Visualizing the evolution from the Mott insulator to a charge-ordered insulator in lightly doped cuprates Peng Cai 1, Wei Ruan 1, Yingying Peng, Cun Ye 1, Xintong Li 1, Zhenqi Hao 1, Xingjiang Zhou,5, Dung-Hai Lee 3,4, Yayu Wang 1,5 1 State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, P.R. China Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China 3 Department of Physics, University of California at Berkeley, Berkeley, CA 9470. 4 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 9470. 5 Innovation Center of Quantum Matter, Beijing 100084, P.R. China Email: yayuwang@tsinghua.edu.cn Contents: Supporting materials text Figure S1 to S6 References NATURE PHYSICS www.nature.com/naturephysics 1 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
1. Similar di/dv spectra in lightly doped La-Bi01 and CCOC a 6 La-Bi01 p 0.03 1. V b 6 CCOC 3 V di/dv (ps) 4 4 nm di/dv (ps) 4 4 Å 0-1.0-0.5 0.0 0.5 1.0 1.5.0 Sample Bias (V) 0-1 0 1 Sample Bias (V) Fig. S1: a. Representative di/dv spectra in the very lightly doped La-Bi01 with p = 0.03. The setup parameters are V = -1.V and I = 4pA. b. The di/dv spectra measured on Ca-cite defect (red) and defect-free cite (black) of pristine CCOC. The color spots in the inset topographic images indicate the position where the spectra are acquired. The di/dv spectra in the very lightly doped La-Bi01 with p = 0.03 are highly analogous to that observed in pristine CCOC with sparse hole-type defects. As shown in Fig. S1a here, the red curve shows a broad in-gap state that extends all the way from the lower Hubbard band to the upper Hubbard band. The DOS at EF remains zero, and the spectral weight of the UHB is strongly suppressed compared to the undoped Mott insulator phase (the black curve). The red curve in Fig. S1b is taken on a Ca-site defect in pristine CCOC Mott insulator. Although the exact nature of the Ca-site defect is unknown, it is most likely due to Ca vacancy or Na substitution. In either case the defect will introduce hole-type carrier into the Mott insulator. Its overall spectral lineshape show remarkable resemblance to the red curve in Fig. S1a. The strong similarity between the spectra in two totally different cuprate systems indicate that the broad in-gap state, the suppression of the UHB spectral weight, and the zero DOS at EF are universal features of the cuprate parent Mott insulator doped with very dilute holes. Another similarity between the two systems is the strong spatial localization NATURE PHYSICS www.nature.com/naturephysics 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
of the in-gap state. In CCOC, the broad in-gap state dies out at 4-5 lattice distances, or around nm, from the defect center. For the La-Bi01, the DOS map shown in Fig. c of the main text reveals that the puddles with broad in-gap state have a typical size of -4 nm. The spatial localization is another character of the electronic states induced by hole-type carriers in underdoped cuprate close to the Mott insulator limit.. Detailed DOS maps of the p = 0.03 sample -0.4 V -0.3 V -0. V -0.1 V 0 V +0.1 V +0. V +0.3 V +0.4 V +0.5 V +0.6 V +0.7 V +0.8 V +0.9 V +1.0 V +1. V +1.4 V +1.6 V +1.8 V +.0 V Fig. S: Detailed di/dv maps of the p = 0.03 sample measured in large energy window. The data are taken with tunneling junction set by V = -1. V and I = 4 pa. The di/dv raw data is linearly scaled to brightness for each map. In Fig. of the main text we display four representative DOS maps of the p = 0.03 samples with bias voltage V = -0.1, 0, 0., and 1.6 V respectively. In this session we show NATURE PHYSICS www.nature.com/naturephysics 3 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
detailed raw data (in gray scale) of the DOS maps with more bias voltages, in which the evolution and correlation of the electronic states can be thoroughly visualized. The di/dv maps in Fig. S are taken on the same area of the p = 0.03 sample as that shown in Fig. of the main text. The maps from -0.4 V to +1.0 V clearly show the absence of gapless excitations at EF and the emergence of the low energy in-gap state at finite biases. All these maps show similar spatial patterns indicative of positive correlation of the low energy states. The brighter features at negative bias reflect the particle-hole asymmetry in the lightly doped cuprate, in which the occupied states have larger DOS than the empty states 1. The contrast reverses above +1.4 V, indicating the spectral weight transfer from the high energy UHB to low energy in-gap states. Above +1.8 V, the structural supermodulation starts to appear in the DOS maps. 3. Detailed DOS maps of the p = 0.07 sample In Fig. 3 of the main text we display five representative DOS maps of the p = 0.07 samples with sample bias V = -5 mv, 0, +5 mv, +50 mv, and 1.7 V respectively. In Fig. S3 we show detailed raw data (in gray scale) of the DOS maps with more bias voltages taken on the same area of the p = 0.07 sample. The checkerboard pattern is most pronounced in the bias range from +5 mv to +100 mv, which is consistent with that observed on BiSrCaCuO8+x (Bi-1) at higher dopings. However, unlike the previous work, the checkerboard can also be observed on the negative bias side, such as 5 mv and 50 mv, although the features are weaker than that on the positive bias side. We note that superconducting La-Bi01 with higher doping level also show checkerboard pattern in both positive and negative bias sides 3. A closer look into their data reads the checkerboard features are also clearer on the positive bias side. The strong resemblance of checkerboard features between insulating (here) and underdoped superconducting samples, including wavevector and energies dependence, underlies a similar origin of checkerboard at different doping regime in cuprates. The slight discrepancy between La-Bi01 and Bi-1 in energies might be attributed to bilayer band splitting. Moreover, the positive correlation between the low bias maps (from -0. V to +0.5 V) and the anticorrelation with the high bias ones (above 1.5 V) 4 NATURE PHYSICS www.nature.com/naturephysics 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
are also present in this sample. Above +1.5 V, the structural supermodulation also starts to appear, just like in the p = 0.03 sample. -0. V -0.1 V -75mV -50mV -5mV 0 V +5mV +50mV +75mV +0.1V +0.V +0.3V +0.4V +0.5V +1.5V +1.6V +1.7V +1.8V +1.9V +.0V Fig. S3: Raw data of di/dv maps of the p = 0.07 sample measured over a large bias range. The maps for biases above +1.5 V are 18 18 pixel images taken with setup parameters V = -1. V and I = 4 pa. To have better energy and spatial resolutions at the low energy range, the maps for biases from -0. V to +0.5 V are 56 56 pixel images taken on the same area with setup parameters V = -0.5 V and I = 4 pa. 4. Checkerboard pattern observed on another p = 0.07 sample To check if the checkerboard pattern observed on the p = 0.07 sample is reproducible, we have performed the same experiment on another piece of La-Bi01 crystal from the same NATURE PHYSICS www.nature.com/naturephysics 5 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
batch. To exclude the possibility of artifacts due to the STM tip or setup parameters, we have retreated and recalibrated the tip in situ. The setup parameters for the di/dv map are also changed to V = -0.3 V and I = 4 pa. Shown in Fig. S4a is the current map taken at bias voltage +100 mv, which clearly reveals the checkerboard pattern that looks the same as that shown in Fig. 4a in the main text. Fig. S4b,c are the FT image of the current map and the linecut along the Cu-O bond direction. The wavevector of the checkerboard is also at 1/4 of the lattice wavevector /a0, indicating a checkerboard along the Cu-O bond direction with periodicity 4 a0. All the checkerboard features shown in the main text are thus confirmed. a b c 4 nm I@ +100 mv Normalized FT Amplitude (a. u.) Q CO Q Cu 0.5 0.50 0.75 1.00 q( /a ) 0 Fig. S4: a. Current map taken at +100 mv on another piece p = 0.07 crystal from the same batch as that shown in the main text. The setup parameters are V = -0.3 V and I = 4 pa. b. Fourier transform (FT) of the current map shown in a, which shows the wavevectors for both the atomic lattice and the checkerboard. c. The line-cut in the FT along the black line (Cu-O bond direction) shows a clear charge order peak at around 1/4 of the lattice wavevector, indicating a real-space checkerboard periodicity of 4 a0. 5. Analysis of the charge order wavevector Figure 4c of the main text shows the ordering momentum of the checkerboard charge order, in which the amplitude of the FT is normalized by that of the lattice peak. The low q background near the charge order peak can be seen directly from the raw data, which is mainly due to the nanoscale inhomogeneity of the electronic structure. In order to extract the 6 NATURE PHYSICS www.nature.com/naturephysics 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
exact ordering momentum, we use a Gaussian profile to fit the lineshape near the peak. The total profile near the peak can be expressed by y = y0+ A1exp(-q/q0) + Aexp(-(q-qCO) /w ), where the background is a constant plus an exponential decay. Here A1 and A represent the amplitude of the background and the charge order, and qco is the center of the charge order peak. Fig. S5 displays the details about the data fitting, from which the charge order momentum can be extracted to be qco ~ 0.54. The correlation length of the charge order CO ~ 18 a0 is estimated from the full width at the half maximum, which is ~ 0.055(±0.007)). The error bar is derived from the standard error of the fitting. Normalized FT Amplitude (a. u.) 4 3 1 0 0.1 0. 0.3 0.4 q ( /a 0 ) Fig. S5: The low q region of Fig. 4c in the main text showing the charge order wavevector of the p = 0.07 sample. The blue solid line is the raw data, and the red solid line is the total fitting including the background (blue dashed line) and Gaussian profile of the charge order peak (black dashed line). 6. Charge order in an underdoped superconducting sample with p = 0.1 In order to reveal the connection between the charge order in the insulating regime NATURE PHYSICS www.nature.com/naturephysics 7 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
reported in the main text and the well-studied charge order in underdoped cuprates (particularly around p = 1/8 doping), we performed STM measurements on an underdoped superconducting La-Bi01 sample with Tc = 19 K and p = 0.1. Fig. S6a shows the topographic image with clear atomic resolution obtained on the cleaved crystal surface. The typical large energy range spectra are shown in Fig. S6b, which reveal the continuous evolution of electronic structure with increased hole doping. The spectral weight of the upper Hubbard band is very small, and the in-gap state becomes very broad and almost flat. The V-shaped pseudogap becomes sharper than that in the p = 0.07 sample and its gap size lies in the range from around 50 mev to 100 mev. A closer examination of the tunneling spectra near the Fermi level shows a small superconducting gap with SC ~ 1 mev inside the pseudogap, but right now at EF the DOS is still finite (Fig. S6c). Compared to the large spatial variation of the pseudogap size, the superconducting gap is much more homogeneous. a b c 60 1 5 nm di/dv (ps) 10 5 1 di/dv (ps) 40 0 1 SC SC 0-1.0-0.5 0.0 0.5 1.0 1.5.0 Sample Bias (V) -40-0 0 0 40 Sample Bias (mv) c 5 mv d Q CO Q Cu e Normalized FT Amplitude (a. u.) Q CO Q Cu 0.5 0.50 0.75 1.00 q( /a 0 ) Fig. S6: Tunneling spectra and charge order in the superconducting sample with p ~ 0.1 (Tc = 19 K). a. Topographic image over a 30 30 Å area acquired at V = -0. V and I = 6 pa. b and c. Typical tunneling spectra with different energy ranges taken on locations marked in a. 8 NATURE PHYSICS www.nature.com/naturephysics 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
The zoom-in spectra in c shows a superconducting gap with SC ~ 4 mev inside a large pseudogap. d. Conductance map at +5 mv in the field of view of a shows a checkerboard charge order. e. FT of the conductance map shows that the charge order is along the Cu-O bond directions. f. Linecut along the Cu-O bond direction in e shows that the charge ordering momentum is ~ 0.5, corresponding to a real space period ~ 4 a0. The red curve is a Gaussian fit with background. The tunneling conductance map shown in Fig. S6d is taken at bias voltage V = 5 mv on the same area as the topographic map. It reveals a clear checkerboard pattern along the Cu-O bond direction, which can be clearly illustrated in the FT (Fig. S6e). Furthermore, the line-cut along the Cu lattice direction shows that the charge ordering momentum is still ~ 0.5, corresponding to a real space period ~ 4 a0. The charge order pattern is consistent with previous STM and resonant x-ray measurements on La-Bi01 with similar doping level 3. The most important point is that the charge order in the superconducting state is very similar to the charge order in the insulating state. Therefore, the checkerboard charge order observed in the AF insulating state reported in the main text can be viewed as the precursor of the ubiquitous charge order that coexists with superconductivity in underdoped cuprates. References: 1 Anderson, P. W. & Ong, N. P. Theory of asymmetric tunneling in the cuprate superconductors. J. Phys. Chem. Solids 67, 1-5 (006). da Silva Neto, E. H. et al. Ubiquitous Interplay Between Charge Ordering and High-Temperature Superconductivity in Cuprates. Science 343, 393-396 (014). 3 Comin, R. et al. Charge Order Driven by Fermi-Arc Instability in Bi Sr xla xcuo 6+δ. Science 343, 390-39 (014). NATURE PHYSICS www.nature.com/naturephysics 9 016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.