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STM/STS Study on 4a X 4a Electronic Charge Order of Superconducting Bi2Sr2CaCu2O8+d

We performed low-bias STM measurements on underdoped Bi2212 crystals, and confirmed that a two-dimensional (2D) superstructure with a periodicity of four lattice constants (4a) is formed within the Cu-O plane at T<Tc. This 4a X 4a superstructure, oriented along the Cu-O bonding direction, is nondispersive and more intense in lightly doped samples with a zero temperature pseudogap (ZTPG) than in samples with a d-wave gap. The nondispersive 4a X 4a superstructure was clearly observed within the ZTPG or d-wave gap, while it tended to fade out outside the gaps. The present results provide a useful test for various models proposed for an electronic order hidden in the underdoped region of high-Tc cuprates.

Recently STM/STS studies on the pseudogap state of Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) at T > T c have revealed a nondispersive two-dimensional (2D) superstructure with a periodicity of about four lattice constants (∼4a×4a superstructure) in the map of energy-resolved differential tunneling conductance dI/dV , proportional to the local density of states (LDOS). 1) The nondispersive 4a×4a structure, electronic in origin, was also reported in the LDOS maps taken on the zero temperature pseudogap (ZTPG) regions of lightly doped Ca 2−x Na x CuO 2 Cl 2 (Na-CCOC) and Bi2212 samples. 2,3) A similar spatial structure was first observed around the vortex cores of Bi2212 exhibiting a pseudogap-like V-shaped spectrum with no coherence peak. 4) Such 2D spatial structures have attracted much attention because they can be a possible electronic order hidden in the pseudogap state.
From the LDOS maps taken for the superconducting (SC) state of Bi2212, Hoffman et al. and McElroy et al. reported a strongly dispersive 2D superstructure. 5,6) This superstructure has been successfully explained in terms of a quasiparticle scattering interference. Furthermore, Howald et al. found a nondispersive ∼4a×4a superstructure with anisotropy in addition to the weakly dispersive one, and claimed that the nondispersive ∼4a×4a superstructure will be due to the so-called stripe order and coexist with superconductivity. 7−10) However, the nondispersive ∼4a×4a superstructure was not confirmed in later LDOS measurements on Bi2212 at T < T c . 1,5) This inconsistency mainly originates from the difficulty in distinguishing the nondispersive ∼4a×4a superstructure from the weakly dispersive ∼4a×4a one resulting from quasiparticle scattering interference. Since the dispersive features in the LDOS are reduced by integrating the LDOS over a wide range of energy, it is desirable to investigate the nondispersive features of the LDOS by using a conventional STM technique which actually maps the LDOS integrated between E F and E F +eV s , where V s is the sample bias voltage. To clarify whether the nondispersive 4a×4a electronic superstructure persists in the SC state (T < T c ) will promote our understanding of the physics in the underdoped region In the present study, we performed low-bias STM measurements on underdoped Bi2212 samples, and succeeded in observing an energy-independent 4a×4a electronic superstructure with a substructure having a periodicity of 4a/3 in the low-bias STM images, which is essentially the same as the electronic checkerboard order reported by Howald et al. and Hanaguri et al. in LDOS maps of lightly-doped Bi2212 and Na-CCOC. 2,7) The present 4a×4a superstructure is accompanied by a d-wave-like gap or ZTPG, and is discussed in terms of a wide variety of unusual electronic orders proposed for the underdoped region of high-T c cuprates.
The single crystal of Bi2212 in the present study was grown by the traveling solvent floating zone method. We estimated doping level p of the sample from the SC critical temperature T c determined from the superconducting diamagnetism and the characteristic temperature T max of the normal-state magnetic susceptibility; T c and T max follow empirical functions of p respectively. 11,12) We performed STM/STS experiments at T ∼9 K on two samples A and B cut from the same single crystal with T c ∼72 K (p ∼0.11). In the present STM/STS experiments, the sample was cleaved in an ultra-high vacuum at T ∼9 K just before the approach of the STM tip to the cleaved surface in situ. As is well known, Bi2212 crystals are usually cleaved between neighboring Bi-O layers. The excess oxygen atoms within Bi-O layers, which provide holes into Cu-O planes nearby, will be lost to a high degree during the process of cleaving. However, if the cleaving is carried out at very low temperatures, the reduction of excess oxygen atoms, thus hole carriers, will be suppressed to some extent. After the approach of the STM tip to the cleaved surface, we obtained STM images of 512×512 pixels in the constant height mode under various constant sample biases, V s 's. The differential conductance dI/dV was measured by using a standard lock-in technique with ac bias modulation of 3 mV and a frequency of 4 kHz.
Shown in Fig. 1(a) is a typical STM image measured at T ∼9 K on sample A under a low-bias voltage (V s = 30 mV), which lies within the pairing gap as will be men-   Fig. 1(b)) is also shown (broken line).
tioned below. Low-bias STM imaging is crucial to investigating the electronic structure of the Cu-O plane within the pairing gap. Such imaging is especially favorable for the study of the Cu-O plane of Bi2212. This is because, when bias voltage V s lies within the semiconducting gap E g (∼200 meV) of the Bi-O plane (V s < E g /e), electron tunneling occurs predominantly not between the STM tip and the Bi-O plane but between the STM tip and the Cu-O plane. 13) Thus low bias STM images provide information about the Cu-O plane selectively. In Fig. 1(a), we can identify a Cu-O bond-oriented, 2D superstructure with a patched structure throughout the whole STM image, which was observed for both positive and negative biases. Fig. 1(b) shows line profiles of STM images under various V s 's, taken along the yellow line shown in Fig. 1(a). (Note that the yellow line runs parallel to the 1D superstructure, which is inherent in the Bi-O plane, to avoid crossing it.) In Fig. 1(b), we can identify a 2D superstructure with a periodicity of 4a, namely a 4a×4a superstructure, at V s =30 and 100 mV in addition to the primitive lattice and its independence from the bias voltage. We also notice that the 4a×4a superstructure is more intense at lower bias voltage, and becomes very weak at a high V s =800 mV where only a primitive lattice is observed. The low-bias STM image for sample B is shown in Fig. 2(a), and we can also identify the 2D superstructure, not throughout the cleaved surface, but over local regions on a nanometer scale. In Fig. 2(b), the line profile of the STM image with V s =10 mV is shown for the region where the 2D superstructure appears most clearly. We can clearly see the superstructure with a periodicity of 4a, but its amplitude is evidently smaller than that observed for sample A. In Fig. 3, a 2D Fourier map F (q x , q y ) of the real-space STM image taken at V s =30 mV is shown for sample A. Besides Fourier peaks corresponding to the underlying primitive lattice (Bragg peaks) and the 1D superstructure of the Bi-O plane, two different Fourier peaks appear along both q x and q y axes: q = (1/4, 0)2π/a and (3/4, 0)2π/a, (0, 1/4)2π/a and (0, 3/4)2π/a. The peaks along the q x axis are stronger than those along the q y axis. The Fourier peak at q = 3/4×(2π/a) indicates that the 4a×4a superstructure has an internal structure with a period of 4a/3. For quantitative analysis of the Fourier maps, line cuts of the 2D Fourier map along the (π/a, 0) direction are shown as a function of V s (Fig. 3(a)). The Fourier peaks at q x = 1/4×(2π/a) and 3/4×(2π/a) are most intense at the lowest bias, 20mV, and decrease rapidly with the increase of V s . Finally they tend to fade out above V s ∼100 mV. It should be noted here that those Fourier peaks show no change in position and no broadening even if V s increases, indicating that the 4a×4a superstructure observed in the present STM experiments is nondispersive. The correlation length determined from the full width at half-maximum of the Fourier peak is rather short, about 6 nm. The line cuts of 2D Fourier map are also shown for sample B along the (π/a, 0) direction ( Fig. 3(b)). We can identify the 1/4×(2π/a) peak up to 50 mV, while the 3/4×(2π/a) peak is very weak. The intensity of the 1/4×(2π/a) peak normalized with the Bragg peak is much weaker than that for sample A, consistent with the results of the line profiles of realspace STM images. The 1/4×(2π/a) peak decreases with increased bias voltage and tends to fade out at bias voltages above ∼50 mV. Peak-like structures are observed at q < 0.2 in A and B samples, but they show almost no energy dependence in peak intensity, meaning that these structures are irrelevant to the superstructure that we focused on (Fig. 3(a) and (b)). Shown in Fig. 5 is an STS spectrum, averaged over the distance of ∼40 nm on the cleaved surface of sample A, which exhibits an intense, nondispersive 4a×4a superstructure throughout the whole STM image. For comparison, a typical ZTPG spectrum reported for lightly doped Na-CCOC is also shown in Fig. 5. 2) The STS spectrum of sample A has a structure very similar to the ZTPG; that is, an asymmetric V-shaped gap without coherence peaks. Width ∆ 0 of the present ZTPG is ∼80 meV on the positive bias side. In Fig. 6, the spatial dependence of STS spectra is shown for the cleaved surface of sample B whose STM image exhibits the 4a×4a superstructure locally. It should be stressed that the STS spectra of sample B are very homogeneous and show a gap structure of the d-wave type. The gap width, ∆ 0 , is ∼60 meV, though it tends to be slightly enhanced over the regions exhibiting the 4a×4a superstructure clearly. The specific, homogeneous d-wave gap means that the doping level is rather homogeneous in sample B and the hole pairs are uniformly formed all over the cleaved surface. However the electronic 4a×4a superstructure appears only locally, as mentioned above. The dynamical 4a×4a charge order probably evolves throughout the cleaved surface of sample B, and some kind of disorder will pin down the dynamical charge order locally. It is worthwhile to point out here that in both samples A and B, the value of ∆ 0 roughly corresponds to the STM bias voltage below which the 4a×4a superstructure can clearly be observed in STM imaging. This fact implies the possibility that in-gap states, namely the hole pairs, will contribute to the formation of the 4a×4a superstructure. In high-T c cuprates, the gap size increases with the decrease in the doping level. 14,15) Thus, the larger gap size measured on the cleaved surface for sample A than for sample B means that the doping level of the cleaved surface of sample A is lower than that of sample B, though both samples are cut from the same single crystal. The 4a×4a superstructure is very intense in sample A and appears throughout the cleaved surface, whereas it is relatively weak in sample B and appears locally over the cleaved surface, as mentioned above. Furthermore, the low-bias STM image previously reported for nearly optimally doped Bi2212 with ∆ 0 ∼35 meV exhibited no 4a×4a superstructure. 13) These results indicate that a low hole doping level favors the formation of the 4a×4a superstructure. It should be noted here that the cleaved surface of sample A has more missing atom rows within the cleaved Bi-O plane than that of sample B, which can be clearly seen in the highbias STM images, predominantly reflecting the electronic structure of the Bi-O plane. (The high-bias STM images of the present samples will be published elsewhere.) If the missing atom rows are introduced within the Bi-O plane during the cleaving process, excess oxygen atoms will also be removed around the missing atom rows at the same time, which leads to the reduction of the average hole doping level of the Cu-O plane. Thus the high density of the random missing atom rows in the cleaved surface of sample A may be a possible reason why the average hole doping level is lower in the cleaved surface of sample A than for sample B, though both samples were cut from the same single crystal. The low density of the random missing atom rows in the cleaved surface of sample B can also explain its homogeneous electronic structure, namely the homogeneous paring gap.
In the present experiments of low-bias STM imaging, namely Cu-O plane selective imaging, on underdoped Bi2212, 13) we confirmed that an intense, nondispersive 4a×4a superstructure was formed within the Cu-O plane. The 4a×4a superstructure has a substructure with a periodicity of 4a/3 and is clearly observed within the pairing energy gap. Such features of the present 4a×4a superstructure are in good agreement with those of the 4a×4a electronic charge order reported for lightly doped Na-CCOC. 2) The intense, nondispersive 4a×4a electronic charge order is different in origin from the dispersive 2D modulation caused by quasiparticle scattering interference. 5) The present nondispersive electronic charge order is consistent with the findings of Howald  Fig. 2(a). Two-headed arrows beside the spectra indicate the regions where the 4a×4a superstructure is clearly observed.
et al. in the LDOS maps for the SC state of Bi2212. 7,8) They claim that the nondispersive superstructure results from the formation of a static stripe order. The present results can be explained in terms of a static stripe order except for the experimental finding for sample B that the paring gap is influenced only slightly even over the region where the dynamical 4a×4a charge order is locally pinned down. Since the formation of the static stripe order causes the superconductivity to seriously deteriorate, as demonstrated for La 2−x Ba x CuO 4 and La 1.6−x Nd 0.4 Sr x CuO 4 systems where simple 1D strips develop, the paring gap would be seriously influenced over the region where the 4a×4a electronic charge order is pinned down. The present 4a×4a electronic charge order, clearly appearing within the pairing gap, is not inconsistent with models for the electronic charge order due to pair density waves, electronic supersolids, or pairedhole Wigner crystallization. 16−22) This work was supported in part by Grants-in-Aid for Scientific Research and the 21 st century COE program "Topological Science and Technology" from the Ministry of Education, Culture, Sports, Science and Technology of Japan.