Evolution of Charge and Pair Density Modulations in Overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_{6+\delta }$

One of the central issues concerning the mechanism of high-temperature superconductivity in cuprates is the nature of the ubiquitous charge order and its implications to superconductivity. Here, we use scanning tunneling microscopy to investigate the evolution of charge order from the optimally doped to strongly overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CuO}}_{6+\delta }$ cuprates. We find that, with increasing hole concentration, the long-range checkerboard order gradually evolves into short-range glassy patterns consisting of diluted charge puddles. Each charge puddle has a unidirectional nematic internal structure and exhibits clear pair density modulations as revealed by the spatial variations of the superconducting coherence peak and gap depth. Both the charge puddles and the nematicity vanish completely in the strongly overdoped nonsuperconducting regime, when another type of short-range order with $\sqrt{2}\times \sqrt{2}$ periodicity emerges. These results shed important new light on the intricate interplay between the intertwined orders and the superconducting phase of cuprates.

Popular Summary

In the copper-oxide-based high-temperature superconductors known as cuprates, electrons tend to organize themselves into regular structures. In particular, various experiments have revealed the emergence of a ubiquitous checkerboard charge pattern that vanishes if the compound is heavily doped with positively charged electron vacancies, or “holes.” There are still many debates regarding the nature of this charge pattern, such as how and why it evolves with increasing hole density as well as its connection (if any) to cuprate superconductivity. Here, we use scanning tunneling microscopy to study the atomic-scale electronic structure of one such cuprate as the hole density increases.

As doping increases, we find that the long-range checkerboard charge pattern gradually evolves into short-range glassy patterns consisting of diluted charge puddles. On the other hand, the unidirectional stripelike internal structure of each charge puddle is impervious to overdoping. Modulations in the density of electron pairs exhibit the same trend and are positively correlated with charge density modulations. Both the charge puddles and the internal stripe pattern vanish completely in the strongly overdoped nonsuperconducting regime, when another type of periodic charge pattern emerges.

Our work provides a complete picture of the doping evolution of charge and pair density modulations in cuprates. The dichotomy between the intrapuddle structure and interpuddle ordering shed important new light on the origin of the intertwined orders and their implications to superconductivity.

Figure 1

The optimally doped Bi-2201 sample with $p=0.16$. (a) Atomically resolved topographic image acquired at bias voltage $V=-80\mathrm{mV}$ and tunneling current $I=5\mathrm{pA}$ over an area of $400\times 400{\AA }^2$. (b) The $dI/dV$ map measured in the same area as (a) at bias voltage $V=10\mathrm{mV}$ and tunneling current $I=20\mathrm{pA}$. (c) The Fourier transform map of (b), where the lattice Bragg peaks are marked by red circles and the $\mathrm{Cu}─\mathrm{O}$ bond direction is indicated by a red dashed line. The blue circle highlights the wave vector of the checkerboard charge order. (d) The autocorrelation map of (b) exhibiting a long-range checkerboard charge order, and the four red circles indicate the distance between neighboring charge puddles. The white dashed line indicates the $\mathrm{Cu}─\mathrm{O}$ bond direction, along which the autocorrelation intensity linecut is acquired. (e) Bias-dependent autocorrelation intensity $AC(\mathit{R})$ linecuts. The red dashed line indicates the position of the charge order peak, which is nondispersive over a wide range of energies.

Figure 2

The overdoped OD-24K sample with $p=0.19$. (a) Atomically resolved topographic image acquired at $V=100\mathrm{mV}$ and $I=5\mathrm{pA}$ over an area of $400\times 400{\AA }^2$. (b) The $dI/dV$ map measured in the same area as (a) at bias voltage $V=10\mathrm{mV}$. (c) The Fourier transform map of (b), where the blue circle indicates the absence of a FT peak for the checkerboard order. (d) The autocorrelation map of (b), where the short-range charge order is revealed by four bright spots in a red circle. (e) Bias-dependent autocorrelation intensity $AC(\mathit{R})$ linecuts along the $\mathrm{Cu}─\mathrm{O}$ bond direction. The red dashed line indicates the nondispersive charge order peak.

Figure 3

The overdoped OD-15K sample with $p=0.21$. (a) Atomically resolved topographic image acquired at $V=-100\mathrm{mV}$ and $I=20\mathrm{pA}$ over an area of $400\times 400{\AA }^2$. (b) The $dI/dV$ map measured in the same area as (a) at bias voltage $V=10\mathrm{mV}$. (c) The Fourier transform map of (b). (d) The autocorrelation map of (b), where the bright arc marked by the red oval indicates the remnant charge order. (e) Bias-dependent autocorrelation intensity $AC(\mathit{R})$ linecuts. The nondispersive first peaks suggest that the fussy arc corresponds to the glassy patterns of charge puddles.

Figure 4

The overdoped OD-0K sample with $p=0.23$. (a) Atomically resolved topographic image acquired at $V=100\mathrm{mV}$ and $I=5\mathrm{pA}$ over an area of $350\times 350{\AA }^2$. (b) The $dI/dV$ map measured in the same area as (a) at bias voltage $V=10\mathrm{mV}$. The patches of short-range $\sqrt{2}\times \sqrt{2}$ order are indicated by the broken yellow squares. (c) The Fourier transform map of (b) displaying the Bragg peaks in the red circles, as well as the short-range $\sqrt{2}\times \sqrt{2}$ charge order in the blue circle. (d) The autocorrelation map of (b), where the central cross and the spot in the circle indicate the short-range $\sqrt{2}\times \sqrt{2}$ charge order in separated patches.

Figure 5

The doping evolution of charge orders. (a) The schematic electronic phase diagram of Bi-2201, and the arrows indicate the hole densities of the four samples studied in this work. (b) Doping dependence of the charge puddle density and the percentage of areas with $\sqrt{2}\times \sqrt{2}$ charge order. (c)–(e) Schematic cartoons illustrating the evolution of charge order with increasing doping. The yellow spheres represent the charge puddles with a size of approximately $4a_0$ and the black lines sketch the internal stripy structure. In the overdoped non-SC sample, the charge puddles with stripy internal structure disappear, and small patches with $\sqrt{2}\times \sqrt{2}$ charge order emerge.

Figure 6

The PDW features in the optimally doped sample. (a) The spectra taken along the yellow arrow in the inset $dI/dV$ map. (b) Three representative curves taken on the colored spots in (a), and the gap depth $H$ of each curve is illustrated by the dashed line. (c) The $D(V)=-d^{3}I/d{V}^3$ curves of the three curves in (b). The $D(V_{\mathrm{sc}})$ value at $V_{\mathrm{sc}}(\mathit{r})\sim 10\mathrm{mV}$ shows the sharpness of the local SC coherence peak. (d) The $H$ map exhibits the distribution of local gap depth $H(\mathit{r})$. (e) The $D$ map displays the spatial distribution of SC coherence peak sharpness at each location. (f),(g) The intensity distribution of cross-correlation $C(\mathit{R})$ between the $H$ map and $D$ map with the $dI/dV(10\mathrm{mV},\mathit{r})$ map in Fig. 1. The maximum value at the center indicates a positive correlation.

Figure 7

The pair density modulation features in two overdoped SC samples. (a),(d) Spectral linecuts along the yellow arrows on the OD-24K and OD-15K samples, respectively. The insets are the corresponding $dI/dV$ maps ($50\times 50{\AA }^2$) taken at bias voltage $V=10\mathrm{mV}$. (b),(e) The $H$ maps of the OD-24K and OD-15K samples, and the insets are the same cross-correlation plots as in Fig. 6. (c),(f) The $D$ maps of the OD-24K and OD-15K samples, and the corresponding cross-correlations are shown in the insets. The maximum at the center indicates a positive correlation between the charge and pair density modulations.