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# High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ

## Abstract

Although copper oxide high-temperature superconductors constitute a complex and diverse material family, they all share a layered lattice structure. This curious fact prompts the question of whether high-temperature superconductivity can exist in an isolated monolayer of copper oxide, and if so, whether the two-dimensional superconductivity and various related phenomena differ from those of their three-dimensional counterparts. The answers may provide insights into the role of dimensionality in high-temperature superconductivity. Here we develop a fabrication process that obtains intrinsic monolayer crystals of the high-temperature superconductor Bi2Sr2CaCu2O8+δ (Bi-2212; here, a monolayer refers to a half unit cell that contains two CuO2 planes). The highest superconducting transition temperature of the monolayer is as high as that of optimally doped bulk. The lack of dimensionality effect on the transition temperature defies expectations from the Mermin–Wagner theorem, in contrast to the much-reduced transition temperature in conventional two-dimensional superconductors such as NbSe2. The properties of monolayer Bi-2212 become extremely tunable; our survey of superconductivity, the pseudogap, charge order and the Mott state at various doping concentrations reveals that the phases are indistinguishable from those in the bulk. Monolayer Bi-2212 therefore displays all the fundamental physics of high-temperature superconductivity. Our results establish monolayer copper oxides as a platform for studying high-temperature superconductivity and other strongly correlated phenomena in two dimensions.

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## Data availability

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

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## Acknowledgements

We thank D.-H. Lee, Z.-Y. Weng, Q.-K. Xue, S.-W. Cheong, Y. Wang, H. Ding and H. Luo for discussions. We also thank X. Jin and D. Feng for their help with the experiment. Part of the sample fabrication was conducted at Nano-fabrication Laboratory at Fudan University. Work at Brookhaven National Laboratory was supported by the Office of Science, US Department of Energy under contract no. DE-SC0012704. Y.Y., L.M. and Y.Z. acknowledge support from the National Key Research Program of China (grant nos. 2016YFA0300703, 2018YFA0305600), National Science Foundation of China (grant nos. U1732274, 11527805, 11425415 and 11421404), Shanghai Municipal Science and Technology Commission (grant no. 18JC1410300) and Strategic Priority Research Program of Chinese Academy of Sciences (grant no. XDB30000000). Y.Y. acknowledges support from the National Postdoctoral Program for Innovative Talents (grant no. BX20180076) and China Postdoctoral Science Foundation (grant no. 2018M641907). P.C. acknowledges support from National Postdoctoral Program for Innovative Talents (grant no. BX201600036), Shanghai Sailing Program (grant no. 17YF1429000), Shanghai Municipal Natural Science Foundation (grant no. 17ZR1442400) and China Postdoctoral Science Foundation (grant no. 2017M610221). X.H.C. acknowledges support from the National Science Foundation of China (grant no. 11888101, 11534010), the National Key R&D Program of China (grant no. 2017YFA0303001 and 2016YFA0300201), Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB25000000) and the Key Research Program of Frontier Sciences, CAS (grant no. QYZDY-SSW-SLH021).

## Author information

Authors

### Contributions

The order of the first two authors was determined arbitrarily. Y.Z. conceived the project. Y.Z. and X.H.C. supervised the experiments. R.Z. and G.D.G. synthesized bulk crystals. Y.Y., L.M. and C.Y. developed sample fabrication techniques. Y.Y. did transport measurements. L.M. led the STM study. L.M., P.C. and C.Y. did STM measurements and J.S. provided support. Y.Y., LM., P.C. and Y.Z. analysed the data and wrote the paper with input from all authors.

### Corresponding authors

Correspondence to Liguo Ma, Xian Hui Chen or Yuanbo Zhang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature thanks Tetsuro Hanaguri and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Extended data figures and tables

### Extended Data Fig. 1 Transport properties of typical monolayer Bi-2212 samples fabricated by various methods.

a, Temperature-dependent resistance of monolayer Bi-2212 samples. Here (#1)–(#5) refer to five typical samples fabricated by different methods indicated in Extended Data Table 1. b, Resistance of a typical cold-welded Bi-2212 monolayer device measured with two-terminal (blue) and four-terminal (red) configurations. The four-terminal configuration is adopted in all our measurements presented in the main text, because it eliminates spurious signals from electrical contacts. The two-terminal resistance in the superconducting state gives an estimate of the contact resistance of the order of 1 Ω.

### Extended Data Fig. 2 Temperature-dependent resistance of a monolayer Bi-2212 sample annealed in ozone.

Annealing cycles were performed under an O3 partial pressure of about 50 Pa at temperatures between 220 K and 240 K. O3 was purged with helium gas between annealing cycles, and data were obtained in helium vapour. Each annealing cycle lasts 5–30 min. Monolayer Bi-2212 was initially at optimal doping (black curve). The annealing cycles progressively increase the doping level of the sample. The red curve was obtained after first annealing, and blue curve was obtained after second annealing.

### Extended Data Fig. 3 Extracting Tc and T* from temperature-dependent resistance of monolayer Bi-2212.

a, Illustration of Tc and T* extraction from temperature-dependent resistance (black curve, which mostly overlaps with the red curve) and its derivative (blue curve). We used two definitions of Tc in our analysis: (i) Tc,diff where the slope of resistance vs temperature curve is maximum70; (ii) Tc0 from fitting with Aslamasov–Larkin paraconductivity model71 $$\varDelta \sigma =\sigma (T)-{\sigma }_{{\rm{normal}}}(T)=a{(T/{T}_{{\rm{c}}0}-1)}^{-1}$$. Near optimal doping, $${\sigma }_{{\rm{normal}}}(T)={(bT+c)}^{-1}$$, so Tc0 can be extracted from fitting with $$R(T)=(bT+c)(T-{T}_{{\rm{c}}0})/(T-{T}_{{\rm{c0}}}+a)$$ (red curve). T* is determined as the temperature at which the derivative of temperature-dependent resistance deviates from constant value (broken blue line; ref. 72). b, c, $${T}_{c,\mathrm{diff}}^{{\rm{\max }}}$$ (b) and $${T}_{{\rm{c}}0}^{{\rm{\max }}}$$ (c) of monolayer and bulk Bi-2212. Bulk data were obtained from optimally doped crystals (OP88). Under both definitions, the highest maximum Tc of monolayers is within the statistical uncertainty range of the Tc in optimally doped bulk crystals.

### Extended Data Fig. 4 Superconductor–insulator transition in monolayer Bi-2212.

a, Temperature-dependent resistivity $${R}_{\square }(p,T)$$ of sample A. The doping level, fixed for each curve, is tuned by repeated annealing cycles under vacuum (pressure below 10−4 mbar). The initially superconducting sample becomes insulating via a QPT. Broken line marks the separatrix where the transition occurs. Blue shaded region indicates the temperature range in which we perform the finite-size scaling analysis; the slight up-turn in resistivity at lower temperatures suggests intermediate phase or additional QCP between the superconducting and insulating phases49. b, Same dataset in a plotted inversely, that is, $${R}_{\square }(p,T)$$ plotted as a function of doping level at fixed temperatures between 6 K and 24 K. Each colour refers to a fixed temperature. Continuous curves are interpolations of data points at different temperatures. The point where all curves cross defines the critical point the QPT, $$({R}_{{\rm{c}}}=10.2\pm 0.6\,{\rm{k}}\Omega ,{p}_{{\rm{c}}}=0.022\pm 0.002)$$. c, Scaling of the same data with respect to variable $$u=|p-{p}_{{\rm{c}}}|t(T)$$. A single set of temperature-dependent parameters t(T) can force all data to collapse to a universal scaling function on both sides of the SIT. d, Temperature-dependent resistivity of sample B. Data were obtained between annealing cycles performed under $${10}^{-1}\,{\rm{mbar}}$$ of air that contains about $$3\times {10}^{-3}\,{\rm{mbar}}$$ of water vapour. The annealing cycles progressively increase the normal state resistivity, and induces SIT in the monolayer. Blue shaded region marks the temperature range in which we perform the finite-size scaling analysis.e, Same resistivity data in d plotted as a function of $$x=194\,\Omega /{R}_{\square }(T=200\,{\rm{K}})$$. Here x is a phenomenological variable that parametrizes the external factor (doping or disorder level) that drives the SIT; the precise value of x does not affect the finite-size scaling analysis according to formula (1). The critical point of the SIT is identified as $$({R}_{{\rm{c}}}=8.7\pm 0.6\,{\rm{k}}\Omega ,{x}_{{\rm{c}}}=0.022\pm 0.002)$$. f, Scaling analysis of the dataset in e. The analysis yields a critical exponent of νz = 2.45. The νz differs from the critical exponent in doping-driven SIT in sample A, but coincides with the value in disorder-driven SIT in sample C. Similar to sample C, sample B also features a two-step superconducting transition (marked by black arrow) that indicates considerable amount of disorder. We therefore conclude that disorder level drives the SIT in sample B. g, Temperature-dependent resistivity of sample C. Curves are obtained between annealing cycles performed under about 10 mbar of air. Such annealing cycles introduce disorders into the monolayer, and the superconductivity transition occurs in two steps. The disorder-driven SIT takes place at the lower-temperature transition (blue shaded region). h, Inverse of the dataset in g. Horizontal axis represents the phenomenological disorder level that is parametrized as $$d=213\,\Omega /{R}_{\square }(T=200\,{\rm{K}})$$. Smooth interpolations of the data points cross at the critical point $$({R}_{{\rm{c}}}=2.86\pm 0.17\,{\rm{k}}\Omega ,{x}_{{\rm{c}}}=0.028\pm 0.002)$$. i, Scaling of the same data in h with respect to variable $$u=|d-{d}_{{\rm{c}}}|t(T)$$. $$t(T)$$ is chosen such that all data collapse to a universal scaling function.

### Extended Data Fig. 5 Critical exponents of superconductor–insulator transitions in copper oxide superconductors.

a, Temperature-dependent parameter $$t(T)$$ obtained from finite-size scaling analysis in Extended Data Fig. 4. Values of $$t(T)$$ from all three monolayer Bi-2212 samples follow power-law dependence; the slope of the line fits (solid lines) yields the critical exponents of the SIT νz = 1.53, 2.45 and 2.35 for samples A, B and C, respectively. b, Critical exponents νz obtained in monolayer Bi-2212 (red circles) and various other copper oxide superconductors (black squares). All νz fall into the neighbourhood of one of the two values, 3/2 and 7/3, that characterize the SIT in the clean and dirty limit, respectively (see text). Solid vertical lines mark the mean, and broken lines the standard deviation, of the νz values in each category.

### Extended Data Fig. 6 Characterization of monolayer Bi-2212 after STM measurements.

a, Optical image of typical Bi-2212 flakes exfoliated on SiO2/Si substrate. The monolayer (light purple region in the centre) is identified from its optical contrast. b, A magnified view of the area marked by the square in a. c, AFM topography of the area marked by the square in b. Both the optical image and the AFM topography were obtained in an Ar atmosphere inside a glove box after STM measurements performed in UHV. d, Line cut of the AFM topography along the line shown in c. The step height of about 1.6 nm confirms that the Bi-2212 flake measured in STM was indeed a monolayer.

### Extended Data Fig. 7 Fourier transform of the conductance ratio map obtained on monolayer Bi2212 at various energies.

Each panel displays a Fourier transform of the conductance ratio map $$Z({\bf{r}},E)$$ of nearly optimally doped monolayer Bi-2212 at the energy labelled on the panel. The $$Z({\bf{r}},E)$$ maps are obtained from a set of 200 × 200-pixel conductance maps taken on an area of 500 Å $$\times$$ 500 Å with an energy resolution of 2 meV. Data were obtained from the same sample in Fig. 4 (here we show the full dataset).

### Extended Data Fig. 8 Energy dispersion of the q-vectors.

Amplitudes of measured qi (in units of 2π/a0) are plotted as functions of energy ($$i=1\ldots 7$$, except that q4 and q5 are too weak to be detected). We followed the method described in ref. 23 to obtain qi. Solid lines are energy dispersion of the q-vectors expected in the octet model.

### Extended Data Fig. 9 Histograms of $${{\boldsymbol{\Delta }}}_{1}({\bf{r}})$$ gap maps in monolayer and bulk Bi-2212.

Solid and empty symbols represent data from monolayer and bulk Bi-2212, respectively. $${\varDelta }_{1}$$ distributions in monolayers shift towards higher energies compared with those in bulk crystals. The shift reflects slight loss of oxygen doping during monolayer sample fabrication. Specifically, the doping level p is directly related to the average value of the pseudogap. From the average pseudogap, we estimate that $$p=0.06\pm 0.02,\,0.16\pm 0.02\,{\rm{and}}\,0.19\pm 0.02$$ for monolayers obtained from UD50, OP88 and OD55, respectively23,36,73. These values are lower than the doping levels extracted in the bulk crystals ($$p=0.08\pm 0.02,\,0.17\pm 0.02\,{\rm{and}}\,0.22\pm 0.01$$ for UD50, OP88 and OD55, respectively). Here we used the relations $$2{\varDelta }_{1}=152\,\,{\rm{m}}{\rm{e}}{\rm{V}}\times (0.27-p)/0.22\,$$ for $$0.1 < p < 0.22$$ and $$2{\varDelta }_{1}=85\,\,{\rm{m}}{\rm{e}}{\rm{V}}\times (0.12-p)/0.02\,$$ for $$0.06 < p < 0.08$$ to estimate the doping level in both bulk crystals and monolayers.

### Extended Data Fig. 10 Wavevector of the CDW order in monolayer Bi-2212 obtained in UD50.

Line cut (blue line) of the FFT of $$g({\bf{r}},E=20\,{\rm{meV}})$$ map in Fig. 5h along the Cu–O bond direction exhibits a peak at $${q}_{{\rm{CO}}}=0.25\,(2{\rm{\pi }}/{a}_{0})$$ that is associated with the charge-ordered state. The magenta line is a Gaussian fit to the peak plus a decaying exponential background. The full-width at half-maximum of the peak yields a correlation length of about 14a0.

### Extended Data Fig. 11 Pair density wave in monolayer Bi-2212.

a, Four representative conductance spectra ($${\rm{d}}I/{\rm{d}}V$$; upper panel) and the negative of their second derivative ($$D=-{{\rm{d}}}^{3}I/{\rm{d}}{V}^{3}$$; lower panel) in under-doped monolayer Bi-2212 obtained from UD50. We additionally define $$H={\rm{d}}I/{\rm{d}}V(E={\varDelta }_{0})-{\rm{d}}I/{\rm{d}}V(E=0)$$, which corresponds to the amount of low-energy DOS gapped out by Cooper pairing (here $${\varDelta }_{0}=15\,{\rm{m}}{\rm{e}}{\rm{V}}$$). The pair density wave can be visualized by spatially mapping either H or D (ref. 32). b, $$H({\bf{r}})$$ map on a $$40\,{\rm{nm}}\times 40\,{\rm{nm}}$$ area. A chequerboard pattern is clearly resolved. c, Fourier transform of the $$H({\bf{r}})$$ map in b. Peaks at $$|{\bf{q}}|=(0.25\pm 0.02)2{\rm{\pi }}/{a}_{0}$$ (marked by broken circles) along the Cu–O bond directions indicate the emergence of pair density wave order32. d–h, $$D({\bf{r}})$$ maps obtained on the same area in b at various energies. i–m, Fourier transform of the $$D({\bf{r}})$$ maps in d–h. The $$|{\bf{q}}|=2{\rm{\pi }}/4{a}_{0}$$ spatial modulations at $$E=15\,{\rm{meV}}$$ (broken circles in j) again indicate the existence of pair density wave32. Red crosses mark $${\bf{q}}=(0,\pm {\rm{\pi }}/{a}_{0})$$ and $$(\pm {\rm{\pi }}/{a}_{0},0)$$. We followed the method described in ref. 32 to obtain $$H({\bf{r}})$$ and $$D({\bf{r}})$$ maps. First, a set of conductance (dI/dV) spectra was taken on a 160 × 160 grid over the 40 nm × 40 nm area. Here we used a set-point bias voltage of −300 mV, which is far beyond the energy scale of the charge-ordered state, to eliminate possible set-point effects. We then fitted each dI/dV spectrum with a second-order polynomial, and took the second derivative of the polynomial to obtain the D spectrum. The $$H({\bf{r}})$$ map is directly obtained from the dI/dV spectra grid.

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Yu, Y., Ma, L., Cai, P. et al. High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ. Nature 575, 156–163 (2019). https://doi.org/10.1038/s41586-019-1718-x

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