Atomic manipulation of the gap in Bi2Sr2CaCu2O8+x

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Science  03 Jan 2020:
Vol. 367, Issue 6473, pp. 68-71
DOI: 10.1126/science.aaw7964

Manipulating the gap

Cuprate superconductors typically have a large amount of spatial inhomogeneity, partly stemming from the inhomogeneity of the chemical doping process. In particular, the size of the spectroscopic gap can vary widely across a single sample. Massee et al. used the tip of a scanning tunneling microscope to manipulate atoms on the surface of a member of the Bi2Sr2CaCu2O8+x cuprate family. Moving bismuth atoms up or down caused adjacent atoms to shift laterally, leading to reversible local changes in the size of the gap. It is expected that the technique can be used to probe the influence of the local lattice on the electronic states of other correlated materials.

Science, this issue p. 68


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 Bi2Sr2CaCu2O8+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.

One of the challenges in the study of high-temperature superconductivity in the cuprates (1) is their intrinsic inhomogeneous nature. This is exemplified by the archetypal system Bi2Sr2CaCu2O8+x (Bi2212), whose complicated crystal structure includes an incommensurate structural supermodulation (2) and interstitial oxygen dopant atoms. Particularly notable is the large variation in spectral gap size over nanometer-scale distances (35), which has been shown to reflect local variations in the superconducting transition temperature Tc (6, 7) and has been correlated to both oxygen dopants (8, 9) and structural inhomogeneity (10). These correlations, however, typically involve averages over a large number of sites. To directly probe the influence of dopants, structural defects, and crystallographic characteristics on the local electronic states at the atomic scale, direct noninvasive control of the dopant positions and the inhomogeneous crystal structure they inhabit is therefore desirable. Unfortunately, common techniques for single-atom manipulation involving short-range forces between the tip and the atom (1113) and/or vibrational excitation using the tunneling current (1416) are not well suited for controllable manipulation of atoms in single-crystal cuprate materials. This is because the dopant atoms are buried under the surface and the diffusion barrier of the surface atoms themselves is too high. Alternatively, the electric field can be used to manipulate a surface (1719); however, because the field profile depends on the size of the tip apex, this process is, in practice, difficult to control unless specific atoms are more sensitive to the field than others owing to their charge or local environment. We discovered that this is exactly the case in Bi2212, where we find two local environments that are more readily influenced by the electric field than the rest of the system.

Figure 1A shows a schematic of the two environments that allow for field-induced atom manipulation: surface Bi atoms on the crest of the periodic modulation of the bulk crystal structure (2), henceforth referred to as the supermodulation, and the recently discovered weakly coupled oxygen dopants (20). To manipulate the atoms, we position our tip above the surface and slowly increase the sample bias voltage, Vs. Upon reaching ~800 mV at a tunnel current of ~100 pA, we start to observe jumps in the current, where each jump corresponds to the manipulation of an atom below the tip. For manipulation voltages Vs ≥ 1.2 V, the current typically shows two types of jumps (Fig. 1B): small ones corresponding to the manipulation of a near-surface oxygen dopant, which we can detect through their signature in the differential conductance (8, 9, 20), and big jumps corresponding to the manipulation of a surface Bi atom on the crest of the supermodulation that are observed directly in the constant current images (Fig. 1C) [section 1 of (21)]. We can freeze-in any new surface-and-dopant configuration by switching back to low bias voltage. Because the spatial extent of the highest electric field is determined by the size of the tip apex, which is typically a few tens of nanometers in diameter, in principle, several hundred Bi and oxygen dopants can be affected. However, unlike in a homogeneous system where the threshold field for manipulation is identical for all field-affected atoms or molecules (19), the existence of intrinsic lattice distortions, the supermodulation, and numerous local dopant environments in Bi2212 (20) leads to a range of threshold fields, enabling selective and reversible manipulation by carefully tuning the tip position and the manipulation voltage. As expected for electric field–induced manipulations, all manipulations we observe are confined to a roughly circular area with a diameter of a few tens of nanometers around the location of the tip during the application of the manipulation voltage (fig. S5). Owing to the aforementioned intrinsic inhomogeneous nature of Bi2212, studying the influence of single atoms on the local electronic structure is normally impossible, and averaging over a large number of sites is required instead. With the ability to locally rearrange a select number of atoms, however, we can effectively remove the inhomogeneous background information by considering the difference in local electronic states before and after manipulation. These difference measurements will only show contrast where the density of states has been altered by the atom manipulation, providing a direct link between single atomic sites and the local electronic structure.

Fig. 1 Electric field–induced atom manipulation.

(A) Illustration of the field-induced manipulation of surface Bi atoms and near-surface oxygen dopants (Bi, blue; O, black or orange; Cu, red). (B) Current as a function of time at Vs = 1.3 V. Small jumps signal oxygen dopant manipulation (O2−), large jumps signal surface Bi rearrangement (Bi). (C) Constant current images, z(r), (Eset = −100 meV; Iset = 100 pA) of reversible surface Bi atom manipulation upon treatment with Vs > 1.2 V. The atoms in the dashed box are manipulated. Scale bars, 1 nm. All measurements throughout this work were performed at temperature T ≤ 4.2 K.

To generate a difference map of the spectral gap, we record low-energy differential conductance maps and extract a map of the peak-to-peak gap, Δi(r), using identical settings before and after atom manipulation. Figure 2, A and B, shows one example of a gap map taken before and after ~10 dopants and Bi surface atoms have been manipulated. Three subsequent electric field manipulation treatments are shown in section 4 of (21). Whereas the topographies and the gap maps are mostly identical, excluding any change of the tip itself, select locations show substantial changes, with gaps increasing and decreasing by >10 meV. The two spectra in Fig. 2C, which are taken at the same location before and after the electric field–induced manipulation, highlight the significance of these changes. The spectra are predominantly affected at the peak energies, whereas the low energy states, |E| < 20 meV, are hardly modified, if at all, highlighting the insensitivity of the latter to disorder (22) (fig. S7). From the two gap maps, we then calculate the difference map, D2−1(r) = Δ2(r) − Δ1(r), which shows directly where the gap has enhanced (blue) or decreased (red) upon the electric field manipulation (Fig. 2D). As the histograms of the gap changes in Fig. 2E show, the average gap size over the entire field of view is preserved: The gap is both reduced and enhanced in equal measure in the vicinity of the manipulated atoms.

Fig. 2 Gap modification.

Maps of the peak-to-peak gap, Δ, taken (A) before and (B) after field-induced atom manipulation at 1.5 V and ~100 pA. Dots mark the locations where Bi atoms have been manipulated. (C) Spectrum taken before and after manipulation on the location indicated by an X in (A) and (B), showing a clear change in Δ. (D) Difference of the gap maps taken (A) before and (B) after manipulation: D2−1(r) = Δ2(r) – Δ1(r). Black dots mark the same locations as in (A) and (B), the dashed box indicates the area of Figs. 1C and 3A. (E) Histograms of D = Δi+1 − Δi for four consecutive manipulations; i = 1 corresponds to the difference map in (D). For all maps, the average change in the gap size is zero. (F) Simulation of the difference map in (D) using our model of a shifting Gaussian. The fitted dipole profile (Fig. 4B, bottom) is placed on every manipulated site (black dots) using the orientation extracted from fits to the data (fig. S13) [see also section 4 of (21)].

Using the topographies taken simultaneously with the gap maps, we can next pinpoint where surface Bi atoms have been manipulated (fig. S8 and S9); the locations of manipulated Bi atoms have been marked with black dots on the two gap maps (Fig. 2, A and B) and in their difference map in Fig. 2D. Similarly, from high energy differential conductance maps we can extract the position of all near-surface oxygen dopants, as well as determine which dopants have changed [section 1 of (21)]. The gap changes in Fig. 2D are clearly linked to the atomic manipulations, but in a rather unexpected manner: The altered Bi sites mark the boundary between regions of increasing and decreasing gaps, whereas the gap on the sites itself is hardly affected. Whereas one would expect the manipulation of oxygen dopants to have a strong effect on the gap, the contribution to the gap modifications of the near-surface dopants we manipulate does not appear to be the dominant one: The correlation between their location and where the gap changes is only moderate, and when we manipulate a single near-surface dopant atom, the gaps in its vicinity shift by a few milli–electron volts at most (fig. S6). This observation is in line with a previous study that found these dopants (i.e., those with a resonance at −1 eV < E < −0.4 eV) to have a much weaker correlation to the intrinsic gap inhomogeneity than the ones closer to the CuO2 plane (9). The dominant contribution of manipulated Bi atoms and the secondary nature of the manipulated oxygen atoms are exemplified by the simulation shown in Fig. 2F. As discussed below, the simulation, which is in good agreement with experiment, uses a model that takes into account only Bi manipulations.

Atomic scale difference images of two consecutive manipulations of the same Bi atom are shown in Fig. 3A. Two observations stand out. First, whenever a surface modification reverts in a subsequent electric field treatment, the gap reverts back as well. Consequently, the difference images between the first and third map, D3−1(r), is featureless (fig. S11), and D3−2(r) = −D2−1(r) (Fig. 3A, right and left, respectively). For isolated manipulation events, even the full spectrum reverts to the original configuration (fig. S12). Second, the direction along which the gap is altered appears to be linked to the direction of the surface Bi atom repositioning. As can be seen from Fig. 3A and as shown schematically in Fig. 3B, each time a Bi atom moves down below (up into) the BiO plane, a neighboring atom laterally shifts toward (away) from it, leading to an enhancement of the spectral gap in the direction of this shift.

Fig. 3 Atomic position dependence of gap changes.

(A) D2−1 = Δ2(r) – Δ1(r) image on the same area as the constant current images in Fig. 1C. The manipulated Bi atoms are marked by circles, the lateral movement upon manipulation is indicated by an arrow. The right panel shows the opposite gap modification upon a reversion of the atomic configuration after a subsequent Vs = 1.5 V manipulation. Scale bars, 1 nm. (B) Schematic of the surface change and its effect on the gap: One atom moves up (down), another shifts laterally away from (toward) it, resulting in gap enhancement in the direction of the shift. More details and examples can be found in sections 1 and 4 of (21).

To quantify the direction of the gap change in more detail, we average the D(r) images around each surface Bi manipulation after aligning their direction of maximum gap increase [see section 4 of (21)]. As Fig. 4A shows, a clear dipole profile, centered at the surface modification in an otherwise unaffected environment, is obtained. The two lobes of the dipole have opposite signs, are a few nanometers in size, and are located at opposite ends, ~1.5 nm distance from the surface manipulation. The horizontal line-cut on the right side of Fig. 4A shows this in more detail. The most straightforward way to create a dipole-shaped profile in a difference image is by subtracting two identical [two-dimensional (2D)] peaks that are laterally shifted with respect to each other (Fig. 4B). In the context of our experiment, this would correspond to a single peak that laterally shifted by the electric field manipulation, which upon generating the difference map is thus subtracted from itself at a slightly different location. The maxima of the subtraction, i.e., the lobes of the dipole, are in the direction of the shift, as we observe in the experiment. For shifts smaller than the width of the peak, the lateral extent of the resulting dipole will depend exclusively on the width, whereas the magnitude of the dipole is a function of the size of the shift and the peak amplitude (Fig. 4B, inset). Using this simple toy model, we can accurately reproduce both the size and shape of the observed dipole when we use a Gaussian profile for the peak, as well as simulate the experimental data (Fig. 2F). Conversely, a Lorentzian profile decays too slowly to properly fit the tails of the difference image, as can be seen from the line-cut comparison in Fig. 4A. For a realistic lateral shift of 2 Å (see, for example, Fig. 1C), the Gaussian requires an amplitude of ~50 meV, which is not unreasonable given the average peak-to-peak gap size of Δ = 96 meV. Lastly, the width of the Gaussian is 1.7 nm, which is comparable to the superconducting coherence length.

Fig. 4 Dipole profile and toy model.

(A) Average D(r) for all topographic modifications after aligning their orientation. The arrow indicates where the vertical line trace on the right is taken for the experimental data (red circles) and for the toy model using a Gaussian (black dashed line) and Lorentzian (blue dashed line) peak profile. (B) A 2D Gaussian (width = 1.7 nm; top left) is shifted by a fraction of a nanometer (top right, shift exaggerated for clarity), leading to a difference (bottom) upon their subtraction with the same shape and length scales as the experimental data in (A). The inset shows how the amplitude of the subtracted Gaussians depends on the shift distance: a 2-Å shift requires an amplitude of Δ ~ 50 meV (dashed lines).

A Gaussian-shaped gap distribution that falls off with length scales on the order of the coherence length is highly suggestive of a local pairing potential originating from a point-like object. When we laterally move this entity using the electric field of the tip, its local pairing potential moves with it, leading to a dipole-shaped feature in the difference image. The physical origin of the object is possibly related to the Bi atoms themselves, although the contribution of the Bi orbitals to the low energy density of states is limited (23). More likely, the apical oxygen atoms directly below the Bi atoms shift concomitant with the Bi manipulation, leading to the gap modifications. The importance of the apical oxygen atoms in both the tunneling process (2426) and the gap size (10) have been stressed previously. Our observations provide additional input for further theoretical investigations—particularly those that take into account on-site correlations (27, 28)—into the origin of the spectral gap, and the tunneling process, in this cuprate superconductor.

An alternative source of the dipole-shaped difference image could be the appearance of topological defects that introduce a 2π-rotation of the phase of the order parameter (29). However, creation and annihilation of topological defects has to occur in pairs. Given our finite field of view, it may be that one-half of the pair is outside our measurement range, but given the large field-of-view topographic before-and-after comparison (fig. S5), and assuming that both pairs will have a signature in topography, this is unlikely. Furthermore, in our optimally doped system we do not find a significant correlation between the gap changes and topological defects in the smectic, or the d-form factor density wave, reported for underdoped samples (30, 31). Extension of our work to lower doping concentrations, where the various charge- and spin-ordered states are more predominant, should give a more definite answer to this issue. Additionally, the influence of dopants and the surface structure on these (ordered) states themselves can be studied directly using the field-induced atom manipulation we introduce in this work.

The observation of a profound influence on the peak-to-peak gap in tunneling experiments of subnanometer shifts in atomic positions highlights the importance of the lattice on the local electronic properties of the cuprates. The spatial profile of the gap modification we observe is highly suggestive of the field-induced lateral movement of a local pairing potential in the CuO2 plane originating from a point-like object. This work demonstrates an avenue to noninvasively and reversibly probe the influence of the local lattice on the electronic states of cuprate high-temperature superconductors and related compounds.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S13

References (3338)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: We thank M. Civelli, A. Mesaros, and P. Simon for fruitful discussions. Funding: F.M. acknowledges funding from H2020 Marie Skłodowska-Curie Actions (grant 659247) and the ANR (ANR-16-ACHN-0018-01). Author contributions: F.M. and M.A. conceived of the study and discussed and interpreted the results. F.M. performed and analyzed all measurements. Y.K.H. grew the samples. F.M. wrote the manuscript with M.A. Competing interests: The authors declare no competing interests. Data and materials availability: The data files for the results presented here are available at (32).

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