Orbital-selective Mott transitions and their relevance to Iron superconductors

Transcription

1 Luca de Medici Laboratoire de Physique des Solides Orsay, France Orbital-selective Mott transitions and their relevance to Iron superconductors Collège de France, 6.5.

2 Mott transition Localization of itinerant electrons by correlations Luca de Medici - LPS Orsay The proximity to a Mott insulator strongly affects the properties of a system: - strong spectral weight transfer - formation of local moments - large mass enhancement/low coherence temperature The Mott insulating state has an extensive entropy: instable to ordered phases at low T Cuprates have been modeled in terms of proximity to a Mott insulating state Limelette et al. Science 3, 89 (3)

3 Correlations in Iron superconductors Luca de Medici - LPS Orsay Iron superconductors show in general no Mott insulating state m /m band Yin et al., Nat Mat, 93 () xy xy/yz EXP optics EXP (AR)PES z x y Moderate to strong mass enhancements Correlated physics DFT + Dynamical mean-field theory 3 FeTe CsFe Se Te/Se FeP KFe Se FeSe LiFeAs NaFeAs KFe As BaFe Se Compounds LaFeAsO CaFeAsF SrFeAsF SrFe As CaFe As LaFePO DENSITY OF STATES a b c W U = U / W =.5 U / W =. d U U / W =.5 E F U E F ENERGY E F + U

4 Hund s rules: atoms Luca de Medici - LPS Orsay Aufbau Hund s Rules In open shells:. Maximize total spin S. Maximize total angular momentum T (3. Dependence on J=T+S, Spin-orbit effects)

5 The two faces of Hund s coupling in metals Luca de Medici - LPS Orsay Multi band Hubbard model J is Janus-faced (has two contrasting effects): lowering of coherence Temp (away from single-filling) enhancement of the Mott gap (away from half-filling) Janus Bifrons In ancient Roman religion and mythology, Janus is the god of beginnings and transitions, then also of gates, doors, doorways, endings and time. Most often he is depicted as having two heads [ ] DENSITY OF.5 c U / W =. d U U / W =.5 LdM, J. Mravlje, A. Georges, PRL 7, 564 () Strong correlations far from a Mott insulator!! E F U E F ENERGY E F + U

6 DFT+ cheap mean fields N. Lanatà, H. Strand, G. Giovannetti, LdM and M. Capone (unpublished) Luca de Medici - LPS Orsay R. Yu and Q. Si, ArXiv:.65 LaFeAsO, J/U=.5 FeSe, J/U=.4 LDA+Slave Spins Slave-spins: LdM, A. Georges and S. Biermann, PRB 7, 54 (5) S. R. Hassan and LdM, PRB 8, 356 () LDA+Gutzwiller Orbital selective physics

7 Orbital-selective Mott transition (OSMT) Luca de Medici - LPS Orsay Coexisting itinerant and localized conduction electrons Metallic resistivity and free-moment magnetic response non Fermi-liquid physics of the intinerant electrons Possibly relevant for: Ca -x Sr x RuO 4, BaVS 3, LiV O 4, α-fe, Fe-Superconductors, Anisimov et al., Eur. Phys. J. B 5, 9 () Koga et al., Phys. Rev. Lett. 9, 64 (4) For a review: M. Vojta J. Low Temp. Phys. 6, 3 () Two-orbital Hubbard model with different bandwidths J favors the OSMT LdM, A. Georges and S. Biermann, PRB 7, 54 (5)

8 OSMT in systems with the same bandwidth Luca de Medici - LPS Orsay 3 bands of the same width Crystal-field (one band up) + Hund s coupling OSMT region widens with J LdM, S.R. Hassan, M. Capone, X. Dai, PRL, 64 (9)

9 OSMT in systems with the same bandwidth Luca de Medici - LPS Orsay 3 bands of the same width Crystal-field (one band up) + Hund s coupling OSMT region widens with J 6 electrons in 5 bands Is it the remaining degeneracy, which plays the role of a larger bandwidth? LdM, S.R. Hassan, M. Capone, X. Dai, PRL, 64 (9) LdM, S.R. Hassan, M. Capone, JSC, 535 (9)

10 OSMT in a 3-band model with equal bandwidths and a symmetric crystal field splitting Δ Crucial: Hund s coupling suppresses the orbital fluctuations, rendering the orbitals independent from one-another Hund s coupling acts as a band-decoupler U LdM, S.R. Hassan, M. Capone, X. Dai, PRL, 64 (9) LdM, Phys. Rev. B 83, 5 () Werner and Millis, Phys. Rev. Lett.99, 645 (7) Δ Δ

11 Non Fermi-liquid properties of the OSMP Metallic phase OSMP U Δ Δ

12 Back to realistic calculations (ab-initio +MF) Luca de Medici - LPS Orsay FeSe, J/U=.4 LaFeAsO, J/U=.5 U(eV) R. Yu and Q. Si, ArXiv:.65 Proximity to an OSMT N. Lanatà, H. Strand, G. Giovannetti, LdM and M. Capone (unpublished)

13 Back to realistic calculations (ab-initio +MF) Luca de Medici - LPS Orsay FeSe, J/U=.4 LaFeAsO, J/U=.5 U(eV) R. Yu and Q. Si, ArXiv:.65 Proximity to an OSMT N. Lanatà, H. Strand, G. Giovannetti, LdM and M. Capone (unpublished)

14 Orbital selective coherence temperature Luca de Medici - LPS Orsay T= T/W=/ A(ε,ω=) U=.45, J=U/, D /D =.5; Ns=8 T=/4 T=/5 T=/7 T=/8 T=/ T=/ T= Total A(k,ω) (ARPES) Orbital (wide band) A (ε,ω=) ε U=.45, J=U/, D /D =.5; Ns=8 T=/4 T=/5 T=/7 T=/8 T=/ T=/ T= ε 4 T U=.45, J=U/, D /D =.5; Ns=8 Orbital (narrow band) E. Winograd and LdM (unpublished) A (ε,ω=) 3 T T=/4 T=/5 T=/7 T=/8 T=/ T=/ T= ε

15 Orbital selective coherence temperature Luca de Medici - LPS Orsay T= T/W=/ Total A(k,ω) (ARPES) Orbital (wide band) τ A (ε,ω=) U=.45, J=U/, D /D =.5; Ns=8 T T=/4 T=/5 T=/7 T=/8 T=/ T=/ T= ε T Orb. Orb. Orbital (narrow band) E. Winograd and LdM (unpublished)

16 OSMT + hybridization = pseudogap orbital filling orb, V= V/D=. orb, V= V/D=. total, V=. V/D= µ large U (OSMP) E. Winograd and LdM (unpublished)

17 OSMT + hybridization = pseudogap orbital filling orb, V= V/D=. orb, V= V/D=. total, V=. V/D= µ large U (OSMP) E. Winograd and LdM (unpublished)

18 Angle-resolved Photoemission Data (Shen s group Stanford) A x Fe -y Se (A=K,Rb) M. Yi et al. (unpublished )

19 Angle-resolved Photoemission Data (Shen s group Stanford) A x Fe -y Se (A=K,Rb) d xy spectral weight diminishes with temperature. d xz /d yz spectral weight does not diminish in the same temperature window. temperature-induced Orbital-Selective Mott Transition M. Yi et al. (unpublished )

20 Other experimental evidences EPR-NMR, Arçon et al., Phys. Rev. B 8, 458 () 3 and itinerant states. n Kex should be negative in sign, as it is indeed observed. It is intriguing that the strong n temperature dependence.4.58 of K can be simulated with n the expression K ( (T /T )) log (T /T ), which has been applied to a number of Kondo lattice materials. Here T is the correlated Kondo temperature and is a measure of the intersite localized state interactions. Excellent agreement with the experimental data for both nuclei (Fig. b) is obtained with the same T 8 K, FIG. 3. (Color online) Contour intensity maps showing the which falls within the 5-8 mev range of the crossover fitted magnetic scattering intensity versus h ω and Q at different energy between quasiparticle states and excitations with temperatures: (a) 4 K, (b) 5 K, (c) K, and (d) 3 K. local character.3 FeSe Te Knight shift scales with local (EPR) and not bulk susceptibility FIG K and 77 K Knight shifts versus (a) bulk susceptibility, χb c and (b) χep R with temperature as an implicit parameter. Neutrons, Xu et al, Phys. 5 from Q outward, as shown in work Fig. 3(c). The saddle point The most important experimental finding of this B 84, 556 () mevrev. actually and the dispersion becomes is that in FeSe Te at 5intrinsic statesdisappears, with localized.4.58 clearly and incommensurate anditinerant almost vertical. There is little character may form, coexist couple with change between and 3 K. states. The coupling between the two electronic compo.35 integrated we plot.65 the intensities, nents governs the normalinasfigs. well4(a) as and the 4(b), superconductalong Q = ( K,K,), of the magnetic scattering and the ing properties. It is suggested that in such strongly spurious peak. The effect of the resonance in the superconductcorrelated systems this coupling plays a vital role in ing phase is observable up to h ω mev. The plot of the suppressing magnetism and promoting high-temperature spurious-peak intensity shows signs of temperature activation, 3 superconductivity. Therefore, in order testinthe and is peaked near 5tomeV; anysupcase, its scale is generally pression of spin fluctuations we turn to the spin-lattice small compared to the magnetic signal. relaxation time, n T data. Fig. 4aresponse shows inthe The magnetic thefrenormal state shows little 77 quency dependence of temperature /77 T T for Se NMR spectra dependence and the main spectral weight is at selected temperatures. It is evident that /77 T T substantially varies over the 77 Se NMR line and the ratio between largest and shortest /77 T T measured for the low- and high-frequency spectral shoulders can be as large as 4 (at 5 K). Therefore, a simple two relaxation-times model earlier applied7,8 to FeSe.9 and Fe.4 Se.33 Te.67 oversimplifies the experimental situation and may even lead to erroneous conclusions. All /77 T T values fall on nearly the same universal Knight shift-dependent curve described by the Korringa relation, γe! 77 T T 77 KS = 4πk β. Here γe and γse are the electron B γ Magnetoresistance, Yuan H-Q et al. ArXiv:.5476 or FeSe.9.8 Interestingly, the ratio, δ 5 ν/ /δ 77 ν/ 3. is significantly larger than that of the corresponding gyromagnetic ratios, 5 γ/77 γ =.65, which is consistent with differences in the p d hybridization between FeTe and FeSe. The room temperature NMR spectra are strongly shifted to higher frequencies with respect to the reference. The Knight shifts are 5 K =.38()% and 77 K =.69()% for 5 Te and 77 Se nuclei, respectively. The resonances shift considerably to lower frequencies with decreasing temperature (Fig. c): 5 K =.54% and 77 K =.36% between 3 and K. A similar decrease of 77 K has been reported for Fe. Se and Fe.4 Se.33 Te However, the Knight shifts, n K (n = 77, 5) do not scale with the bulk spin susceptibility over the entire temperature range (Fig. 3a). NMR data thus provide direct evidence that the local and bulk spin susceptibilities are different in the investigated sample. On the other hand, comparing n K with always located at higher in the superconducting s (below the gap) does ap when the resonance n almost unchanged with f is consistent with the sy at low temperature, and from the elastic channe upon heating. The lack magnetic excitation spec 5 and 3 K, suggests a magnetic response. We from a near hour-glass sh 5 K) to a waterfall sh and 3 K). This change to the behavior reported occurs at temperatures w origin is not entirely und Our key result is obtai over Q and h ω. The me intensity is proportional tion S(Q,ω) =!χ ## (Q,ω)! sum rule that BZ dq where v is the volume the normalized spectral obtain a lower bound o the Q integration, we longitudinal direction is that the response is unif previous measurements. the interval mev! h extrapolation indicated From this integral, we o.7(3)µb per Fe. The tem is negligible, as shown in little temperature depend is also evidenced in th magnetism is dominated The moment we hav of the total moment p measurements have show way up to a few hundre low-energy magnetic resp larger than what is expe For example, taking the d of.5 states/ev from FeSe, the corresponding from electrons near the F more than of order. range of mev. Even in Magnetic transition insensitive to large magnetic fields: magnetism of local origin. Also: two-component Hall resistance analysis FeSe Te Integrated magnetic spectral weigth up to mev shows little change with T Se and nuclear gyromagnetic ratios and 77 KS is obtained

21 OSMT dependence on doping and U quasiparticle weight x -y xz and yz z -r xy FeSe (hole doping) total filling (electron doping) quasiparticle weight LdM, G. Giovannetti and M. Capone (unpublished) e g U=4. (FeSe) U=3.3 () U=3. () t g U=4. (FeSe) U=3.3 () U=3. () (hole doping) total filling (electron doping) <U> (ev) FeSe Mott NFL FL FeAsLaO Gap size (mev) seem 5 to be located on opposite sides of the Fermi-l 6 to non-fermi-liquid spin freezing transition. Tc 4 inner 5 A. L. likes to thank M. Aichhorn, middle R. Arita, E. Gu outer 4 Haule, 3 A. Millis and Ph. Werner, for fruitful discuss 3 The calculations were carried out on the Jülich Ju computer. This research was supported in part by National Science Foundation under Grant PHY5-5 Tc (K) n Liebsch and Ishida PRB 8,556 () ARPES [] BaK-: Y. Kamihara, Malaeb et T. al. Watanabe, ArXiv:4.36 M. Hirano, and H. Ho FIG. 5: (Color online) Schematic phase diagram for FeSe and J. Am. Chem. Soc. 3, 396(8). LaFeAsO. Solid curve: spin freezing transition indicating the [] F. C. Hsu et al., Proc.Natl.Acd.Sci.USA5,...4 x.6.8.

22 OSMT dependence on doping and U quasiparticle weight <U> (ev) x -y xz and yz z -r xy FeSe.9 e g U=4. (FeSe) U=3.3 () TRANSPORT PROPERTIES AND ASYMMETRIC....8 U=3. () PHYSICAL REVIEW B 84,845() It is known that the parent phase has identical areas of electron and hole Fermi pockets in the nonmagnetic phase, 5.6 therefore 5.8 we can 6 assume identical 6. charge carrier 6.4 densities (hole doping) n e and n h total for filling the two bands (electron (n e n h doping) n ). Considering m h >m e,asrevealedbyarpes 5 and specific heat data, 6 and assuming that τ e > τ h,theconductivityisthusdominated by the electron band. With electron doping, the term n e τ e m h is getting much larger than n h τ h m e,whichreducestheresistivity further. At the optimal doping at about x =.8, n e has increased a lot, perhaps doubled. This reduces the resistivity to almost its half value. In the case of K-, the situation is different. If wefese still adopt the relation of n e τ e m h n h τ h m e, doping holes will decrease n e but increase n h,inthiscase, the resistivity should increase instead of decrease. Actually, Mott NFL FL hole doping will decrease n e and increase n h, but more important it will lower down the m FeAsLaO h and /τ h.inthiscase,the resistivity is determined by a balance between the quantities of n e τ e m h and n h τ h m e,andshowsaweakdopingdependence.a quantitative understanding would require a detailed doping dependence of n i, τ i, and m i (i = e, h). This is beyond what we can get from a simple resistivity measurement and analysis. Some calculations indicate that the conductivity for electrons grows strongly upon electron doping, while the hole 5 conductivity6 varies weakly compared7to that of the electrons. 7 Thus the resistivity n of hole-doped Ba x K x Fe As at 3 K changes less than that for electron-doped Ba(Fe x Co x ) As. The multiband effect in which one band is strongly coupled and relatively clean (electron band), while the other band is weakly coupled and characterized by much stronger impurity scattering (hole band) will cause anomalous T dependence of quasiparticle weight According to the simple two-band model, the conductivity can be written as σ = i σ i,whereσ i = n i e τ i /m i is the conductivity, n i is the charge carrier density, τ i is the relaxation time, and m i is the mass of the ith band (i = e or h for the electron and hole bands, respectively). Therefore the resistivity can be described as m e m h ρ = e (n e τ e m h + n h τ h m e ). () LdM, G. Giovannetti and M. Capone (unpublished) Gap size (mev) Tc 4 inner 5 A. L. likes to thank M. Aichhorn, middle R. Arita, E. Gu outer 4 Haule, 3 A. Millis and Ph. Werner, for fruitful discuss 3 computer. This research was supported in part by. t g U=4. (FeSe) U=3.3 () U=3. () (hole doping) total filling (electron doping) seem 5 to be located on opposite sides of the Fermi-l 6 to non-fermi-liquid spin freezing transition. The calculations were carried out on the Jülich Ju National Science Foundation under Grant PHY5-5 Liebsch and Ishida PRB 8,556 () Resistivity ARPES BaK-: [] BaK-: Y. Kamihara, Bing Malaeb Shen et et T. al. al. Watanabe, PRB ArXiv: , 845 M. Hirano, () and H. Ho FIG. 5: (Color online) Schematic phase diagram for FeSe and FIG.. J. (Color Am. online) Chem. (a) Temperature Soc. dependence 3, of 396(8). the inplane LaFeAsO. Solid curve: spin freezing transition indicating the [] resistivity F. normalized C. Hsuby its etvalue al., at 3 Proc.Natl.Acd.Sci.USA5, K of Ba x K x Fe As...4 x.6.8. Tc (K)

23 Decoupled band picture quasiparticle weight orbital filling x -y xz and yz z -r xy (hole doping) total filling (electron doping) x -y xz and yz z -r xy quasiparticle weight orbital degenerate Hubbard model filling per band U/D=. U/D=.5 U/D=. U/D=3. U/D=4. U/D= (hole doping) total filling (electron doping)

24 Analogies 4 Temperature (K) strange metal AF Fermi-liquid Mott SC doping filling per band

25 Analogies 4 Temperature (K) strange metal AF Fermi-liquid Mott SC doping filling per band

26 Analogies 4 Temperature (K) strange metal AF Bi- Fermi-liquid Mott SC doping filling per band

27 Analogies Z K quasiparticle weight tum differentiation regime) the two sectors have different temperature dependence at low temperature, with the Z K! " (K,) n n n (",), #t = 7.5 ("/,"/), #t = 7.5 (",), #t =.8 ("/,"/), #t = (",), #t =, a.c. ("/,"/),.6 #t =, a.c n.6.8 n n FIG. : Estimators of quasiparticle weight/velocity renormalization factor Z (upper panel) and scattering rate Σ (K, ) obtained from extrapolation of Matsubara axis self n K (n) energies for the K =(π, ) and K =(π/, π/) sectors of 8- site cluster at temperatures T = t/7.5 andt/, along with n estimates obtained by maximum entropy analytical continuation x -y (a. c.). Vertical dashed lines denote.8 the x -y boundaries separating xz and yz the regime consistent with Fermi xz and liquid yz theory (βγz K -r < π) fromtheregimethatisclearlynotfermiliquid. z -r xy.75 xy Mott total doping per orbital per spin orbital filling Mott total doping per orbital per spin sistance experiments. For highly overdoped cuprates these experiments reveal a scattering rate which is reasonably isotropic around the Fermi surface and exhibits a relatively conventional temperature dependence. Below a critical doping a momentum space differentiation appears, with the antinodal scattering rate being larger and exhibiting a weaker temperature dependence. V. SECTOR SELECTIVE REGIME In this section we discuss in more detail the sector selective 8 - Siteregime, which has been characterized in Sec. III by the existence of a plateau in the n K (µ) curveforthesectors containing (, π) (and symmetry-related points) and the absence of such a plateau in the sectors containing (±π/, ±π/). We first observe that, as seen for example in Fig. 9, the approach to the sector selective phase in clusters 4, 8 and 6 is marked by a rapid increase of the absolute value of Σ ( (, π), ) and Σ ( (π/, π/), ), with Σ ( (, π), ) being much larger. In the (, π) sector the increase is associated with the formation of a pole in the sector self energy. This pole is responsible for the sector selective insulating behavior, as discussed in detail in Refs. 38, 39, and 4. However we also see that as doping is decreased the (π/, π/) sector self energy 4 increases, and in fact becomes large enough that (at least at the temperatures accessible to us in this study) this sector is clearly in a non-fermi liquid regime (although as seen it is compressible). It is an interesting, but so far Temperature (K) strange metal Mott SC doping per band Ba- Fermi-liquid

28 Conclusions: Luca de Medici - LPS Orsay Hund s coupling crucial influence makes Iron Superconductors: Correlated, but away from the n=6 Mott insulating state (Janus effect) Acting as a band-decoupler through the suppression of orbital fluctuations favors orbital selectivity: Fe-SC are in proximity of an Orbital-Selective Mott Phase OSMT scenario as a proximity to the n=5 Mott insulator? FeSC are like cuprates? Experimental support for OSMT physics in Fe-SC EPR-NMR: Arçon et al., Phys. Rev. B 8, 458 () Neutrons: Xu et al, Phys. Rev. B 84, 556 (), Magnetoresistance: Yuan H-Q et al. ArXiv:.5476 ARPES BaK-: Malaeb et al. ArXiv:4.36 ARPES A x Fe -y Se : Ming Yi et al (unpublished, ) Scenarios for magnetism and superconductivity in Fe-SC based on OSMT A. Hackl and M. Vojta, New J. Phys., 5564 (9), Kou et al. Europhys. Lett (9), You Y-Z et al., Phys. Rev. Lett.7, 67 () LdM, S.R. Hassan, M. Capone, X. Dai, PRL, 64 (9) LdM, S.R. Hassan, M. Capone, JSC, 535 (9) LdM, PRB 83, 5 ()