Review of results on FeSe

Review of results on FeSeP Hirschfeld, 9/19(Data only up to 6/2014)Thanks to:

Taka Shibauchi Tetsuo Hanaguri Frederic Hardy (+Anna Boehmer, Christoph Meingast)

Basic properties N and S states New physics from new crystalsRelatively correlated materialZ. P. Yin, K. Haule, & G. Kotliar, Nat. Mat. 10, 932935 (2011)

LDA+DMFT exercise:Fix interactions U,J, varymaterialFeSe: nonmagnetic 8K superconductor, but:

Medvedev et al 2010: Tc37K under pressure

BurrardLucas et al 2012Tc43K molecular intercalationS. He et al aXv::1207.6823

ARPES gap Wang et al. Chin. Phys. Lett. 2012 1 layer Tc35K under tensile strain4Pressure dependence of bulk FeSe

Medvedev et al 2010

Bendele et al 2012: magnetic state at low pressure

Margadona et al 2010

Pressure enhances spin fluctuations

Imai, Cava PRL 2009But note difference from other systems

FeSe Spin fluctuations seem to wait until orthorhombic transition happensAre the chalcogenides generally more correlated? Bad metals?

Mizuguchi et al 2011

Morosan et al (Rice group) 2013Fang et al 2009

A tale of two Fe-chalcogenides

Mizuguchi et al 2011Kasahara et al, unpublished (2014) crystals fromA. Bhmer et al., PRB 87, 180505(R) (2013)Bad metal physics not evident in FeSer(Tc)~0.1WcmHigh-quality stoichiometric FeSe single crystal grown @KIT

A. Bhmer et al.,PRB 87, 180505(R) (2013).Tc ~ 10 K (cf. ~8 K for typical samples)Large RRR and MR indicate that samples are very clean.

S. Kasahara et al.,unpublished?

F.-C. Hsu et al., PNAS 105, 14262 (2008).

S. Kasahara et al., unpublished?

How good are new KIT crystals really?r0= 250 mWcm at 8Kr0= 10 mWcm at 10KRRR~6.5RRR~40Consistent with (r(T0) =0)Electronic specific heat

JY Lin et al, PRB 84, 220507(R) (2011)

Hardy et al, unpublishedold new Old and new very similar small influence of disorder on SCSdH (Terashima arXiv:1405.7749)

SdH

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

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

topographyspectrumdefectvortexFeSe: CL Song et al, Science 2011, PRL 2012a and b are only ~0.1% different! But strong C4 symmetry breaking in SC state.Tunneling spectra

Low energy spectrum (6 mV)Multigap SC

High energy spectrum (95 mV)FT-dI/dV/(I/V)Unidirectional quasi-particle interference

45 nm45 nm, +50 mV/100 pAT ~ 1.5 K

dI/dV/(I/V)Topograph

BraggaliasUnidirectional dispersing featuresin qa and qb directions.aFebFeaFebFeqaqb

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 crystals19Extremely small EF ~ DBCS-BEC crossover regime?

QPI Bandstructure (note: over small 1-domain window!)

Electron-likeHole-likealong qa along qb FT-dI/dV/(I/V)Orthogonal electron- and hole-like dispersionsB = 12 TB = 12 Timp.imp.+D-D+D-DEFEFOrbital 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?Lifting the orbital degeneracy

Band calc. (by Dr. H. Ikeda)Orbital characterOrthorhombic distortion onlyEyz-Exz= 0.05 eVEyz-Exz= 0.1 eVOrthorhombic distortion alone cannot explain the unidrectional dispersions.Orthorhomicity isnot a player but a spectator.Orbital order?More detailed calculations are indispensablePenetration depth and thermal conductivity resultsIntroduction: FeSexCan-Li Song, et al., Science 332. 1410 (2010). Nodal superconductivityMBE-STM

Defect-free stoichiometric films

Nodeless multiple gapsSpecific heatThermal ConductivityJ.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

Magnetic field penetration depth

Quasi T-linear at T/Tc < 0.2T*imp ~ 2 KFinite qusiparticle excitation at low temperatures

No Curie term (No excess irons)cf) clean YBCOLarge temperature dependencePresence of line nodesDl ~T1.4Thermal conductivity in a stoichiometric FeSe single crystalWiedemann-Franz lawkn/T=L0/r0 ~ 1.43 (W/K2m)~ 30-40% of the normal state value

kn/T

r0 ~ 1.70 mWcmk0n/T ~ 1.06 (W/K2m)r0 ~ 2.30 mWcmStrong evidence for the line nodesIncrease of the quasiparticle life time below TcLarge residual value

Tck0/T=L0/r0L0: Lorentz numberk0/T~ 0.4 (W/K2m)Discussion: Origin of the different behavior

DGfNodes can be removed

DfAccidental nodes00Quasi T-linear l(T)Finite residual k0/TNegligibly small k0/T at 0 T Present study (Clean single crystals)Earlier study (Dirty crystals)Nodeless(Anisotropic s-wave)

Nodal SuperconductivityGap anisotropy is smeared by strong scatteringJ.K. Dong, et al., PRB (2009).Nodal s-wave state in FeSeDiscussion: Origin of the different behaviorV. Mishra et al.,PRB, 80, 224525 (2009).

G

DfAccidental nodes0

~ 0.3-0.4

x: coherence length ~ 5 nml: mean free path ~ 200 nmSlope parameter of gap at nodes1/m ~ 6 - 8node

Magnitude of the residual term2-band modelNodes are nearly vanishingPresent results

DfNodes can be removed0Gap anisotropy is smeared by strong scattering

0fDNodal s-wave state in FeSeInconsistent with d-wave 28\simeq \frac{2}{\mu}\frac{\xi}{l}\frac{\kappa_n}{T}\frac{\kappa_00}{T}\frac{1}{\mu}=\frac{1}{\Delta_0}\frac{d|\Delta(\phi)|}{d\phi}Anomalous field dependence of thermal conductivityLong QP mean free path lQP

m0FeSeStrong reduction of k/T at low fieldsPlateau at high fieldskel/T ~ N(EF)vFl

N(E)~ H1/2Doppler shiftDifferent from ordinal behaviorsAnomalous field dependence of thermal conductivity

CeCoIn5Y. Kasahara et al.,PRB, 72, 214515 (2005).Long QP mean free path lQP

N(E)~ H1/2l ~ H-1/2Long m.f.p. & vortex scattering

m0FeSeStrong reduction of k/T at low fieldsPlateau at high fieldskel/T ~ N(EF)vFlDoppler shiftCancelation Plateau Vortex scattering due to long mean free path(av ~ H-1/2)Anomalous field dependence of thermal conductivityl =vFt ~ 200 nmDr/r0 = (wchth )(wcete) ~(wct )2Dr/r0 ~ (wct )2

l =vFt ~ 0.2 mmMagnetoresistance

m0FeSeStrong reduction of k/T at low fieldsPlateau at high fieldskel/T ~ N(EF)vFl

FeSeLong mean free pathHard to explain a sharp kink at low fieldsand a plateau in a nearly whole vortex state Vortex scattering due to long mean free pathAnomalous field dependence of thermal conductivity

m0FeSeStrong reduction of k/T at low fieldsPlateau at high fields Possible phase transition in the SC state

K. Krishana, et al.,Science (1997).BSCCOField induced change of gap symmetry

dx2-y2 dx2-y2 + idxy or dx2-y2 + isFeSes s + id (???)Anomalous field dependence of thermal conductivity

m0FeSeStrong reduction of k/T at low fieldsPlateau at high fields 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

High-field anomaly in thermal conductivityH*Proposed new high-fied phase

Summary FeSe Tc 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)