Variational MonteCarlo Study of the ironbased superconductors Fan

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

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

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

The iron-based superconductors

The iron-based superconductors + - + - + Fe + Similar layered-structure As above Fe-plane Similar phase-diagram As below Fe-plane with cuprates!

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

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

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

The iron-based superconductors : LDA from 1 2 Kuroki (Fe. As-SC), Zhong-Yi Lu (Fe. Se-SC) 3 : intra(inter)-orbital Hubbard; 4 5 : Hund-rule coupling

Band Structure Band structure and FS of La. OFe. As----SC , Kuroki, et al

Band structure of KFe. Se----- SC , Miao Gao, Zhong-Yi Lu

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

Go beyond weak-coupling: VMC : Mott-limit : Mean-field Fan Yang, Hui Zhai, Fa Wang, Dung-Hai Lee, Phys. Rev. B 83, 134502 (2011)

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

How to calculate observables on How many in Monte-Carlo: Sampling ? ? by Markov-process

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

Iron-pnictide : 10*10*5 Fan Yang, et al, n=5. 9 Phys. Rev. B 83, 134502 (2011) Both s-pm and extended-s are possible !!

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

Iron-selenide : 12*12*5 (10) single-layed n=6. 22 double-layed d-wave : leading symmetry s-pm : close competitor n=6. 11

S-Plus-Minus Nodaless d-wave:

Normal-state FS-distortion ® Pomeranchuk. Instability

n=5. 87 Main panel: Inset: (a): FS before distortion (b): FS after distortion Pocket-shrink !! Fan Yang, et al, Phys. Rev. B 83, 134502 (2011)

Orbital order in the AFM state

n=6 AFM drives the orbital-order !! Fan Yang, et al, Phys. Rev. B 83, 134502 (2011)

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

Conclusion • 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

Thanks !