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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, Christoph Meingast)

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Basic properties N and S states New physics from new crystals

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

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

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

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Pressure enhances spin fluctuations Imai, Cava PRL 2009

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

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

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A tale of two Fe-chalcogenides Mizuguchi et al 2011 Kasahara et al, unpublished (2014) crystals from A. Böhmer et al., PRB 87, 180505(R) (2013) Bad metal physics not evident in FeSe (T c )~0.1 cm

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High-quality stoichiometric FeSe single crystal grown @KIT A. Böhmer et al., PRB 87, 180505(R) (2013). T c ~ 10 K (cf. ~8 K for typical samples) Large RRR and MR indicate that samples are very clean. S. Kasahara et al., unpublished?

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 S. Kasahara et al., unpublished?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

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Electronic specific heat JY Lin et al, PRB 84, 220507(R) (2011) Hardy et al, unpublished old new Old and new very similar – small influence of disorder on SC

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SdH (Terashima arXiv:1405.7749)

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SdH

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

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

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Signatures of electronic nematicity in FeSC STM in SC state topography spectrumdefect vortex FeSe: CL Song et al, Science 2011, PRL 2012 a and b are only ~0.1% different! But strong C 4 symmetry breaking in SC state.

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

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FT-dI/dV/(I/V) Unidirectional quasi-particle interference 45 nm×45 nm, +50 mV/100 pA T ~ 1.5 K dI/dV/(I/V)Topograph Bragg alias Unidirectional dispersing features in q a and q b directions. a Fe b Fe a Fe b Fe qaqa qbqb Small orthorhombicity yet large anisotropy in the band structure! cf. NaFeAs: E. P. Rosenthal et al., Nat. Phys. 10, 225 (2014). Hanaguri group using KIT crystals

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Extremely small E F ~ BCS-BEC crossover regime? QPI Bandstructure (note: over small 1-domain window!) Electron-likeHole-like along q a along q b FT-dI/dV/(I/V) Orthogonal electron- and hole-like dispersions B = 12 T imp. EFEF EFEF

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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? Possible intra-orbital scattering S. Graser et al., New J. Phys. 11, 025016 (2009). Can we reproduce orthogonal electron and hole dispersions using the orbital-order model?

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Lifting the orbital degeneracy Band calc. (by Dr. H. Ikeda) Orbital character Orthorhombic distortion only E yz -E xz = 0.05 eV E yz -E xz = 0.1 eV Orthorhombic distortion alone cannot explain the unidrectional dispersions. Orthorhomicity is not a player but a spectator. Orbital order? More detailed calculations are indispensable…

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Penetration depth and thermal conductivity results

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

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Magnetic field penetration depth Quasi T-linear at T/T c < 0.2 T * imp ~ 2 K Finite qusiparticle excitation at low temperatures No Curie term (No excess irons) cf) clean YBCO Large temperature dependence Presence of line nodes ~T 1.4

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Thermal conductivity in a stoichiometric FeSe single crystal Wiedemann-Franz law n /T=L 0 / 0 ~ 1.43 (W/K 2 m) ~ 30-40% of the normal state value n/Tn/T 0 ~ 1.70 cm 0 n /T ~ 1.06 (W/K 2 m) 0 ~ 2.30 cm Strong evidence for the line nodes Increase of the quasiparticle life time below T c Large residual value TcTc 0 /T=L 0 / 0 L 0 : Lorentz number 0 /T~ 0.4 (W/K 2 m)

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

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

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Anomalous field dependence of thermal conductivity Long QP mean free path l QP 00 FeSe Strong reduction of /T at low fields Plateau at high fields e l /T ~ N(E F )v F l N(E)~ H 1/2 Doppler shift Different from ordinal behaviors

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Anomalous field dependence of thermal conductivity CeCoIn 5 Y. Kasahara et al., PRB, 72, 214515 (2005). Long QP mean free path l QP N(E)~ H 1/2 l ~ H -1/2 Long m.f.p. & vortex scattering 00 FeSe Strong reduction of /T at low fields Plateau at high fields e l /T ~ N(E F )v F l Doppler shift Cancelation Plateau ① Vortex scattering due to long mean free path (a v ~ H -1/2 )

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Anomalous field dependence of thermal conductivity l =v F ~ 200 nm c h h )( c e e ) ~ c ) 2 ~ c ) 2 l =v F ~ 0.2 m Magnetoresistance 00 FeSe Strong reduction of /T at low fields Plateau at high fields e l /T ~ N(E F )v F l FeSe Long mean free path Hard to explain a sharp kink at low fields and a plateau in a nearly whole vortex state ① Vortex scattering due to long mean free path

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Anomalous field dependence of thermal conductivity 00 FeSe Strong reduction of /T at low fields Plateau at high fields ② Possible phase transition in the SC state K. Krishana, et al., Science (1997). BSCCO Field induced change of gap symmetry d x2-y2 d x2-y2 + id xy or d x2-y2 + is FeSe s s + id (???)

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Anomalous field dependence of thermal conductivity 00 FeSe Strong reduction of /T at low fields Plateau at high fields ③ Lifting nodes under magnetic field V. Mishra et al., Phys. Rev. B, 80, 224525 (2009). Plateau with finite /T Small SC gap already suppressed at low fields

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High-field anomaly in thermal conductivity H*

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Proposed new high-fied phase

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Summary FeSe T c 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)

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