Supplementary Material Giant increase of critical current density and vortex pinning in Mn doped KxFe2-ySe2 single crystals Mingtao Li1,2, La Chen1,a), Wen-Long You3, Junyi Ge4, Jincang Zhang1,2,b) 1 Department of Physics, Shanghai University, Shanghai 200444, China 2 Materials Genome Institute, Shanghai University, Shanghai 200444, China 3 College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China 4 INPAC-Institute for Nanoscale Physics and Chemistry, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium To study the temperature evolution of 𝐽𝑐 (𝜇0 𝐻) and vortex pinning mechanism, we measured the isothermal MHLs at different temperatures. The typical MHLs for S2 sample are shown in Fig. S1(a) and S1(b), and 𝐽𝑐 (𝜇0 𝐻) curves are plotted in Fig. S1(c) and S1(d). For 𝐻 ∥ 𝑐, the MHLs exhibit high symmetric feature with respect to 𝜇0 𝐻. Similar to high quality KxFe2-ySe2 single crystal,27 the ZFCP of the MHLs is absent below 𝑇=15 K. It was pointed out by Liu et al that the absence of ZFCP is a sample-dependent phenomenon,14 whose occurrence depends on the uniform and contiguous distribution of the superconducting phase. Contrary to other “122” systems,4,5 the SMP effect disappears quickly for S2/S3 samples with increasing temperature. As the temperature goes up to 27 K, the opening area of MHLs shrinks gradually which evidences a reduction of capability of carrying supercurrent towards high magnetic field. Furthermore, the calculated 𝐽𝑐 (𝜇0 𝐻) exceeds 104 A/cm2 for 𝐻 ∥ 𝑐 while 103 A/cm2 for 𝐻 ∥ 𝑎𝑏 below 11 K, and 𝐽𝑐 has a weak field dependence. a) Present address: Peter Grünberg Institute (PGI-8), Forchungszentrum Jülich, D-52425 Jülich, Germany b) Corresponding author, E-mail: [email protected] FIG. S1. REFERENCES 4 H. Yang, H. Q. Luo, Z. S. Wang and H. H. Wen, Appl. Phys. Lett. 93, 142506 (2008). 5 D. L. Sun, Y. Liu, C. T. Lin, Phys. Rev. B 80, 144515 (2009). 14 Y. Liu, Q. Xing, K. W. Dennis, R. W. McCallum, T. A. Lograsso, Phys. Rev. B 86, 144507 (2012). 27 B. Shen, B. Zeng, G. F. Chen, J. B. He, D. M. Wang, H. Yang and H. H. Wen, Europhys. Lett. 96, 37010 (2011). Figure captions_Mingtao Li et al., FIG. S1. (a) and (b) show the isothermal MHLs at various temperatures for S2 sample with 𝐻 ∥ 𝑐 and 𝐻 ∥ 𝑎𝑏, respectively. Shown in (c) and (d) are the corresponding magnetic field dependence of critical current density.