Effect of Structural Supermodulation on Superconductivity in Trilayer Cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$

We investigate the spatial and doping evolutions of the superconducting properties of trilayer cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ by using scanning tunneling microscopy and spectroscopy. Both the superconducting coherence peak and gap size exhibit periodic variations with structural supermodulation, but the effect is much more pronounced in the underdoped regime than at optimal doping. Moreover, a new type of tunneling spectrum characterized by two superconducting gaps emerges with increasing doping, and the two-gap features also correlate with the supermodulation. We propose that the interaction between the inequivalent outer and inner ${\mathrm{CuO}}_2$ planes is responsible for these novel features that are unique to trilayer cuprates.

Figure 1

(a) Schematic half-unit-cell crystal structure of Bi-2223. (b) Illustration of the spatial phase $\theta$ of supermodulation. (c) Topographic image ($24\times 24{\mathrm{nm}}^2$) and (d) spatial variation of tunneling spectra of an underdoped (UD) Bi-2223, where the blue arrows indicate the direction along which the spectra are displayed. (e),(f) The same plots for an OPT Bi-2223 sample. The topographic images in (c) and (e) are taken with bias voltage $V=-250\mathrm{mV}$ and tunneling current $I=10\mathrm{pA}$ and $I=40\mathrm{pA}$, respectively.

Figure 2

The topographic image (a), the spatial distribution of relative gap size variation (b), and coherence peak height variation (c) of the underdoped Bi-2223 extracted from the spectral grid. (d)–(f) The same set of maps in the OPT Bi-2223. The underdoped sample exhibits much more pronounced periodic variations with the supermodulation than the optimally doped sample.

Figure 3

(a) Averaged $dI/dV$ curves on the supermodulation ridge and valley in UD (lower panel) and OPT (upper panel) Bi-2223, normalized to the background conductance $dI/dV(+135\mathrm{mV})$. (b) Normalized gap size (lower panel) and coherence peak height (upper panel) of three different samples as a function of $\theta$. The solid symbols are experimental data, and the curves are fittings by a cosine function.

Figure 4

Emergence of two SC gaps in OPT Bi-2223. (a) Eight representative $dI/dV$ curves showing two SC gaps. Although most spectra show the two-gap feature, the spatial average of them tends to smear it out and leads to a broad peak as shown in Figs. 1 and 3 (see Supplemental Fig. S5 [20] for details). (b) Histogram of the larger IP gap (blue) and smaller OP gap (red), which can be fit by Gaussian functions (the solid lines) that peak at ${\mathrm{\Delta }}_{\mathrm{OP}}=40\mathrm{meV}$ and ${\mathrm{\Delta }}_{\mathrm{IP}}=52\mathrm{meV}$, respectively. (c) Peak heights of the fitted double Lorentzian curves as a function of $\theta$. The red and blue curves are cosine fittings of the statistical data.