Review of results on FeSe

1. Review of results on FeSe P Hirschfeld, 9/19 (Data only up to 6/2014) Thanks to: Taka Shibauchi Tetsuo Hanaguri Frederic Hardy (+Anna Boehmer, ChristophMeingast)

2. Basic properties N and S states • New physics from new crystals

3. Relatively correlated materialZ. P. Yin, K. Haule, & G. Kotliar, Nat. Mat. 10, 932–935 (2011) LDA+DMFT exercise: Fix interactions U,J, vary material

4. FeSe: nonmagnetic 8K superconductor, but: Wang et al. Chin. Phys. Lett. 2012 1 layer Tc35K under tensile strain Medvedev et al 2010: Tc37K under pressure ARPES gap Burrard‐Lucas et al 2012 Tc43K molecular intercalation S. He et al aXv::1207.6823

5. Pressure dependence of bulk FeSe Margadona et al 2010 Bendele et al 2012: magnetic state at low pressure Medvedev et al 2010

6. Pressure enhances spin fluctuations Imai, Cava PRL 2009

7. But note difference from other systems FeSe Spin fluctuations seem to wait until orthorhombic transition happens

8. Are the chalcogenides generally more correlated? “Bad metals”? Fang et al 2009 Morosan et al (Rice group) 2013 Mizuguchi et al 2011

9. A tale of two Fe-chalcogenides Kasahara et al, unpublished (2014) crystals from A. Böhmer et al., PRB 87, 180505(R) (2013) Mizuguchi et al 2011 r(Tc)~0.1Wcm Bad metal physics not evident in FeSe

10. High-quality stoichiometricFeSe single crystal grown @KIT A. Böhmeret al.,PRB 87, 180505(R) (2013). S. Kasaharaet al.,unpublished? • Tc ~ 10 K (cf. ~8 K for typical samples) • Large RRR and MR indicate that samples are very clean.

11. How good are new KIT crystals really? F.-C. Hsu et al., PNAS 105, 14262 (2008). S. Kasaharaet al., unpublished? r0= 250 mWcm at 8K r0= 10 mWcm at 10K RRR~40 RRR~6.5 Consistent with (r(T0) =0)

12. Electronic specific heat new old JY Lin et al, PRB 84, 220507(R) (2011) Hardy et al, unpublished Old and new very similar – small influence of disorder on SC

13. SdH(Terashima arXiv:1405.7749)

14. SdH

15. Large orbital ordering in ARPES Nakayama et al. arXiv:1404..0857

16. Signatures of electronic nematicity in FeSC generally ARPES: orbital ordering (0,p) (p,0) (0,p) (p,0) Yi et al PNAS 2011

17. Signatures of electronic nematicity in FeSC STM in SC state FeSe: CL Song et al, Science 2011, PRL 2012 topography vortex spectrum defect a and b are only ~0.1% different! But strong C4 symmetry breaking in SC state.

18. Tunneling spectra • Low energy spectrum(±6 mV) • High energy spectrum(±95 mV) Multigap SC

19. Unidirectional quasi-particle interference Hanaguri group using KIT crystals Topograph FT-dI/dV/(I/V) dI/dV/(I/V) T ~ 1.5 K Bragg Small orthorhombicityyet large anisotropy in the band structure! alias bFe bFe qb aFe aFe qa 45 nm×45 nm, +50 mV/100 pA Unidirectional dispersing featuresin qa and qb directions. cf. NaFeAs: E. P. Rosenthal et al., Nat. Phys. 10, 225 (2014).

20. QPI Bandstructure (note: over small 1-domain window!) along qa along qb FT-dI/dV/(I/V) B = 12 T B = 12 T imp. imp. EF +D +D EF -D -D Electron-like Hole-like • Orthogonal electron- and hole-like dispersions • Extremely small EF ~ DBCS-BEC crossover regime?

21. Possible intra-orbital scattering • Orbital character changes when we go around the FS pockets. • If only intra-orbital scatterings are allowed, QPI patterns may be unidirectional. • Why one of the orbitals is active? Orbital order? Can we reproduce orthogonal electron and hole dispersions using the orbital-order model? S. Graseret al.,New J. Phys. 11, 025016 (2009).

22. Lifting the orbital degeneracy Orbital character Band calc. (by Dr. H. Ikeda) More detailed calculations are indispensable… Orthorhombic distortion only Orthorhombic distortion alonecannot explain the unidrectional dispersions. Eyz-Exz= 0.05 eV Orthorhomicity isnot a player but a spectator. Orbital order? Eyz-Exz= 0.1 eV

23. Penetration depth and thermal conductivity results

24. Thermal Conductivity MBE-STM J.K. Dong, et al., PRB (2009). Specific heat Can-Li Song, et al., Science 332. 1410 (2010). J.-Y.Lin, et al., PRB (2011).  Single crystals (off-stoichiometry)  Defect-free stoichiometric films  Nodeless multiple gaps  Nodal superconductivity Introduction: FeSex Superconducting gap symmetry ---- A key for the mechanism  The simplest structure  Strong correlation F.C. Hsu, et al., PNAS (2008).

25. Magnetic field penetration depth • Large temperature dependence • Quasi T-linear at T/Tc < 0.2 Dl ~T1.4 T*imp ~ 2 K • No Curie term (No excess irons) cf) clean YBCO Finite qusiparticle excitation at low temperatures Presence of line nodes

26. Thermal conductivity in a stoichiometric FeSe single crystal r0~ 2.30 mWcm k0n/T ~ 1.06 (W/K2m) Tc • Increase of the quasiparticle life time below Tc kn/T • Large residual value k0/T=L0/r0 k0/T~ 0.4 (W/K2m) Wiedemann-Franz law kn/T=L0/r0 ~ 1.43 (W/K2m) L0: Lorentz number r0~ 1.70 mWcm ~ 30-40% of the normal state value Strong evidence for the line nodes

27. Discussion: Origin of the different behavior D f 0 Accidental nodes Present study (Clean single crystals) Quasi T-linear l(T) Finite residual k0/T Nodal Superconductivity Earlier study (Dirty crystals) Negligibly small k0/T at 0 T Gap anisotropy is smeared by strong scattering G D 0 f Nodes can be removed J.K. Dong, et al., PRB (2009). Nodeless (Anisotropic s-wave) Nodal s-wave state in FeSe

28. Discussion: Origin of the different behavior D ~ 0.3-0.4 f 0 D Accidental nodes node 0 f Magnitude of the residual term Present results x: coherence length ~ 5 nm l:mean free path ~ 200 nm 1/m ~ 6 - 8 Inconsistent with d-wave Slope parameter of gap at nodes Gap anisotropy is smeared by strong scattering Nodes are nearly vanishing G D 0 f Nodes can be removed 2-band model V. Mishra et al., PRB, 80, 224525 (2009). Nodal s-wave state in FeSe

29. Anomalous field dependence of thermal conductivity m0 • Strong reduction of k/T at low fields FeSe • Plateau at high fields kel/T ~ N(EF)vFl • Different from ordinal behaviors Doppler shift N(E)~ H1/2 Long QP mean free path lQP

30. Anomalous field dependence of thermal conductivity m0 • Strong reduction of k/T at low fields FeSe • Plateau at high fields kel/T ~ N(EF)vFl ① Vortex scattering due to long mean free path CeCoIn5 Y. Kasahara et al., PRB, 72, 214515 (2005). Doppler shift N(E)~ H1/2 Long m.f.p. & vortex scattering l ~ H-1/2 (av ~ H-1/2) Cancelation  Plateau Long QP mean free path lQP

31. Anomalous field dependence of thermal conductivity m0 • Strong reduction of k/T at low fields FeSe • Plateau at high fields kel/T ~ N(EF)vFl ① Vortex scattering due to long mean free path Magnetoresistance FeSe Dr/r0 = (wchth)(wcete) ~(wct)2 Dr/r0~ (wct)2 l =vFt ~ 0.2 mm Long mean free path Hard to explain a sharp kink at low fields and a plateau in a nearly whole vortex state l =vFt ~ 200 nm

32. Anomalous field dependence of thermal conductivity m0 • Strong reduction of k/T at low fields FeSe • Plateau at high fields ② Possible phase transition in the SC state BSCCO Field induced change of gap symmetry dx2-y2dx2-y2 + idxy or dx2-y2 + is K. Krishana, et al., Science (1997). FeSe ss + id (???)

33. Anomalous field dependence of thermal conductivity m0 • Strong reduction of k/T at low fields FeSe • Plateau at high fields ③ Lifting nodes under magnetic field V. Mishra et al., Phys. Rev. B, 80, 224525 (2009). • Plateau with finite k/T • Small SC gap already suppressed at low fields

34. High-field anomaly in thermal conductivity H*

35. Proposed new high-fied phase

36. Summary • FeSeTc very sensitive to pressure • Apparent strong orbital ordering in ARPES, STM, • no magnetism strong nematic ordering • (resistivity anisotropy???) • Big challenge to electronic structure theory! • SC state consistent with weak nodes • (easily removed by perturbation)