameter ∼3 nm) in energy-gap images Embedded Image (911), and nanoscale disorder in low-bias topographic images Embedded Image (11). Although dopant disorder was suspected to cause these effects, this was impossible to verify directly because simultaneous atomic-resolution images of the dopant atom locations and the superconducting electronic structure were unattainable.

Locating the atomic-scale sources of electronic disorder. Here we focus on Bi-2212, a cuprate superconductor that is hole-doped by adding a number δ of nonstoichiometric oxygen atoms per unit cell. The floating zone–grown crystals, prepared with variable oxygen dopant densities, can be cleaved to reveal the BiO layer (Fig. 1A). Although analyses of x-ray and neutron scattering studies imply that the oxygen dopant atoms may be located either within or between BiO layers (12, 13), their exact locations have never been determined. To attempt location of oxygen dopants by SI-STM, one needs to identify an electronic impurity state characteristic of dopant atoms only. The stoichiometric oxygen atoms are invisible to low-bias SI-STM because their contributions to the BiO band structures occur far from the Fermi energy. By contrast, each nonstoichiometric oxygen dopant atom is a –2e charged impurity, so they might be expected to generate an electronic impurity state somewhat below the Fermi level. To search for such dopant-induced impurity states, we acquired Embedded Image images with large field of view over a range of energies –1.2 eV < E < –0.15 eV. At typical tunnel junction resistance RJ = 109 ohms with V ∼1 V, the electric field exceeds ∼109 V/m and can rupture the BiO surface; therefore, new techniques for LDOS imaging with RJ up to 1011 ohms were developed for these studies.

Fig. 1.

(A) Atomic-resolution topographic image of the BiO surface of Bi-2212 taken at VB = –0.9 V and RJ = 3 × 1010 ohms. The inset compares the shape of a high-voltage spectrum at one of the bright features in (B) with that of a spectrum typical of regions far from any bright feature (spectra were taken at different junction resistance and have different normalizations). An Embedded Image image [simultaneously acquired with (A)] of the differential tunneling conductance measured at V = –0.9 V with a modulation amplitude of 50 mV. It shows about 600 atomic-scale regions of high differential conductance, which occur because there is a peak in the differential conductance spectrum near V = –0.96 V at each of these locations. This is the only energy in our window where such effects were detected. Examples of the high-voltage spectra on and off these bright regions are shown in the inset of (A); an arrow indicates the peak in tunnel conductance. Shown schematically in the inset of (B) is the line parallel to the c axis along which we believe the dopant defect is located. It is not possible to determine which layer of the crystal it lies in.

Figure 1A shows a typical Embedded Image topograph with sample bias VB = –0.9 V. Figure 1B, which shows the simultaneous Embedded Image image at energy E = –0.9 ± 0.05 eV, reveals a random distribution of bright maxima in the LDOS, each with radius ∼4 Å. The inset of Fig. 1A compares the shape of the high-voltage spectrum at one of the bright features in Fig. 1B with that of a spectrum typical of regions far from them; we see that the contrast in Fig. 1B occurs because each bright region exhibits a broad peak (arrow in Fig. 1A) in the spectrum at V = –0.96 V.

By cross-correlating the simultaneous topographic and LDOS(V = –0.96 V) images (e.g., Fig. 1A with Fig. 1B), we determined that the “–0.96 eV features” occur at a distance of ∼1.9 Å away from the nearest Bi along the BiO bond direction but in an unknown plane (inset, Fig. 1B). The precision of this determination is not high because of crystal spatial disorder and the extended nature (diameter ∼8 Å) of the impurity state. One possible explanation for these features is a dopant atom residing above the BiO layer. This scenario, although not ruled out, is not supported by observations of adatoms at these locations. Another possibility is a vacancy at the stoichiometric oxygen site in the BiO layer, but here topography does not reveal the anticipated displacements of Bi atoms. A well-known electronic defect (4) is substitution of a Bi atom on the Sr site, but this cannot explain the –0.96 eV impurity state because it is positively charged (Bi3+ on the Sr2+ site), so its impurity state should exist above the Fermi level; in fact it is observed at E = +1.7 eV (9). A final possibility is that, at whichever site within the crystal the O–2 dopant atom resides, it generates a local electronic impurity state somewhere below the Fermi level.

To test whether the “–0.96 V features” could be such impurity states, we repeated the LDOS(V = –0.96 V) imaging experiments on several samples with different oxygen dopant densities. Typical results are shown in Fig. 2, where the locations of spectra exhibiting –0.96 V peaks are marked as white dots superimposed on the simultaneously acquired gap maps Embedded Image. The hole density p per CuO2 decreases from Fig. 2A to Fig. 2C, as evidenced by the increasing average gap magnitude Embedded Image; in break junction studies of Bi-2212, Embedded Image meV (14). From images of the –0.96 eV features, we find that their density per CuO2 plaquette, n, also diminishes from Fig. 2A to Fig. 2C and is related to the average gap magnitude Embedded Image meV. These data are all consistent with every –0.96 eV state being associated with the contribution of ∼2 holes to the CuO2 plane. It is then reasonable to postulate that each is due to a single oxygen dopant atom, and hereafter we refer to them provisionally as the “dopant defects.” These –0.96 eV impurity states, independent of their microscopic cause or electronic structure, occur at the primary sources of the nanoscale electronic disorder (see below).

Fig. 2.

(A to C) Three gap maps, with identical field of view sizes of 49 nm (corresponding to ∼16,000 CuO2 plaquettes) and color scales, measured on samples with three different oxygen doping levels. Average gap magnitudes Embedded Image are shown at the top, together with values of N, the total number of –0.96 V features (shown as white circles) in the field of view. Those in (B) were derived from the LDOS image in Fig. 1B. Note that the black regions have a distinct spectrum with a wide gap and no superconducting coherence peaks (23), as also shown by the black curve in (D). (D) The average spectrum associated with each superconducting gap value is color-coded to associate each gap-average spectrum with regions of the same color in all gap maps. As coherence peaks decrease and local gap values increase near dopant defects, the spectral weight shifts from below to above 250 meV for filled states and from below to above 150 meV for empty states. To make these observations, we used setup voltages of +600 meV and –600 meV, yielding simultaneous topographs with minimal nanoscale disorder and almost identical sets of spectra. Thus, no renormalization of these spectra to compensate for topographic disorder (11) was required. Further, the –600 meV setup voltage is sufficiently far below the –960 meV peak at the dopant sites to avoid tip elevation errors due to the impurity states.

Superconducting electronic disorder phenomena in Bi-2212. The simplest type of electronic disorder in Bi-2212 appears in Embedded Image images generated from tip-sample differential tunneling conductance Embedded Image measurements: Embedded Image(1) Differential conductance images revealed weak quasi-periodic modulations exhibiting up to 16 inequivalent sets of energy-dispersive wave vectors in Embedded Image, the Fourier transform magnitude of Embedded Image. When analyzed as scattering-induced quasi-particle interference patterns (1517), these sets of dispersing Embedded Image-vectors yielded elements of the Fermi surface and momentum space Embedded Image in excellent agreement with photoemission (8, 18, 19). However, the identity of the scattering centers that generate these quasi-particle interference patterns was unknown.

Intense disorder is also universally seen in atomically resolved images of the superconducting energy gap Embedded Image (911, 2023). Gap values range from below 20 meV to above 65 meV within adjacent nanoregions; the data shown in Fig. 2, A to C, are typical. Explaining these Embedded Image phenomena has become a key challenge in cuprate studies.

The disorder seen in low-bias (–150 mV < VB < 0) topographic images of Bi-2212 is also exceptionally strong (11). For example, the low-bias topograph in Fig. 3B (with the ∼2.6 nm wavelength surface undulations removed by Fourier filtering) reveals the disorder contrast as dark and light nanoregions. STM topographic imaging actually measures the vertical tip displacement Embedded Image required to maintain constant tunnel current I(VB) for sample bias voltage VB. With z0 as the exponential tunneling factor, the current at VB is given by Embedded Image(2) Embedded Image Embedded Image(3) In this simple single-particle picture, the spatial charge density variations within states up to E = eVB would then be Embedded Image(4) For this reason, the disorder seen in low-bias topographs z(Embedded Image, –150 mV < VB < 0) has been interpreted via Eqs. 3 and 4 as a logarithmic image of charge density disorder (11, 24).

Fig. 3.

(A) A series of cross-correlations Embedded Imageamong the simultaneously measured Embedded Image, Embedded Image and Embedded Image images. These show the angular average Embedded Image for f:g pairs Embedded Image, Embedded Image, Embedded Image, Embedded Image, and Embedded Image. We note that because Embedded Image is an image with intensity in only a few percent of this field of C view (see Fig. 1B), any correlation Embedded Image is actually quite strong. The images in Fig. 2, A to C, show directly that the Embedded Image correlation, while strong, is not obviously deterministic, as might be expected for a nonlocal quantum mechanical system. (B) A typical low-bias topographic image Embedded Image, with the 2.6 nm “supermodulation” surface undulation removed but retaining the crystalline structure, and showing the low-bias disorder as dark patches. (C) A high-bias topographic image Embedded Image, from the same field of view as (B) with the same gray scale, with the 2.6 nm “supermodulation” surface undulation removed but retaining the crystalline structure. Here, minimal nanoscale electronic disorder can be detected.

Modeling the cause of nanoscale electronic disorder in cuprates. Nanoscale electronic disorder effects in cuprates (511, 2023) pose critically important questions. Are there really intense nanoscale CuO2 plane charge density variations in near-optimal high-Tc superconductors? Is the observed electronic disorder due to some form of electronic self-organization or to dopant disorder? If the latter, what is the microscopic mechanism? Is it scattering from dopant atoms that produces the quasi-particle interference modulations (8) and superconducting coherence peak suppression (10, 22, 23)? Which specific dopant atom or defect locations most strongly diminish Tc (3, 4)?

Theoretical studies of the effects of dopant atoms explore several hypotheses. In one such model (2426), poor electrostatic screening of the –2e charge on each dopant atom produces a repulsive potential for electrons, causing holes to accumulate at that location. This local increase in hole density produces reduced energy-gap values near the dopant atoms (2426). Thus, in such a “hole accumulation” model, the disorder in Embedded Image is created electrostatically by the dopant atoms via hole density variations in the CuO2 plane. The second class of model (27) holds that, because of their displacement from the CuO2 plane, the dopant oxygens produce only small-angle scattering, which is nonetheless sufficient to result in both the observed quasi-particle interference modulations and the gap disorder (27). A third model is that the dopants generate local crystalline stress/strain at the nanoscale (2, 3, 28, 29). In this picture, the local electronic disorder occurs because various hopping matrix elements in the crystalline unit cell are altered by crystal distortions near dopants. It seemed reasonable that the exact cause of cuprate nanoscale electronic disorder could contain some contributions from all these, and perhaps other, effects.

Correlating dopant defect locations with electronic disorder. To explore these issues, we acquired simultaneous atomically resolved (i) topographs Embedded Image, (ii) Embedded Image images, (iii) gap maps Embedded Image, and (iv) Embedded Image dopant-defect images for each sample (more than 3 × 105 individual spectra for this study). To analyze such data, we define the normalized cross-correlation Embedded Image between two-dimensional images Embedded Image and Embedded Image as Embedded Image(5) where Embedded Image(6) For simplicity, we designate Embedded Image as C[f:g]. Identical images Embedded Image yield C[f:g] = 1, an image and its negative Embedded Image yield C[f:g] = –1, and C[f:g] = 0 for no local correlation. We calculate a series of cross-correlations between the simultaneously measured Embedded Image, Embedded Image, Embedded Image, and Embedded Image images, yielding similar results at all dopings studied. A typical set of Embedded Image data averaged azimuthally (Fig. 3A) immediately reveals the strong spatial correlations between dopant defects and the electronic disorder.

Important deductions emerge from more detailed analysis of these cross-correlations. It is well known that low-bias topographic disorder and gap maps are anticorrelated (11), and Fig. 3A shows that our measured cross-correlation coefficient between Embedded Image and Embedded Image, Embedded Image, in good agreement. But we can now demonstrate that this effect is indeed generated by dopant defects, because (Fig. 2, A to C; Fig. 3A) strong correlations exist between dopant defect images Embedded Image and both (i) low-bias topographic disorder Embedded Image, Embedded Image, and (ii) simultaneous gap maps Embedded Image, Embedded Image. But these correlations are inconsistent with dopant-induced hole accumulation models (2426) because the sign of the correlation Embedded Image is positive. This means that instead of diminished gap magnitudes, we find predominantly increased gap magnitudes near each dopant defect (Fig. 2, A to C; Fig. 3A). We find that the sign of Embedded Image is negative for both signs of sample bias. This means that low-bias Embedded Image is almost equally diminished for states above and below the Fermi energy. Even more important, as VB is increased, correlations with pairs of topographs of opposite VB remain identical, but the topographic Embedded Image disorder itself begins to moderate near VB = ±0.25 V and is greatly diminished above VB = ±0.60 V (Fig. 3C). Consistent with this, Fig. 3A shows that Embedded Image because disorder in Embedded Image is very weak. All these data indicate that, when integrated over states in the range VB ≈ ±0.9 V, variations in Embedded Image are significantly weaker than had been originally suspected [as had been anticipated from nuclear magnetic resonance studies (30, 31)]. Within the single-particle picture, we estimate that root mean square charge density fluctuations are Embedded Image in the states up to VB ≈ ±0.9 V.

How do the dopant defects generate the electronic disorder? Because disorder in topography clearly exists at low-bias VB ≤ ±0.25 V but diminishes markedly above VB ≈ ±0.60 V, the low-bias electronic disorder must be compensated by contributions of the opposite sign beginning above VB ≈ ±0.25 V. This can occur only if the low-energy LDOS spectral weight diminutions near dopant defects are balanced by equal enhancements at intermediate energies. To test this deduction, we measured Embedded Image images up to high voltage (but well below the ∼–0.96 eV impurity state) and identified the average spectrum associated with each superconducting gap value. The results (Fig. 2D) are color-coded to associate each gap-averaged spectrum with regions of the same color in all gap maps. These shifts are correlated with dopant defect locations to the same degree that the gap map is (Fig. 2, A to C; Fig. 3A, blue line). Therefore, as coherence peaks are suppressed and local gap values increase near dopant defects (Fig. 2, A to C; Fig. 3A), spectral weight shifts from below to above E = 250 meV for filled states and E = 150 meV for empty states are seen (arrows, Fig. 2D). Total spectral weight is conserved within the range |E| 0.9 eV. These effects are most easily detected at intermediate doping (p ≈ 0.14); we anticipate that they will diminish at very low and very high doping.

Because charge density variations are significantly weaker than previously suspected, a non–charge-driven mechanism for the nanoscale electronic disorder effects should be considered. It is known that substitutional atomic disorder at the Sr site suppresses superconductivity strongly (4), most likely by distortions of the crystalline unit cell and associated changes in the hopping matrix elements and superconducting correlations (24, 28, 29). Dopant atoms might act similarly, perhaps by displacing the Sr or apical oxygen atoms nearby, thereby changing the vibration frequencies and/or hopping integrals. Very recently, on the basis of the results reported here, Nunner et al. proposed a new model for the cuprate electronic disorder mechanism (32) in which the dopants not only produce some charge disorder, but also strongly perturb the local superconducting pairing potential on individual bonds between Cu sites. This proposal, that atomic-scale electron pairing–potential variations are paramount, offers a novel explanation for the complex phenomenology described here and in (811, 2023).

Correlating dopant defects with quasi-particle interference modulations. Another long-standing mystery has been the source of the very weak low-energy quasi-particle scattering interference modulations (8) and the much stronger superconducting coherence peak suppressions (8, 10, 22, 23) in Bi-2212. The analysis of correlations between the dopant defects and quasi-particle interference patterns Embedded Image shown in Fig. 4A reveals directly that they are strongly correlated over a wide energy range. The negative sign of these correlations means that minima of LDOS modulations preferentially occur at the dopant defects. This is true at all energies, even though the actual quasi-particle interference patterns are quite different (8). This can be seen directly in images of Embedded Image at E = –14 meV, –24 meV, and –34 meV (Fig. 4, B to D, respectively), with dopant defect locations shown as red dots. In all cases we see that the dopant defects have a very high probability of being found at the minima in the LDOS, even though the patterns are quite different between energies. This implies a fixing of the spatial phase of the LDOS modulations at scattering sites, an effect first seen in cuprates at oxygen vacancy defects in YBa2Cu3O6–δ (5). Perhaps more important, Fig. 4D shows that suppression of superconducting coherence peaks is found primarily near the dopant defect clusters, and the bright regions with the sharp coherence peaks—usually associated with strong superconductivity—occur between them. The correspondence between dopant defect locations and LDOS minima for a variety of LDOS patterns occurring at different energies (Fig. 4) provides clear and direct evidence that these dopant defects generate the LDOS modulations and also suppress superconducting coherence peaks in Bi-2212.

Fig. 4.

(A) R= 0 cross-correlation values C[O(r),LDOS(r,E)] for all energies |E| < 60 meV. These correlations begin to be significant around E = 10 meV and are intense for 30 meV < |E| < 50 meV. The sign is always negative; hence, LDOS is low when the intensity of the –0.96 V peak in the Embedded Image map (e.g., Fig. 1B) is high. This is true even though the LDOS modulation images look completely different at energies that differ by less than 10 meV. (B) Image of oxygen dopant defect locations (red dots) and LDOS at E = –14 meV. The modulations are weak at this energy and consist of numerous wave vectors. Nonetheless, the tendency for the dopant defects to lie in the minima of LDOS modulations can be detected by eye. (C) Image [simultaneous with (B) and (D)] of dopant defect locations and LDOS at E = –24 meV. Here the modulations are strong and more clearly reveal the tendency for the dopants to be at the minima. (D) Image [simultaneous with (B) and (C)] of dopant defect locations and LDOS at E = –34 meV. Here the long-wavelength modulations no longer exist, and the contrast basically represents the height of the –34 meV coherence peaks. The tendency for these peaks to be strongly diminished where the dopants are clustered is obvious.

Our simultaneous imaging of apparent dopant-induced impurity states and superconducting electronic structure points to solutions for several outstanding problems. The results provide direct evidence for the concept of an atomic-scale source for the nanoscale electronic disorder in cuprates (11, 2426). Strong correlations between dopant defect distributions and both gap map and coherence peak amplitude show that the dopant defects are responsible for most (but perhaps not all) of the superconducting electronic disorder in Bi-2212. Further, scattering leading to quasi-particle interference can now be ascribed almost completely to whichever atomic-scale perturbation produces the dopant defects. Finally, the topographic disorder and related superconducting electronic disorder are due empirically to spectral weight shifts from low to high energy near each dopant defect. These data indicate that high-energy spectral weight redistributions, strong coherence peak suppressions, and very weak scattering of low-energy quasi-particles are dominant elements in the atomic-scale mechanism of superconducting electronic disorder in Bi2Sr2CaCu2O8+δ. Similar phenomena arelikelytobecommoninallnonstoichiometric oxygen-doped high-Tc cuprates.

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