By using scanning tunneling microscopy/spectroscopy, we investigate the electronic structure on the atomic scale near Zn impurities in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\left({\mathrm{Cu}}_{1-x}{\mathrm{Zn}}_x\right)}_2{\mathrm{O}}_{8+\delta }$. In the Fourier-transformed differential-conductance image measured at zero bias, two characteristic spots are observed with the wave vectors of about 0.13($2\pi /a_0$) and 0.23($2\pi /a_0$), which correspond to the local density of states modulations with real-space periods of about eight unit cells ($8a_0$) and four unit cells ($4a_0$), respectively. We argue that the $8a_0$ modulation may be the consequence of a pair density wave (PDW), while the $4a_0$ modulation is the coexistent charge density wave or another PDW. The two modulations emerge exactly near the Zn impurities when the superconductivity is suppressed nearby, suggesting that the related phases may be the competing order of superconductivity. The $8a_0$ and $4a_0$ modulations have strong amplitudes near the Zn impurities. The effective range of the PDW modulation is similar to the scale of the Cooper-pair condensate, but much larger than that of the impurity resonance state of quasiparticles. In addition, both oscillations have the local maxima at Zn impurities, providing direct phase information of the two coexisting phases. Our results provide additional insight into the relationship between the superconducting coherent state and the PDW state in cuprates.

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• Impurities in superconductors
• Pair density wave
• Superconductivity
• Cuprates
• Scanning tunneling spectroscopy