1. Variational Monte-Carlo Study of the iron-based superconductors Fan Yang Beijing Institute of Technology

2. Collabrators: Hui Zhai, Fa Wang, Dung-Hai Lee Acknowledge: Zheng-Yu Weng, Tao Xiang, Miao Gao, Zhong-Yi Lu, Tao Li, Ying Ran, Hong Yao

3. Outline Introduction to the Iron-based SC Approach Problems studied Superconductivity Band-structure distortion Oribital-order and AFM Conclusion

4. The iron-based superconductors

5. Similar layered-structure Similar phase-diagram with cuprates! + + + + + + - -- - Fe - As above Fe-plane As below Fe-plane

6. Are the iron-based SC a copy of the cuprates? The iron-based superconductors No! Metal at AFM state! not Mott-insulator!

7. Are the iron-based SC BCS mediated by phonons? The iron-based superconductors No! LDA: Experiment:

8. Electron-electron interaction originated. Model: 5-band Hubbard-Hund model: The iron-based superconductors What’s the origin of the SC in this system?

9. : LDA from Kuroki (FeAs-SC), Zhong-Yi Lu (FeSe-SC) The iron-based superconductors 12354 : intra(inter)-orbital Hubbard; : Hund-rule coupling

10. Band Structure Band structure and FS of LaOFeAs----SC, Kuroki, et al

11. Band structure of KFeSe----- SC, Miao Gao, Zhong-Yi Lu

12. Weak coupling : RPA, FLEX, FRG, …… iron-superconductors: really weak-coupling ?? Strong coupling : Doped Mott--insulator? parent compound : Metal !! Mean-field: No SC !! Problem: repulsion SC How ? Optical: M. M. Qazilbash, et al, Nature Physics 5, 647 (2009).

13. Go beyond weak-coupling: VMC : Mott-limit : Mean-field Fan Yang, Hui Zhai, Fa Wang, Dung-Hai Lee, Phys. Rev. B83, 134502 (2011)

14. What’s the explicit formulism of ? Set Go beyond weak-coupling: VMC the Bloch-wave-function

15. Monte-Carlo: Sampling by Markov-processHow many in ?How to calculate observables on ?

16. Superconductivity : conv-s : d-wave : s-pm : ext-s

17. Both s-pm and extended-s are possible !! Iron-pnictide : 10*10*5 n=5.9 Fan Yang, et al, Phys. Rev. B83, 134502 (2011)

18. S-Plus-Minus ARPES, Andereev, Optical, ……. Nodal S-wave: extended-s Tuneling, NMR, Specific heat, ……

19. double-layed n=6.11single-layed n=6.22 Iron-selenide : 12*12*5 (10) d-wave : leading symmetry s-pm : close competitor

20. S-Plus-Minus Nodaless d-wave:

21. Normal-state FS-distortion  Pomeranchuk- Instability

22. (a): FS before distortion (b): FS after distortion Pocket-shrink !! Main panel: Inset: n=5.87 Fan Yang, et al, Phys. Rev. B83, 134502 (2011)

23. Orbital order in the AFM state

24. AFM drives the orbital-order !! n=6 Fan Yang, et al, Phys. Rev. B83, 134502 (2011)

25. Consequence of the orbital-order: Lattice expansion along the AFM-axis !!

26. The iron-based SC is sth sitting in between BCS and cuprates! With VMC approach, we have studied, SC: s-pm + ext-s Band-distortion: pocket---shrink Orbital-order: driven by AFM Electron-electron interaction is the driving force of SC and other important physical properties Conclusion

27. Thanks !