Anomalous Doping Evolution of Superconductivity and Quasiparticle Interference in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ Trilayer Cuprates

We use scanning tunneling microscopy to investigate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ trilayer cuprates from the optimally doped to overdoped regime. We find that the two distinct superconducting gaps from the inner and outer ${\mathrm{CuO}}_2$ planes both decrease rapidly with doping, in sharp contrast to the nearly constant $T_C$. Spectroscopic imaging reveals the absence of quasiparticle interference in the antinodal region of overdoped samples, showing an opposite trend to that in single- and double-layer compounds. We propose that the existence of two types of inequivalent ${\mathrm{CuO}}_2$ planes and the intricate interaction between them are responsible for these anomalies in trilayer cuprates.

Figure 1

(a) Temperature dependent magnetic susceptibility of four Bi-2223 samples with different dopings, which exhibit nearly constant $T_{\mathrm{C}}$. Inset: the crystal structure of Bi-2223 with inequivalent IP and OPs. (b) The topographic image of an OPT sample taken with tunneling current $I=5\mathrm{pA}$ and bias voltage $V=-250\mathrm{mV}$. (c) Spatially averaged $\mathrm{d}I/\mathrm{d}V$ curves of the OPT, OD1, OD2, and OD3 samples. The average superconducting gap size decreases significantly with increasing doping.

Figure 2

(a) Representative individual $\mathrm{d}I/\mathrm{d}V$ spectra in the four samples showing two coherence peaks corresponding to the superconducting gaps from the IP and OP (denoted by ${\mathrm{\Delta }}_{\mathrm{IP}}$ and ${\mathrm{\Delta }}_{\mathrm{OP}}$). The locations of the spectra are indicated in Supplemental Material Fig. S1 [24]. The setting current for $\mathrm{d}I/\mathrm{d}V$ measurement is $I=100\mathrm{pA}$ and the bias modulation is 3 mV. (b) In each sample the distribution of ${\mathrm{\Delta }}_{\mathrm{IP}}$ and ${\mathrm{\Delta }}_{\mathrm{OP}}$ can be fitted well by a Gaussian line shape. Both ${\mathrm{\Delta }}_{\mathrm{IP}}$ and ${\mathrm{\Delta }}_{\mathrm{OP}}$ decrease rapidly with increasing doping.

Figure 3

(a) to (d) The conductance ratio maps $z(\mathit{r},E)=g(\mathit{r},E)/g(\mathit{r},-E)$ at selected energies for the OPT, OD1, OD2, and OD3 samples, where the dispersive QPI patterns can be clearly visualized. The scale bar corresponds to 10 nm in each image. Note the systematic decrease of energy scales with increasing doping, which reflects the reduction of superconducting gap size. The last columns in each panel display the FT maps corresponding to the second column $z$ maps with most pronounced QPI patterns.

Figure 4

(a) Schematic illustration of the $d$-wave gap structure and the QPI wave vectors $q_1\sim q_7$ in the “octet” model. (b) The underlying FSs of the four samples derived from their FT-QPI patterns, which exhibit systematic doping dependence. (c) and (d) Left panels: the schematic band structures of the IP (red) and OP (blue) for the OPT and OD3 samples. Right panels: the $k$ dependence of ${\mathrm{\Delta }}_{\mathrm{IP}}$ and ${\mathrm{\Delta }}_{\mathrm{OP}}$ with $d$-wave gap function. The solid blue and red dots indicate the tip of the Fermi arc with effective superconducting gap ${\mathrm{\Delta }}_{\mathrm{SC}}\sim 21\mathrm{meV}$ for the two samples.