Scanning tunneling microscopy and spectroscopy study of $4a\times 4a$ electronic charge order and the inhomogeneous pairing gap in superconducting ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$

We performed scanning tunneling microscopy and scanning tunneling spectroscopy (STS) measurements on underdoped Bi2212 crystals with doping levels $p\sim 0.11$, $\sim 0.13$, and $\sim 0.14$ to examine the nature of the nondispersive $4a\times 4a$ charge order in the superconducting state at $T⪡T_c$. The charge order appears conspicuously within the pairing gap, and low doping tends to favor the charge order. We point out the possibility that the $4a\times 4a$ charge order will be dynamical in itself, and pinned down over regions with effective pinning centers. The pinned $4a\times 4a$ charge order is closely related to the spatially inhomogeneous pairing gap structure, which has often been reported in STS measurements on high-$T_c$ cuprates.

Figure 1

(Color online) Schematic energy diagram of Bi2212 and illustration of STM measurements at (a) high $(V_s>{\Delta }_{\mathrm{Bi}\text{−}\mathrm{O}})$ and (b) low biases $(V_s<{\Delta }_{\mathrm{Bi}\text{−}\mathrm{O}})$. The density of states $N\left(E\right)$ for Cu-O and Bi-O layers are schematically represented by thin and thick lines, respectively. In the high-bias STM experiment, electron tunneling occurs predominantly between the STM tip and the Bi-O layer when the tip-sample separation is large, whereas in the low-bias STM experiment, it occurs between the STM tip and the Cu-O layer when the tip-sample separation is small.

Figure 2

(Color online) (a) Part of a low-bias STM image of sample A, measured at a bias voltage of $V_s=30\mathrm{mV}$ and an initial tunneling current of $I_t=0.08\mathrm{nA}$ at $T\sim 9\mathrm{K}$, showing a $4a\times 4a$ superstructure, together with individual atoms. The inset is part of a high-bias STM image of sample A, measured at $V_s=600\mathrm{mV}$ and $I_t=0.3\mathrm{nA}$ at $T\sim 9\mathrm{K}$. The image shows a one-dimensional (1D) superlattice, inherent in the Bi-O layer, with missing atom rows. (b) Line profiles taken along the solid line in the STM image [Fig. 2a] for various bias voltages. The solid line is cut perpendicular to the $b$ axis, that is, 45° from the orientation of the $4a\times 4a$ superstructure so that the 1D superlattice of the Bi-O layer does not obscure the profile of the $4a\times 4a$ superstructure. Note that, in the line profile for the lowest bias, the spatial variation due to the underlying host lattice is partly cut over the intense $4a\times 4a$ superstructure because of saturation of the STM amplifier.

Figure 3

(Color online) (a) Part of a low-bias STM image of sample B, measured at $V_s=10\mathrm{mV}$ and $I_t=0.08\mathrm{nA}$ at $T\sim 9\mathrm{K}$. The inset is part of a high-bias STM image of sample B, measured at $V_s=600\mathrm{mV}$ and $I_t=0.3\mathrm{nA}$ at $T\sim 9\mathrm{K}$. Note that it shows almost no missing atom rows in contrast with that of sample A [the inset of Fig. 2a]. (b) Line profile of STM image taken along the solid line in Fig. 3a at $V_s=10\mathrm{mV}$ (solid line). For comparison, the line profile at $V_s=30\mathrm{mV}$ for sample A [Fig. 2b] is also shown (dashed line). The dashed line for sample B is a guide to the eye.

Figure 4

(Color) (a) 2D Fourier maps of the STM images of sample A, taken at $V_s=30\mathrm{mV}$ at $T\sim 9\mathrm{K}$ (the lower inset) and $\sim 82\mathrm{K}$ $(>T_c)$ (the upper inset), and cut along the $(0,0)\text{−}(\pi ,0)$ line in the Fourier maps at various bias voltages. The Fourier amplitude is normalized by the intensity of the Bragg peak except the amplitude at the lowest bias, which is normalized so that its background level agrees with those for other biases. (b) Fourier map of the STM image of sample B, taken at $V_s=30\mathrm{mV}$ at $T\sim 9\mathrm{K}$ (the inset), and cut along the $(0,0)\text{−}(\pi ,0)$ line at various bias voltages. The Fourier amplitude is also normalized by the intensity of the Bragg peak.

Figure 5

(Color online) (a) Part of a low-bias STM image of sample C, measured at $V_s=30\mathrm{mV}$ and $I_t=0.09\mathrm{nA}$ at $T\sim 9\mathrm{K}$, showing a $4a\times 4a$ superstructure. The inset is part of a high-bias STM image of sample C, measured at $V_s=300\mathrm{mV}$ and $I_t=0.3\mathrm{nA}$ at $T\sim 9\mathrm{K}$. (b) Line profiles, taken along the solid line in STM image [Fig. 5a], at different bias voltages (the solid lines). For comparison, the line profile at $V_s=30\mathrm{mV}$ for sample A [Fig. 2b] is also shown (the dashed line). The dashed line for sample C is a guide to the eye. (c) Part of a low-bias STM image of sample D, measured at $V_s=30\mathrm{mV}$ and $I_t=0.08\mathrm{nA}$ at $T\sim 9\mathrm{K}$, showing a very weak $4a\times 4a$ superstructure. The inset is part of a high-bias STM image of sample D, measured at $V_s=300\mathrm{mV}$ and $I_t=0.3\mathrm{nA}$ at $T\sim 9\mathrm{K}$.

Figure 6

(Color online) (a) Part of a low-bias STM image of sample E, measured at $V_s=20\mathrm{mV}$ and $I_t=0.08\mathrm{nA}$ at $T\sim 9\mathrm{K}$, showing a $4a\times 4a$ superstructure. The inset is part of a high-bias STM image of sample E, measured at $V_s=800\mathrm{mV}$ and $I_t=0.3\mathrm{nA}$ at $T\sim 9\mathrm{K}$. (b) Part of a low-bias STM image of sample F, measured at $V_s=20\mathrm{mV}$ and $I_t=0.08\mathrm{nA}$ at $T\sim 9\mathrm{K}$, showing a very weak $4a\times 4a$ superstructure. The inset is part of a high-bias STM image of sample F, measured at $V_s=800\mathrm{mV}$ and $I_t=0.3\mathrm{nA}$ at $T\sim 9\mathrm{K}$.

Figure 7

(Color) Line cuts of 2D Fourier maps of STM images along the $(0,0)\text{−}(0,\pi )$ lines at various bias voltages for samples C, D, E, and F. Here the Fourier amplitude is normalized by the intensity of the Bragg peak. The insets of (a), (b), (c), and (d) are 2D Fourier maps of STM images shown in Figs. 5a, 5c, 6a, 6b, respectively.

Figure 8

(a) Averaged STS spectra of samples A, C, D, and E on the positive bias side $(V_s⩾0)$. (b) Energy (bias) dependence of the Fourier amplitude at $\mathit{q}\sim 1∕4$ for sample pairs (A, B), (C, D), (E, F) and sample ${\mathrm{D}}^{\prime }$. The data referred to as samples D and ${\mathrm{D}}^{\prime }$ were measured on different areas of the same cleaved surface. The arrow shows the sample bias $V_s$ corresponding to gap size ${\Delta }_0$ in the averaged STS spectrum shown in Fig. 8a.

Figure 9

(a) Spatial dependence of STS spectra at $T\sim 9\mathrm{K}$ for sample A. Solid and dashed lines represent the asymmetric V-shaped ZTPG and the symmetric V-shaped gap with no peaks at the gap edge. (b) STS spectrum averaged over a distance of $\sim 35\mathrm{nm}$ on the cleaved surface of sample A at $T\sim 9\mathrm{K}$. Typical ZTPG spectra of lightly doped Na-CCOC (dotted line) and Bi2212 (dashed line) are also shown for comparison (Refs. 1, 2).

Figure 10

Spatial dependence of the STS spectra of sample B, taken at $T\sim 9\mathrm{K}$ along the dashed line with a length of $\sim 30\mathrm{nm}$ in Fig. 3a. Two-headed arrows next to the spectra indicate the regions where the $4a\times 4a$ superstructure is clearly observed.

Figure 11

(Color) Spatial dependence of STS spectra of sample C, taken along the dashed line with a length of $\sim 30\mathrm{nm}$ at $T\sim 9\mathrm{K}$ in Fig. 5a. Representative gap structures are colored. (b) Representative gap structures shown by the colored lines in Fig. 11a. The dashed line shows the STS spectrum averaged over all the STS spectra in Fig. 11a.

Figure 12

(Color online) Illustration for “the Fermi arc.” Note that the pairing gap is inhomogeneous around the antinodes near $(\pi ,0)$ and $(0,\pi )$.

Figure 13

(a) Spatial dependence of STS spectra of sample D, taken along the dashed line with a length of $\sim 40\mathrm{nm}$ at $T\sim 9\mathrm{K}$ in Fig. 5c. (b) STS spectra averaged over all spectra for samples C and D.

Figure 14

(Color) (a) Spatial dependence of STS spectra of sample E, taken along the dashed line with a length of $\sim 30\mathrm{nm}$ at $T\sim 9\mathrm{K}$ in Fig. 6a. Representative gap structures are colored. (b) Representative gap structures shown by the colored lines in Fig. 14a. The dashed line shows the STS spectrum averaged over all the STS spectra in Fig. 14a.

Figure 15

Line cuts of the Fourier spots associated with the 1D superlattice in samples C and D, obtained from the insets of Figs. 7a, 7b. Here the peak intensities for samples C and D were normalized with their Bragg-peak intensities. The line cuts were taken along (1,0)-(0,1) lines around the Bragg spots, as shown by dotted boxes in the inset. The inset is the 2D Fourier map for sample D shown in Fig. 7a, although its contrast is enhanced so that the Fourier spots associated with the 1D superlattice will clearly be visible in the inset.

Figure 16

(a) Spatial dependence of STS spectra of sample F, taken along the dashed line with a length of $\sim 15\mathrm{nm}$ at $T\sim 9\mathrm{K}$ in Fig. 6b. (b) STS spectra averaged over all spectra for samples E and F.