Physics of iron-based high-t c superconductors

Transcription

1 Physics of iron-based high-t c superconductors Y. Matsuda Department of Physics Kyoto University, Kyoto, Japan

2 Physics of iron-based high-t c superconductors 1) Why are Fe-based superconductors important? 2) Mechanism of superconductivity Similarities and differences between cuprates and Fe-pnictides 3) Quantum critical point and non-fermi liquid properties 4)BCS-BEC crossover in FeSe

3 Collaborators Kyoto Univ. S.Kasahara T. Watashige T. Yamashita Y. Shimoyama K. Hashimoto (Tohoku U.) Y. Mizukami (U. Tokyo) H. Shishido (Osaka pref. U.) M. Yamashita (U.Tokyo) R. Okazaki (Nagoya U.) T. Shibauchi (U.Tokyo) Riken T. Hanaguri Y. Kohsaka Univ. of Bristol, UK B. J. Arnold A.Serafin I.Guillamón P. M. C. Rourke P. Walmsley C.Putzke A. Carrington Ames, USA M.Tanatar R.Prozorov Univ. of Illinois, USA Karlsruhe Institute of Technology, Germany T. Wolf C. Meingast H. von Löhneysen Univ. of Oxford, UK M.D. Watson A.I. Coldea N. Salovich National Institute for Matals R. W. Giannetta T. Tearshima Univ. of Wisconsin-Madison S. Uji USA A. Levchenko

4 1) Why are Fe-based superconductors important? 2) Mechanism of superconductivity Similarities and differences between cuprates and Fe-pnictides 3) Quantum critical point and non-fermi liquid properties 4)BCS-BEC crossover in FeSe

5 Superconductivity in Fe-Pnictides Discovery H. Hosono Hosono s group was not looking for superconductor, but trying to create new kind of transparent semiconductors for flat-panel display. LaFePO LaFeP(O,F) LaFeAs(O,F) SmFeAs(O,F) FeSe T c =4 K T c =7 K T c =26 K T c =56 K T c =65 K (110 K??) Only two months!

6 Are iron-pnictides an Electron-Phonon Superconductor? Electron-phonon coupling is not sufficient to explain superconductivity in the whole family of Fe-As based superconductors iron + e Cooper pair electron ー electron e Attractive electron-phonon interactions ー e Debye frequency Electron-phonon coupling Comparable to the conventional metals

7 A new class of high temperature superconductors T c (K) 200 cuprates H 2 S (200 GPa) 150 Fe-pnictides BCS SCs HgBa 2 Ca 2 Cu 3 O y (Under pressure) HgBa 2 Ca 2 Cu 3 O y Tl 2 Ba 2 Ca 2 Cu 3 O y 100 Bi 2 Sr 2 Ca 2 Cu 3 O y FeSe (one monolayer??) YBa 2 Cu 3 O 7 liquid N 2 FeSe (one monolayer) (La,Sr) (La,Ba) 2 CuO Hg Pb Nb NbN Nb 3 Sn Nb 2 CuO 4 3 Ge 4 V 3 Si MgB SmO 0.9 F 0.1 FeAs LaO 0.89 F 0.11 FeAs (Under pressure) LaO 0.89 F 0.11 FeAs LaOFeP 2020 Year They knocked the cuprates off their pedestal as a unique class of high temperature superconductors.

8 A new family of unconventional superconductors Iron pnictide (Fe) Cuprate (Cu) Heavy fermion compound (Ce, U) Ce La In Co Weakly localized 3d-electrons Weak correlation Strongly localized 3d-electrons Very strongly localized 4f, 5f electrons Strong correlation

9 Fe-based high-t c superconductors (32522) 2D square lattice of Fe Ca Al O La Ba Li (A 4 M 2 O 6 ) Fe 2 As 2 Ln FeAsO BaFe 2 As 2 LiFeAs FeSe T c (max)=47k T c (max)=55k T c (max)=38k T c = 18 K T c = 8 K Zhu et al.(2009) Ogino et al. (2009) Y. Kamihara et al.(2008) M. Rotter et al.(2008) X.C.Wang et al.(2008) F.C.Hsu et al.(2008)

10 1) Why are Fe-based superconductors important? 2) Mechanism of superconductivity Similarities and differences between cuprates and Fe-pnictides 3) Quantum critical point and non-fermi liquid properties 4)BCS-BEC crossover in FeSe

11 Similarities and differences between cuprates and pnictides Cuprates Phase diagram Fe-pnictides O Cu Superconductivity in 2D planes Cu O Fe As, P. Se Enhanced fluctuations suppression of magnetic order

12 Similarities and differences between cuprates and pnictides Cuprates Phase diagram Fe-pnictides O Cu CDW Superconductivity occurs in the vicinity of magnetic order In Fe-pnictides, structural (Ts) and AFM transition (TN) lines follow closely each other

13 Similarities and differences between cuprates and pnictides Cuprates Fe-pnictides O Cu Parent compound Cu3d O2p Cu3d U W U : Coulomb ~ 8eV W : Band width ~ 3eV Strong electron-electron correlation Mott insulator b a S=1/2 Cu Stripe SDW order U~W~2-3 ev Intermediate correlation Spin density wave (SDW) metal

14 Similarities and differences between cuprates and pnictides Cuprates Fe-pnictides O Cu One hole band One orbital x 2 -y 2 Well separated hole and electron bands xz+yz Mainly three orbitals xy 3z 2 -r 2 hole electron Tl 2 Ba 2 CuO 6+d BaFe2 As 2 N. E. Hussey et al., Nature (2003).

15 Coulomb Magnetic fluctuation s-wave Why is d-wave pairing realized d-wave superconductivity in cuprates k y d-wave k y k+q -k Exchange of boson (spin fluctuations) between two fermions (electrons) k x k Q=(p,p) k x -k-q AF Brillouin zone V(q) V(q): pairing interaction phonon V(q) AFM spin fluctuations 0 q 0 Q=(p,p) q V(q) is negative and constant ( attractive ) V(q) is positive and peaks at q=q ( repulsive )

16 s-wave Why is d-wave pairing realized d-wave superconductivity in cuprates k y + d-wave k y Node + + k x + Q=(p,p) + k x + AF Brillouin zone Gap equation Coulomb Magnetic fluctuation >0 D(k+Q)D(k) < 0 sign change

17 s-wave Why is d-wave pairing realized d-wave superconductivity in cuprates k y + d-wave k y Node + + k x + Q=(p,p) + k x + AF Brillouin zone D(k+Q)D(k) < 0 sign change y repulsive attractive x Real space

18 Iron pnictides: candidate for the SC state Pairing due to purely repulsive electronic interaction (enhanced by spin fluctuations) V 0 cf. d-wave cuprate k y + Q=(p,p) + k x G Q=(p,0) I. I. Mazin et al., PRL 101, (2008). K. Kuroki et al., PRL 101, (2008). & PRB 79, (2009). A. V. Chubkov et al., PRB 80, (R) (2009). S. Graser et al., NJP 11, (2009). H. Ikeda, PRB 81, (2010). K. Seo et al., PRL 101, (2008). F. Wang et al., PRL 102, (2009). Spin fluctuations between the same orbitals

19 Iron pnictides: candidate for the SC state Pairing due to attractive interaction caused by charge/orbital fluctuations. V 0 Orbital fluctuations (Quadrupole fluctuation) Charge fluctuations between different orbitals + X e - + G hole xz xy electron Charge up Charge down Occupation number of each orbit at each Fe site fluctuates + H. Kontani & S. Onari, PRL 104, (2010). F. Kruger et al., PRB 79, (2009). Y. Yanagi et al., PRB 81, (2010).

20 Iron pnictides: candidate for the SC state Structural (Ts) and AFM transition (TN) lines follow closely each other AF Magnetic order Ferro-orbital ordering Chicken or the egg? Who is the driver? Spin fluctuation or orbital fluctuation?

21 S+- or S++? 1. Phase sensitive test 2. NMR 3. Neutron scattering 4. Quasi-particle interference 5. Impurity effect?? No conclusive experimental evidence so far

22 1) Why are Fe-based superconductors important? 2) Mechanism of superconductivity Similarities and differences between cuprates and Fe-pnictides 3) Quantum critical point and non-fermi liquid properties 4)BCS-BEC crossover in FeSe

23 Quantum Critical Point (QCP) Non-Fermi liquid properties Quantum critical regime Quantum time scale Thermal time scale フェルミ液体 QP excitations are well defined (Quantum critical point) g: pressure, chemical substitution, magnetic field S. Sachdev, Quantum Phase Transitions Physical properties are seriously influenced by QCP at g=g c. Ordinary phase transition driven by thermal fluctuations Quantum phase transition driven by zero temperature quantum fluctuations associated with Heisenberg s Uncertainty Principle

24 Quantum Critical Point (QCP) Non-Fermi liquid properties Quantum critical regime Fe-pnictide Heavy Fermion SC フェルミ液体 (Quantum critical point) g: pressure, chemical substitution, magnetic field S. Sachdev, Quantum Phase Transitions Does the QCP lie beneath the SC dome? Cuprate 1. Mechanism of superconductivity 2. non-fermi liquid properties CDW

25 Parent compound BaFe 2 As 2 (AF Metal) Superconductivity in BaFe 2 As 2 systems K x Fe 2-y Se 2 (T c opt ~ 31 K) Ba(Fe 1-x Co x ) 2 As 2 (T opt c ~ 24 K) electron-doping (Ba 1-x K x )Fe 2 As 2 (T opt c ~ 38 K) T c hole-doping SC x [Co] SC SC x [K]

26 Parent compound BaFe 2 As 2 (AF Metal) Superconductivity in BaFe 2 As 2 systems K x Fe 2-y Se 2 (T c opt ~ 31 K) Ba(Fe 1-x Co x ) 2 As 2 (T opt c ~ 24 K) electron-doping (Ba 1-x K x )Fe 2 As 2 (T opt c ~ 38 K) T c hole-doping SC x [Co] SC SC SC x [K] x=0.6 x [P] Ground state can be tuned without doping carriers BaFe 2 (As1-xPx) 2 isovalent (Tc opt ~ 30 K) substitution S. Jiang et al. JPCM (09)

27 Doping evolution of the transport property BaFe 2 (As 1-x P x ) 2 r xx (T) T a a Quantum critical region?? BaFe 2 (As 1-x P x ) 2 FL QCP? S. Kasahara et al., PRB 81, (10) See also S. Sachdev and B. Keimer, Physics Today (11) T-linear resistivity at x=0.33 just beyond SDW end point (x c =0.3 ) Hallmark of non-fermi liquid T 2 -dependence at x=0.71 Fermi-liquid behavior

28 T (K) 200 Doping evolution of normal electrons r xx (T) T a a n Quantum oscillations (dhva) FL DC SDW T s T N nfl dhva FL m*/m b H. Shishido, Y.M. et al. PRL(12) Specific heat SC x 0.4 T c QCP Effective mass m* is strongly enhanced at x=0.3 P. Walmsley, Y.M. et al. PRL(13) T. Shibauchi, A. Carrington and Y. M., Annu. Rev. Condens. Matter Phys. 5, 113 (14)

29 Doping evolution of the superfluid density in BaFe 2 (As 1-x P x ) 2 QCP at x=0.3 2 L (0) m0n s e * m 2 Al coating Nodal slope Magnetic force microscopy Y. Kamhot et al. Microwave cavity K. Hashimoto, Y.M. et al. Science ( 12) Striking enhancement of L2 (0) on approaching x=0.3 from either side. The data represents the behavior at the zero temperature limit.

30 Temperature QCP lies QCP beneath x=0.3 the dome BaFe 2 (As 1-x P x ) 2 Magnetic order Quantum critical region SC2 SC SC1 QCP Fermi liquid Control parameter SDW T N T S SC2 SC 1 QCP Tetracritical point 2 nd order transition 1. The QCP is the origin of the non-fermi liquid behavior above T c. 2. Microscopic coexistence of superconductivity and SDW. 3. The quantum critical fluctuations help to enhance the high-t c superconductivity. K. Hashimoto, Y.M. et al. Science 336, 1554 (12). K. Okazaki, Y.M. et al. Science 337, 1314 (13). S. Kasahara, Y.M. et al. Nature 486, 382 (12) Review: T. Shibauchi, A. Carrington and Y. M., Annu. Rev. Condens. Matter Phys. 5, 113 (14) T c

31 1) Why are Fe-based superconductors important? 2) Mechanism of superconductivity Similarities and differences between cuprates and Fe-pnictides 3) Quantum critical point and non-fermi liquid properties 4)BCS-BEC crossover in FeSe

32 If you ask a student What do Neutron star metals nuclei atoms have in common? When fermions become bosons: Pairing in ultracold gases Carlos Sa de Melo, Physics Today (2008) Undergraduates They are made of fermions, i.e. neutrons, protons, quarks and electrons. Graduates These fermions may exhibit a collective and macroscopic properties called superfluidity, in which a large number of particles can flow coherently without any friction or dissipation of heat.

33 Superconductivity (Metal) Critical Temperature Neutron stars Nuclear matter Superconductors Helium-3 Cold atoms BEC (Ultracold atom) Fermionic superfluidity Color superconductivity (neutron star) Type of Matter Superfluidity (Helium)

34 BCS-BEC crossover 0.4 Unitary Fermi gas Fermi liquid Bose liquid T/T F 0.2 T c condensation 0-2 BCS cooperative Cooper pairing pair size Conventional superconductors D/e F ~ High-T c cuprates D/e F ~ crossover crossover regime regime attraction 1/k F a strongly interacting pairs pair size 0 1 BEC tightly bound molecules pair size

35 FeSe F.-C. Hsu et al., PNAS 105, (2008). T c =9 K (30 K under pressure)

36 FeSe: High temperature superconductor Only electron pockets ARPES S. Tan et al., Nature Mater. (13). Meissner effect T c up to 65 K Z. Zhang et al., Science Bulletin (15). High-T c superconductivity in monolayer FeSe Q.-Y. Wang, et al., Chin. Phys. Lett. 29, (2012). Resistivity T c >100 K J-F. Ge et al. Nature Mat. (14)

37 FeSe: single crystals grown by chemical vapor transport +95 mv/100 pa T ~ 0.4 K F.-C. Hsu et al., PNAS 105, (2008). b F e b Fe > a Fe a F e 5 nm S. Kasahara, T. Watashige, et al., PNAS (2014). Small residual resistivity, large RRR, huge MR effect Extremely small level of impurities and defects (1/2000 sites)

38 Extremely Fermi surface small Fermi of bulk energy FeSe Quantum oscillations ε ε F h μ ε F e electron band hole band Terashima, Y.M. et al., PRB (2014) b g d 1 hole + 1 electron (+ 1 very small electron, a-branch) FeSe b d Extremely small Fermi surface & Fermi energy M. Watson, Y.M. et al., PRL (2015).

39 Fermi energy comparable to the SC gap along q a FT-dI/dV/(I/V) along q b B = 12 T B = 12 T +D D +D D Electron-like Hole-like S. Kasahara, T. Watashige, et al., PNAS (2014).

40 Extremely small Fermi energy Quasi-particle interference (STM) S.Kasahara, et al., PNAS(2014). 12 T 12 T ARPES e F e D -D e F h D -D (Å -1 ) (Å -1 ) M. D. Watson et al., PRB (2015). A possible BCS-BEC crossover regime e F ~ D Never realized in any other superconductors! cf.) Cold atoms

41 Extremely small Fermi energy Quasi-particle interference (STM) S.Kasahara, et al., PNAS(2014). 12 T 12 T FeSe D ~ 3 mev Ele-pocket: e F ~2-3 mev e F e D -D e F h D -D D/e F ~ 1 Hole-pocket: e F ~10 mev D/e F ~ 0.3 Conventional superconductors D/e F ~ (Å -1 ) (Å -1 ) High-T c cuprates D/e F ~ A possible BCS-BEC crossover regime e F ~ D Never realized in any other superconductors! cf.) Cold atoms

42 Extremely small Fermi energy 5.7 mev 4.2 Topograph Spatially-modulated SC gap T ~ 1.5 K Gap (2D) map 1/2k F 100 nm 100 nm, +20 mv/100 pa T. Hanaguri et al, in preparation SC gap is modulated at q ~ 2k F. Friedel oscillations Observable only in the system with very small k F

43 Extremely small Fermi energy Vortex lattices in FeSe di/dv(e F ) T ~ 1.5 K 500 nm 500 nm, +10 mv/0.1 na 0.1 T 0.25 T 0.5 T 1 T Fe Fe Twin boundary low high T. Watashige, Y.M., et al. Phys. Rev. X (15)

44 Extremely small Fermi energy Vortex-core spectroscopy di/dv T ~ 0.4 K, B = 0.1 T D D 2 e F e F D b Fe Fe a Fe 50 nm 50 nm, +10 mv/100 pa No zero-bias conductance peak at the core center T. Hanaguri et al, in preparation Vortex core is in the quantum limit Large D 2 /e F

45 Very strong coupling superconductivity Superconducting-gap structure of FeSe D 2 D 1 Multi-gap 2D 1 k B T c ~ 9 Very strong coupling 2D 2 k B T c ~ 6.5 BCS-BEC crossover See also C.-L. Song et al., Science (2011).

46 Preformed Cooper pairs and pseudogap above T c 0.4 Unitary Fermi gas Fermi liquid Preformed pairs Pseudogap Bose liquid M.Randeria Annu. Rev. Condens. Matter Phys (14) T/T F 0.2 T c condensation 0-2 BCS cooperative Cooper pairing pair size -1 crossover crossover regime regime attraction FeSe 1/k F a strongly interacting pairs pair size 0 1 BEC tightly bound molecules pair size

47 Preformed Cooper pairs and pseudogap above T c 0.4 Unitary Fermi gas Fermi liquid Preformed pairs Pseudogap Bose liquid M.Randeria Annu. Rev. Condens. Matter Phys (14) T/T F 0.2 T c condensation crossover crossover regime regime attraction FeSe 1/k F a 0 1 Preformed Cooper pairs and pseudogap formation above T c Ultracold atom: preformed pairs and pseudogap remain unclear Fermi liquid behavior even in the unitary Fermi gas Cuprates: pseudogap is observed but is unlikely to be caused by preformed pairs non-fermi liquid behavior in the pseudogap regime

48 Phase diagram of FeSe Pseudogap? Resistivity Nernst Nernst Resistivity Nonlinear diamagnetic response >> Gaussian fluctuations Phase fluctuations S. Kasahara, Y.M. et al. a preprint

49 New high-field phase in the superconducting state k/t (W/K 2 m) B Resistivity Torque Thermal conductivity m 0 H (T) H irr B-phase H* m 0 H (T) Possible preformed pairs A 5 T (K) Preformed Normal pairs K 1.1 K 0.76 K 12 A-phase K T (K) m 0 H (T) 0.39 K 15 S.Kasahara, T. Watashige et al. PNAS (2014)

50 New high-field phase in the superconducting state B Resistivity Torque Thermal conductivity B-phase 16 H irr m 0 H (T) 10 Possible preformed pairs FFLO? Maki parameter m 0 H (T) 14 B-phase H* 0 0 A 5 T (K) Preformed Normal pairs a M >1.5 is required in the BCS limit a M ~ 5 in electron pocket 2.5 in hole pocket 12 A-phase T (K) S.Kasahara, T. Watashige et al. PNAS (2014) 3 B-phase may not be a simple FFLO phase Multiband system FFLO state is not stable in the crossover regime L. Radzihovsky and D.E. Sheehy, Rep. Prog. Phys. ( 10)

51 Summary 1) Why are Fe-based high-t c superconductors exciting? A new family of unconventional superconductors 2) Mechanism of superconductivity Spin fluctuation or orbital fluctuation? 3) What lies beneath the superconducting dome? Quantum critical point 4) FeSe The first superconducting system in which BCS-BEC crossover is realized.