Introduction

Copper oxide high-temperature superconductors have been widely studied owing to their high critical temperature (Tc) exceeding the Bardeen–Cooper–Schrieffer (BCS) limit1,2. The mechanism responsible for the formation of Cooper pairs is not explained by electron–phonon interactions of BCS theory, remaining one of the big mysteries in the field of physics.

The two-dimensional CuO₂ plane is widely regarded as the most crucial element of high-Tc cuprate superconductors. The physical properties in the ab-plane have been intensively investigated from various perspectives. Many of the early experimental measurements such as dc resistivity3,4,5, infrared conductivity6,7,8,9,10,11,12, and penetration depth13 were performed for single-domain YBa2Cu3O7−δ (Y123), which the anisotropy was attributed to the quasi-one-dimensional CuO chains. In contrast, Bi2Sr2CaCu2O8+δ (Bi2212) provides a better opportunity to study the intrinsic anisotropy, as there are no chains in these Bi-based cuprates.

Previous optical studies demonstrated that the reflectance of Bi2212 exhibits anisotropy both above and below Tc in both ab and ac-planes14,15,16. While reflectivity measurements also contribute to understanding of “bulk properties” of the material, there is a lack of studies focusing on the optical anisotropy of these materials using optical “transmittance” measurements, which more directly provide us the insight. Considering the suggestion that strong electron-phonon interaction may become a key mechanism for superconductivity in high-temperature superconductors (HTSCs), it may be essential to scrutinize the characteristics of phonons and/or low-energy excitation properties in these materials more thoroughly. Meanwhile, by utilizing ultraviolet (UV) and visible (Vis) light as optical probes, it is possible to simultaneously obtain insights into the electromagnetic properties of these materials, which specifically relating to “transitions of outer shell electrons.” These transitions can reveal crucial information about the electronic band structure, including energy gaps.

Using the generalized high-accuracy universal polarimeter (G-HAUP)17,18,19,20,21,22,23,24,25,26, the wavelength dependence of the optical anisotropy of Bi2212 along its c axis in UV-Vis regions was evaluated through transmission measurements26. G-HAUP allows us simultaneous transmission measurement of optical anisotropy such as linear birefringence (LB) and linear dichroism (LD) and chiroptical properties such as optical activity (OA) and circular dichroism (CD) in UV-Vis region while assessing the systematic errors of the optical system. To measure the LB and LD of Bi2212, very thin plate specimens of Bi2212 crystal were prepared such that visible and ultraviolet light could be transmitted through the crystal by exfoliating the Bi2212 crystal. Transmission measurements using thin plate specimens revealed that the LB and LD spectra exhibited large peaks at R.T. at approximately 345 and 330 nm, respectively. The fourfold rotational symmetry of Bi2212 is broken in the ab plane. However, optical anisotropy is anticipated to be small because the lattice constants of a and b axes are nearly identical. Nevertheless, large LB and LD peaks were observed. Bi2212 exhibits an incommensurate modulation, in which the periodicity of the modulation does not belong to the periodicities of the basic structure along the b axis. (The period of the incommensurate modulation is approximately 4.8b, where b is the lattice constant of the b axis.)27 Therefore, the origin of the large LB and LD may be from the incommensurate modulation along the b axis.

Previous studies uphold that the partial substitution of Bi by Pb in Bi2212 crystals leads to a significant enhancement of the critical current densities and the critical magnetic field owing to the pinning effect28. Additionally, the modulation structure is suppressed as the lead content x increases in Pb-doped Bi2212, Bi2−xPbxSr2CaCu2O8+δ.29,30,31 TEM observation and electron diffraction revealed that the modulation structure disappears at x = 0.629,31. In this study, single crystals of Bi2−xPbxSr2CaCu2O8+δ with varying lead contents (x = 0, 0.4, and 0.6) were grown using the floating zone (FZ) method, and the wavelength dependences of the LB and LD along the c axis were examined using G-HAUP to clarify whether the origin of the large LB and LD is from incommensurate modulation. The insights gained into the optical anisotropy of Bi2−xPbxSr2CaCu2O8+δ from this study are significant for discussing its origin of the mechanism of high-Tc superconductivity.

Methods

Crystal growth of Bi 2− x Pb x Sr 2 CaCu 2 O 8+ δ

 Single crystals of Bi2−xPbxSr2CaCu2O8+δ were grown using the FZ method. The initial polycrystalline materials were synthesized via a solid-state reaction using a mixture of Bi2O3, PbO, SrCO3, CaCO3, and CuO powders in appropriate proportions. After several provisional heat treatments (calcine) at 750 °C in air, cylindrical rods with a diameter of 8 mm were obtained under a pressure of 20 MPa. Subsequent heat treatments (sinter) at 750 °C in air were applied to these rods, which were then mounted onto the FZ furnace. Densification was achieved by moving the molten zone and adjusting the speed and rotational speed of the feed and seed rods, respectively, in air. To compensate for potential Pb evaporation during the FZ process, the composition of the starting mixture adjusted to include a slight excess of PbO while essentially referring to the literature28. Any anneal treatment was not applied in this study.

Characterization of Bi 2− x Pb x Sr 2 CaCu 2 O 8+ δ

The actual composition of the samples prepared by dissolving the crystals in nitric acid was determined by inductively coupled plasma optical emission spectrometry (ICP-OES). ICP-OES measurements were conducted using an Agilent 5100 instrument (Agilent Technologies). The actual ratios of Bi:Pb:Sr:Ca:Cu determined by ICP-OES were 1.61:0.41:1.76:1.00:1.84 for x = 0.4 and 1.41:0.61:1.79:1.00:1.74 for x = 0.6 (with Ca set to 1.00). The crystal structure of the Bi2−xPbxSr2CaCu2O8+δ was characterized by XRD with Cu Kα radiation (λ = 1.5418 Å). X-ray photoelectron spectroscopy (XPS) measurements were performed using a JPS-9010TR (JEOL) with a nonmonochromatic Mg Kα (1253.6 eV) X-ray source. The confirmation of whether the incommensurate modulations of Bi2−xPbxSr2CaCu2O8+δ were suppressed was verified through scanning transmission electron microscopy (STEM) observation and electron diffraction. STEM images were acquired using a JEM-ARM300F (JEOL) for focused ion beam specimens at an accelerating voltage of 300 kV. The temperature dependence of the magnetic susceptibility was measured using a superconducting quantum interference device (SQUID) to determine Tc. SQUID measurements were conducted using a VSM SQUID (Quantum Design).

Optical measurements with the G-HAUP 17,18,19,20,21,22,23,24,25,26

G-HAUP utilized a simple optical configuration comprising only two optical elements: polarizer (P) and analyzer (A). The axes of P and A are set in the crossed-Nichols configuration, with light traveling through P, the sample (S), and A, successively. We can obtain LB, LD, OA, and CD recovered from the transmitted light intensity as a function of the rotational angles P and A. The details of the measurement theory have been described in previous studies17,18,19,20,21,22,23,24,25,26. Ultrathin (001) plate specimens, approximately 0.2 mm in diameter, were prepared by exfoliating crystals with a water-soluble tape. The specimens were then mounted on a stainless-steel pinhole plate, also 0.2 mm in diameter, to enhance the signal-to-noise ratio of the transmitted light intensity. To confirm whether the specimens consisted of a single domain, a polarized light microscope (Leica DMLP, Leica) with a λ plate was employed. The thicknesses of the specimens were measured using field emission-scanning electron microscopy (FE–SEM; SU-8240, Hitachi High-Tech) and were found to be almost identical to those measured by atomic force microscopy (SPM-9700, Shimadzu), as detailed in the Supporting Information.

Results and discussion

Figure 1A depicts the XRD patterns of the resulting Bi2−xPbxSr2CaCu2O8+δ single crystals with different Pb contents. The peaks were observed at nearly identical 2θ positions regardless of the Pb content x and closely matched those previously reported (JCPDS #46–0431)32,33. The lattice constants determined from the XRD patterns for each crystal are presented in Table S1. The calculated values are consistent with those reported previously29,34,35,36,37, with a notable observation that the lattice constants along with a and c axes decreased for the x = 0.4 sample and subsequently increased for the x = 0.6 sample. The intensities of some of the peaks indicated by * marks (at 2θ of ~ 25.9°, ~ 31.9°, and ~ 55.2°) increased with increasing Pb content, probably owing to the slight changes in the atomic arrangement and chemical bonding in the crystals. Figure 1B depicts the XPS spectra of Bi2−xPbxSr2CaCu2O8+δ with Pb contents x = 0, 0.4, and 0.6 after background subtraction. The observed doublet corresponding to Pb 4f7/2 and Pb 4f5/2 at ~ 137 and ~ 142 eV can be fitted by two sets of doublets: one at 136.9 and 141.8 eV and the other at 138.2 and 143.1 eV, with varying ratios depending on the Pb content (see Figure S1 for details). In the Cu 2p3/2 region, the main (at ~ 933 eV) and satellite (from 938 to 946 eV) peaks were observed: the shape and width of the main peak, which are indicative of the mixed valence state, and the intensity ratio of the satellite to the main peaks changed with x (see Figure S2 for details). The interpretation of the components of the Cu 2p3/2 main peak varies slightly in the literature38,39,40,41,42,43. In contrast, the observed doublet of Bi 4f7/2 and Bi4f5/2 at ~ 158 and ~ 163 eV, respectively, likely comprises a dominant doublet related to Bi3+ and an additional doublet of approximately one-tenth intensity at the higher-binding-energy side38,39,43, exhibited minimal change with x (Figure S3). The two Pb components can be attributed to Pb4+ and Pb2+, although their specific assignments vary in the literature44,45,46,47. As the Pb content increases, the formal valence of Cu was suggested to increase gradually, while that of Bi remains relatively changed. For Sr2+ and Ca2+ ions, which can substitute for each other, the spectra of Sr 3d and Ca 2p can be simulated by considering two sets of doublets: one set corresponds to ions occupying the “Sr site” in the SrO plane (between BiO and CuO2 planes) and the other set corresponds to ions occupying the “Ca site” positioned between adjacent CuO2 planes43,45,46,47. As the Pb content increases, the proportion of Sr2+ in the Ca site increased at x = 0.4, but then decreased again at x = 0.6, and correspondingly the proportion of Ca2+ in the Ca site decreased and increased at x = 0.4 and 0.6, respectively (Figures S1 and S4). These results suggest that in the synthesized samples, Pb2+ substitutes for Bi3+ in the BiO plane, leading to a mixed state of Pb4+/Pb2+, where the component with the lower binding energy is slightly in excess for x = 0.4, and more in excess for x = 0.6, which induces an increase in the valency of Cu with increasing x and also changes the site occupations of Sr2+ and Ca2+ to be more uniform (random) at x = 0.4, and more selective at x = 0.6. Assuming that some of the Pb4+ and Pb2+ ions are located in the BiO plane and also in the Sr and Ca sites, the site distributions of Sr2+ and Ca2+ ions may rely on x, which likely correlates with the aforementioned changes in the lattice constants along the a and c axes computed from the XRD patterns. Figure 1C shows the temperature dependences of the magnetic susceptibility of Bi2−xPbxSr2CaCu2O8+δ with Pb contents x = 0, 0.4 and 0.6. Both samples exhibit clear Tc, characterized by the onset of diamagnetism, in both field cooling at 100 or 1,000 Oe and zero-field cooling conditions. The measured Tc values were 76 and 84 K for x = 0.4 and 0.6 samples, respectively, both lower than the Tc of 93 K for x= 0 sample26. Several previous studies have investigated the effects of Pb doping on the lattice parameters and Tc in Bi2212, particularly focusing on the relationship between hole concentration and excess oxygen in the CuO2 plane48,49,50,51,52,53,54,55,56. In the present study, we observed that both the lattice parameters and Tc decrease at a Pb concentration of x = 0.4 and 0.6 compared to x = 0. The decrease in lattice parameters and Tc by Pb doping can be explained by a reduction in excess oxygen48 and a change to an overdoped state caused by an increase in the Cu valence49, as supported by the XPS analysis. The subsequent increase in both lattice parameters and Tc from x= 0.4 to 0.6 is attributed to several complex factors such as the Coulomb repulsion50 and change of bond length due to the increasing the Cu valence51, and a widening of the BiO-SrO interlayer distance by changing the average angle between Bi-O bonds and the plane35, and the increase in effective hole concentration as the Cu ionic radius decreases52. The randomness of the Sr2+ and Ca2+ ions confirmed by XPS could be related to these changes.

Fig. 1
figure 1

Powder-XRD (A), XPS (B), and SQUID (C) measurements of the Bi2−xPbxSr2CaCu2O8+δ with three typical Pb contents x = 0 (black), 0.4 (blue), and 0.6 (red). In (A), the intensities of some of the peaks indicated by * marks (at 2θ of ~ 25.9°, ~ 31.9°, and ~ 55.2°) increased with increasing Pb content, probably owing to the slight changes in the atomic arrangement and chemical bonding in the crystals.

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To investigate the crystal structure in more detail and the incommensurate modulation of the synthesized Bi2−xPbxSr2CaCu2O8+δ crystals, STEM images and electron diffraction patterns were observed. Figure 2A depicts the high-angle annular dark-field (HAADF) and bright-field (BF) STEM images along the [100] axis of the Bi2−xPbxSr2CaCu2O8+δ crystals with three typical Pb contents x = 0, 0.4, and 0.6. BiO, SrO, CuO2 and Ca planes of Bi2−xPbxSr2CaCu2O8+δ were distinctly resolved in both HAADF- and BF-STEM images. In particular, BiO planes with heavy Bi atom are observed as bright in the HAADF-STEM images and dark in the BF-STEM images. In the images corresponding to Pb content x = 0 (1st line), clear modulation can be observed in the BiO planes along the horizontal slow-axis direction. The length of the modulation aligns with that previously reported (λ ~ 4.8b= 26 Å)27, and the modulation becomes weaker in the x = 0.4 (2nd line) and nearly disappears in the x = 0.6 (3rd line). It is worth noting that this modulation can be seen not only in the BiO planes but also in the SrO and CuO2 planes for x = 0 and 0.4. Figure 2B illustrates the electron diffraction results along the [100] axis of the Bi2−xPbxSr2CaCu2O8+δ (x = 0, 0.4, and 0.6). In the image corresponding to Pb content x = 0 (1st line), clear satellite spots are evident, indicating the formation of a superstructure along the b axis direction around the main diffraction spots, and these satellite spots become weaker in the x = 0.4 (2nd line) and nearly disappear in the x = 0.6 image (3rd line) (But even in the x = 0.6 sample, slight satellite reflections can be found). These STEM and electron diffraction results suggest that the superstructure in Bi2−xPbxSr2CaCu2O8+δ is suppressed with increasing Pb content.

Fig. 2
figure 2

HAADF-STEM, BF-STEM (A), and electron diffraction images (B) along the [100] axis of the Bi2−xPbxSr2CaCu2O8+δ with three typical Pb contents x = 0 (top), 0.4 (middle), and 0.6 (bottom).

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Thin (001) plate specimens with a diameter of approximately 0.2 mm were prepared by exfoliating the crystal. For each Pb content (x = 0, 0.4 and 0.6), ultrathin (001) plate specimens were prepared. Utilizing a polarized light microscope, we confirmed that these specimens were single domain and exhibited high homogeneity, as illustrated in Fig. 3A. This high homogeneity facilitates high-precision LB and LD measurements. Moreover, we observed a decrease in optical anisotropy with increasing Pb content. The thicknesses of the specimens were estimated to be 457 nm, 678 nm and 992 nm for x = 0, 0.4 and 0.6, respectively, based on FE–SEM observations. Despite the x = 0 sample being thinner than the x = 0.4 or 0.6 sample, clear addition and subtraction phenomena were observed with a λ plate even in the thinner x = 0 sample. Considering these thickness variations, the comparative analysis of polarized light microscopic images between x = 0 and 0.4 or 0.6 specimens provide qualitative yet direct evidence of the decrease in optical anisotropy with increasing Pb content.

Five specimens were prepared to quantitatively compare the LB and LD magnitudes for each Pb content (x= 0.4 and 0.6). The G-HAUP theory17,18,19,20,21,22,23,24,25,26 reveals that LB and LD are related to the total phase difference Δ and the total linear dichroism E of the specimen, respectively, as follows:

$$\:\text{LB}=\frac{\varDelta \lambda}{2 \pi d},$$
(1)

and

$$\:\text{LD}=\frac{E \lambda}{2 \pi d},$$
(2)

where d and λ are the thickness of the specimen and the wavelength of the incident light, respectively. Here, Δ and E are derived from the coefficients of a quadratic function that describes the relative intensity ratio of transmitted light to incident light as a function of the rotation angles of the polarizer and analyzer. We measured the wavelength dependencies of the total phase difference (Δ) and the total LD (E) along the c axis at 298 K (Figure S6). Then, Δ and E were normalized using the specimen thickness determined by FE–SEM to calculate LB and LD, as depicted in Fig. 3B and 3C. The magnitude of the spectra at each wavelength was derived from the average results of the five different specimens, and the error bars in the figures were estimated from the standard deviation of these specimens. The LB and LD spectra for each Pb content (x = 0, 0.4, and 0.6) exhibited peaks at λ = 345 and 330 nm, respectively, regardless of x. However, the magnitudes of the LB and LD varied among the different Pb contents, as depicted in Fig. 3B and 3C. The consistent monotonic decrease in LB and LD magnitudes with increasing Pb content suggests that the origin of LB and LD is associated with incommensurate modulation along the b axis.

Several reports exist on the measurement of LB for the incommensurate phase of crystals by HAUP57,58,59,60,61,62,63. Variations in crystal structure and symmetry during the incommensurate phase transition influence the magnitude of LB. Additionally, as reported for (C3H7NH3)2MnCl4, LB is strongly related to mechanical interlayer strain distortions61. Therefore, it seems natural that suppression of incommensurate modulation by Pb doping leads to smaller optical anisotropy. Figure 3D illustrates the wavelength dependence of absorption for each Pb content (x = 0, 0.4, and 0.6). The absorption spectra showed relatively similar patterns across all samples, indicating that Pb doping did not result in additional localized energy bands in this region. By plotting the Tauc relation (αhν)2 = A(αhν – Eg), where α represents the absorbance, h denotes Planck’s constant, ν signifies the frequency, and Eg is the optical bandgap64 (Inset of Fig. 3D), the optical bandgaps are qualitatively estimated to be 3.4, 3.27, and 3.3 eV for the samples with x = 0, 0.4, and 0.6, respectively. The Urbach tail due to Pb doping (essentially impurities) may cause this small change.

Fig. 3
figure 3

(A) Polarized light microscope images with different azimuth angles θ of the Bi2−xPbxSr2CaCu2O8+δ with x = 0 (top), 0.4 (middle) and 0.6 (bottom). (B, C, D) Wavelength dependences of LB (B) and LD (C), and absorbance (D) of the Bi2−xPbxSr2CaCu2O8+δ with x = 0 (black), 0.4 (blue), and 0.6 (red). The values and error bars of LB and LD were derived from the average value and standard deviation, respectively, for five specimens with different thicknesses. Tauc plots of each absorption spectrum are depicted in the inset of (D).

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Conclusion

It is noteworthy that we have elucidated the origin of this strong optical anisotropy through optical “transmission” measurements employing ultrathin plate specimens, which allowed ultraviolet and visible (UV–Vis) light to pass through the crystal. Additionally, we observed that substituting Bi with Pb in Bi2212 crystals significantly reduced the optical anisotropy, such as LB and LD, concurrent with the suppression of incommensurate modulation. This reduction in optical anisotropy is crucial, as it allows for a more accurate determination of optical activity (OA) and circular dichroism (CD) in future experiments. In the G-HAUP measurement using a light source with a spectral linewidth dispersed by a monochromator, smaller optical anisotropy is more useful for the precise measurement of OA and CD17,18,19. Therefore, while the present study focuses on the reduction of optical anisotropy, future research will involve measuring the temperature-dependent optical anisotropy (OA) and circular dichroism (CD) of Bi2−xPbxSr2CaCu2O8+δ, with careful attention to minimizing the influence of residual optical anisotropy. By elucidating the reciprocal and non-reciprocal property of OA and CD25,65,66,67,68, we try to explore the question of whether the spatial-inversion symmetry and time-reversal symmetry are broken in the pseudogap and superconducting phases.