1. Zlatko Tesanovic, Johns Hopkins University zbt@pha.jhu.edu http://www.pha.jhu.edu/~zbtzbt@pha.jhu.eduhttp://www.pha.jhu.edu/~zbt o Iron-pnictide HTS are semimetals with significant electron correlations but are ultimately itinerant (in contrast to cuprates) o Things might be different in iron-chalcogenides  closer to the Mott limit o FePn superconducting state is likely s+- driven by interband repulsion o When interactions ~ effective bandwidth, preferred ground state of parent FePn is combination of SDW and perpendicular orbital current DW o This predicted orbital current DW is not easy to observe directly (“hidden order”) but could play key role in phenomenology of FePn Spin-Orbit Interplay and Spin-Orbit Interplay and “Hidden Order” in FePn J. Kang and ZT, PRB 83, 020505 (2011)

2. Fe-pnictides: Semimetals  Superconductors In contrast to cuprates, all d-bands in FeAs are either nearly empty (electrons) or nearly full (holes) and far from being half-filled. This makes it easier for electrons (holes) to avoid each other.  FeAs are less correlated than cuprates (correlations are still important !! )

3. Important: Near E F e and h bands contain significant admixture of all five Wannier d- orbitals, d xz and d yz of odd parity (in FeAs plane) and the remaining three d-orbitals of even parity in FeAs plane  “Minimal Model” of FeAs Layers V. Cvetkovic and ZT, EPL 85, 37002 (2009) C. Cao, P. J. Hirschfeld, and H.-P. Cheng, PRB 77, 220506 (2008) K. Kuroki et al, PRL 101, 087004 (2008) d xz odd parity even parity d yz d xy d xx-yy d 2zz-xx-yy

4. Nesting Tendencies in Fe-pnictides Moderately strong interactions promote pairing of e-h pockets  valley density-wave (VDW) VDW = itinerant multiband CDW (structural), SDW (AF) and orbital orders at q = M = ( ¼, ¼ ) SemiconductorSemimetal  d c dd cc SDW, CDW, ODW or combinations thereof  VDW V. Cvetkovic and ZT, EPL 85, 37002 (2009) Precise form of VDW is set by interactions

5. Interactions in FeAs I V. Cvetkovic and ZT, PRB 80, 024512 (2009); J. Kang and ZT, PRB 83, 020505 (2011)

6. Interactions in FeAs II Typically, we find W s is dominant  Valley density-wave(s) (VDW) in FeAs h1h1 h2h2 e1e1 e-h These “Josephson” terms are not crucial for SDW  Could they induce superconductivity ?? Hirschfeld, Scalapino, Kuroki, Bernevig, Thomale, Chubukov, Eremin,

7. Interband pairing acts like Josephson coupling in k-space. If G 2 is repulsive  antibound Cooper pairs (s’SC) M Two Kinds of Interband Superconductivity Type-A (conventional) interband SC: c FS cd d Type-B (intrinsic) interband SC: cd FS sSC s’SC G2G2 sSC s’SC G2G2 ZT, Physics 2, 60 (2009)

8. If G 1, G 2 << U, W  relevant vertices: U, W, & G 2 Interactions in FeAs III V. Cvetkovic & ZT (RG) ; A. V. Chubukov, I. Eremin et al (parquet); F. Wang, H. Zhai, Y. Ran, A. Vishwanath & DH Lee (fRG) R. Thomale, C. Platt, J. Hu, C. Honerkamp & A. Bernevig (fRG) The condition for interband SC is actually milder: suffices to have G 2 * > U* even if G 2 << U

9. RG flows (near SDW): RG Theory of Interband Mechanism of SC in FeAs V. Cvetkovic and ZT, PRB 80, 024512 (2009) In Fe-pnictides interband superconductivity (s’ or s+- state) is a strong possibility but there is some fine tuning with SDW/CDW/ODW

10. What is a (THE) Model for Iron-Pnictides ?  U(4) £ U(4) Theory of Valley-Density Wave (VDW) Key assumption I: Eremin, Knolle Hirschfeld, Kuroki, Bernevig, Thomale, Chubukov, Eremin, Key assumption II:

11. U(4) £ U(4) Theory of Valley-Density Wave (VDW)  U(4) £ U(4) symmetry  unified spin and pocket/orbital flavors V. Cvetkovic and ZT, PRB 80, 024512 (2009); J. Kang and ZT, PRB 83, 020505 (2011)

12. Hierarchy of RG Energy Scales U, W >> G 1, G 2  U(4) £ U(4) Theory of Valley-Density Wave (VDW) U(4) £ U(4) symmetry at high energies  Spin and pocket/orbital flavors all mixed  VDW ground state (any combination of SDW/CDW/P(O)DW) At low energies, numerous terms break this U(4) £ U(4) symmetry Key assumptions: V. Cvetkovic and ZT, PRB 80, 024512 (2009); J. Kang and ZT, PRB 83, 020505 (2011)

13. U(4) £ U(4) Symmetry vs Reality Since ¸ 1 » 0 el-ph interaction or dynamical polarization from Pn orbitals could easily lead to ¸ 1 < 0  Pnictides are near ¸ 1 = 0 QCP !! J. Kang and ZT, PRB 83, 020505 (2011)

14. “Near” U(4) £ U(4) Symmetry and Experiments J. Kang and ZT, PRB 83, 020505 (2011) Orbital current AF (OCrDW)  Can this pattern be observed by neutrons? NMR/NQR? ¹ SR?

15. Fermiology of Valley-Density Wave (VDW) J. Kang and ZT, PRB 83, 020505 (2011) New ordered state: orbital current AF (OCrDW) perpendicular to SDW Not easy to observe OCrDW directly (“hidden order”): charge currents are small since d xz and d yz orbital currents nearly cancel