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				In his seminal work published in Acta Physica Sinica in 1965, Yu Lu pointed out that the superconducting gap exhibits weak modulations near the pair-breaking magnetic impurity in a superconductor. In the past ten year, a series high-resolution scanning tunneling microscopy works reported weak superconducting gap modulations in certain superconductors and explained these phenomena as pair density waves. In line with Yu Lu’s discovery, Lee D H et al. pointed out that in many cases, the interference effect of pair-breaking scattering can also lead to superconducting gap modulations in space. We will discuss the distinction and unification of these two kinds of mechanisms, as well as their relevance to recent experimental observations.- 
													Keywords:
													
- superconductivity /
- pair density waves /
- scanning tunneling microscopy
 [1] Bardeen J, Cooper L N, Schrieffer J R 1957 Phys. Rev. 108 1175  Google Scholar Google Scholar[2] Fulde P, Ferrell R A 1964 Phys. Rev. 135 A550  Google Scholar Google Scholar[3] Larkin A I, Ovchinnikov Y N 1965 Sov. Phys. JETP 20 762 [4] Hamidian M, Edkins S D, Joo S H, et al. 2016 Nature 532 343  Google Scholar Google Scholar[5] Du Z Y, Li H, Joo S H, Donoway E P, Lee J, Séamus Davis J C, Gu G D, Johnson P D, Fujita K 2020 Nature 580 65  Google Scholar Google Scholar[6] Chen H, Yang H T, Hu B, et al. 2021 Nature 599 222  Google Scholar Google Scholar[7] Liu X, Chong Y X, Sharma R, Davis J C S 2021 Science 372 1447  Google Scholar Google Scholar[8] Zhao H, Blackwell R, Thinel M, et al. 2023 Nature 618 940  Google Scholar Google Scholar[9] Liu Y Z, Wei T C, He G Y, Zhang Y, Wang Z Q, Wang J 2023 Nature 618 934  Google Scholar Google Scholar[10] Aishwarya A, May-Mann J, Raghavan A, Nie L M, Romanelli M, Ran S, Saha S R, Paglione J, Butch N P, Fradkin E, Madhavan V 2023 Nature 618 928  Google Scholar Google Scholar[11] Gu Q, Carroll J P, Wang S Q, Ran S, Broyles C, Siddiquee H, Butch N P, Saha S R, Paglione J, Séamus Davis J C, Liu X L 2023 Nature 618 921  Google Scholar Google Scholar[12] Agterberg D F, Séamus Davis J C, Edkins S D, et al. 2020 Annu. Rev. Condens. Matter Phys. 11 231  Google Scholar Google Scholar[13] 于渌 1965 物理学报 21 75  Google Scholar Google ScholarYu L 1965 Acta Phys. Sin. 21 75  Google Scholar Google Scholar[14] Gao Z Q, Lin Y P, Lee D H 2023 arXiv: 2310.06024 [cond-mat.supr-con] [15] Ambegaokar V, Baratoff A 1963 Phys. Rev. Lett. 11 104  Google Scholar Google Scholar[16] Jin J T, Jiang K, Yao H, Zhou Y 2022 Phys. Rev. Lett. 129 167001  Google Scholar Google Scholar[17] Deng H B, Qin H L, Liu G W, et al. 2024 Nature DOI: 10.1038/s41586-024-07798-y 
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[1] Bardeen J, Cooper L N, Schrieffer J R 1957 Phys. Rev. 108 1175  Google Scholar Google Scholar[2] Fulde P, Ferrell R A 1964 Phys. Rev. 135 A550  Google Scholar Google Scholar[3] Larkin A I, Ovchinnikov Y N 1965 Sov. Phys. JETP 20 762 [4] Hamidian M, Edkins S D, Joo S H, et al. 2016 Nature 532 343  Google Scholar Google Scholar[5] Du Z Y, Li H, Joo S H, Donoway E P, Lee J, Séamus Davis J C, Gu G D, Johnson P D, Fujita K 2020 Nature 580 65  Google Scholar Google Scholar[6] Chen H, Yang H T, Hu B, et al. 2021 Nature 599 222  Google Scholar Google Scholar[7] Liu X, Chong Y X, Sharma R, Davis J C S 2021 Science 372 1447  Google Scholar Google Scholar[8] Zhao H, Blackwell R, Thinel M, et al. 2023 Nature 618 940  Google Scholar Google Scholar[9] Liu Y Z, Wei T C, He G Y, Zhang Y, Wang Z Q, Wang J 2023 Nature 618 934  Google Scholar Google Scholar[10] Aishwarya A, May-Mann J, Raghavan A, Nie L M, Romanelli M, Ran S, Saha S R, Paglione J, Butch N P, Fradkin E, Madhavan V 2023 Nature 618 928  Google Scholar Google Scholar[11] Gu Q, Carroll J P, Wang S Q, Ran S, Broyles C, Siddiquee H, Butch N P, Saha S R, Paglione J, Séamus Davis J C, Liu X L 2023 Nature 618 921  Google Scholar Google Scholar[12] Agterberg D F, Séamus Davis J C, Edkins S D, et al. 2020 Annu. Rev. Condens. Matter Phys. 11 231  Google Scholar Google Scholar[13] 于渌 1965 物理学报 21 75  Google Scholar Google ScholarYu L 1965 Acta Phys. Sin. 21 75  Google Scholar Google Scholar[14] Gao Z Q, Lin Y P, Lee D H 2023 arXiv: 2310.06024 [cond-mat.supr-con] [15] Ambegaokar V, Baratoff A 1963 Phys. Rev. Lett. 11 104  Google Scholar Google Scholar[16] Jin J T, Jiang K, Yao H, Zhou Y 2022 Phys. Rev. Lett. 129 167001  Google Scholar Google Scholar[17] Deng H B, Qin H L, Liu G W, et al. 2024 Nature DOI: 10.1038/s41586-024-07798-y 
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