New insights into high-temperature superconductivity

Transcription

1 New insights into high-temperature superconductivity B. Keimer Max-Planck-Institute for Solid State Research introduction to conventional and unconventional superconductivity empirical approach to quantitative understanding of unconventional superconductivity discovery of charge density wave & relationship to superconductivity

2 Max Planck Institute for Solid State Research

3 Collaborators photon scattering M. Minola, H. Gretarsson, M. Le Tacon MPI Stuttgart G. Ghiringhelli, L. Braicovich, G. Dellea, Y. Peng Politecnico Milano N.B. Brookes ESRF T. Schmitt SLS, PSI H. Yavas PETRA-III, DESY neutron scattering T. Loew, J. Porras, J. Bertinshaw, B.J. Kim MPI Stuttgart Y. Sidis, P. Bourges LLB, Saclay D. Abernathy SNS, ORNL A. Ivanov ILL Grenoble J.T. Park FRM-II Munich theory G. Khaliullin MPI Stuttgart J. Chaloupka Masaryk University samples D. Chen, C.T. Lin MPI Stuttgart

4 Cooper pairs in conventional superconductors Leon Cooper 1956 electron deforms lattice positive polarization cloud second electron is attracted by positive cloud, moves faster than nuclei retarded attraction, formation of bosonic Cooper pair

5 Macroscopic wave function bosonic Cooper pairs condense at critical temperature T c T > T c incoherent superposition of electron waves scattering from impurities, defects T < T c coherent superposition of electron waves macroscopic wave function

6 Conventional superconductors understanding based on quasiparticles pairing boson electron electron fermionic spectrum from tunneling tunnel spectrum calculation based on phonon spectrum Savrasov, PRB 1996

7 Neutron scattering neutron E 1 q 1 E 2 q 2 excitation: E= E 2 -E 1 q=q 2 -q 1 interaction strong (nuclear) interaction elastic lattice structure inelastic phonons magnetic (dipole-dipole) interaction elastic magnetic structure inelastic magnons possible pairing bosons

8 Phonon dispersions in Pb Brockhouse, PRL 1962

9 Resonant mode in conventional superconductors T > T c phonons broadened by electron-phonon coupling T < T c feedback of Cooper pairing on pairing boson Pb linewidth ~ 10 µev energy gap neutron scattering with 1 µev resolution nuclear Aynajian et al., Science 2008; N. Munnikes et al. magnetic Bayrakci et al., Science 2006, PRL 2013

10 High temperature superconductivity temperature (K) different mechanism? boiling point of nitrogen LaFeAsO 1-x F x mechanism phonon-mediated Cooper pairing BCS 1956, Eliashberg 1960 s BaFe 2-x (Co,Ni) x As 2 year

11 Cuprates lattice structure YBa 2 Cu 3 O 7 (T c ~ 90 K) electronic structure Cu d-orbitals x 2 -y 2 CuO 2 3z 2 -r 2 CuO 2 yz xz xy dopant O 2- ions arranged in chains minimal disorder hole content in x 2 -y 2 orbital can be modified by chemical substitution

12 Cuprate phase diagram Mott insulator temperature (K) Review in Keimer et al. Nature 2015 AFI SC crystallization of conduction electrons due to Coulomb correlations antiferromagnetic ordering minimizes kinetic energy hole concentration

13 Iron pnictide phase diagram lattice structure LaFeAsO phase diagram T c 55 K T c 39 K lattice structure different from cuprates phase diagrams similar focus on magnetic mechanisms of Cooper pairing Luetkens et al. Nature Mater. 2009

14 Magnetically driven Cooper pairing assumption: short-range antiferromagnetic order need to verify experimentally single electron generates string of broken bonds Cooper pair with spin = 0 does not disrupt magnetic order

15 Magnetically driven Cooper pairing nearest neighbors favorable for singlet Cooper pair formation next-nearest-neighbors unfavorable d-wave symmetry of pair wave function _ + + _ Cooper pair quantum numbers L=2, S=0 optimal binding energy for Cooper pair experimentally verified

16 Magnetically driven Cooper pairing hypothesis Cooper pairing by magnetic excitations electron paramagnon electron key challenges detect paramagnons in high-t c superconductors by inelastic scattering detect feedback mechanims of superconductivity on paramagnon spectrum quantify strength of pairing interaction calculate T c, energy gap,

17 Progress through purity: YBa 2 Cu 3 O 6+x dopant atoms arranged in chains minimal disorder, inhomogeneity quantum oscillations neutron resonance ~ 100 crystal mosaic 4K 65K intrinsic width 0.5 mev Sebastian et al. Rep. Prog. Phys. T. Loew, J. Porras

18 Spin dynamics from neutron scattering antiferromagnetic insulator superconductor E 300 mev E mev temperature (K) (π, π) spin waves q (π, π) q magnetic resonant mode AFI SC hole concentration

19 Magnetic resonant mode Neutron intensity Energy (mev) Energy (mev) Inosov et al., Nature Phys Suchaneck et al., PRL 2010 feedback effect of superconductivity on magnon spectrum similar amplitude, T-dependence in two families of high-t c superconductors

20 Stoner model ), ( ) ( 1 ), ( ), ( 0 0 ω χ ω χ ω χ q q J q q = enhanced by electronic correlations (RPA) + = + + k k q k k q k i E E E f E f q ε ω ω χ ) ( ) ( ) ( ), 0 ( spin susceptibility of independent electrons Fermi sphere E q J(q) peaked at q=0, sufficiently strong ferromagnetism e.g. Fe, Ni

21 Magnetic resonant mode spin excitations of a d-wave superconductor RPA reproduces lower branch of hour-glass dispersion Imχ excitonic collective mode superconducting energy gap 2 _ + + _ incoherent spin flips ω dispersion of resonant mode q (π,π) direct Umklapp momentum-space signature of Cooper-pair wave function Eremin et al. PRL 2005

22 Spin dynamics from neutron scattering antiferromagnetic insulator superconductor E 300 mev E mev temperature (K) AFI (π, π) spin waves q SC (π, π) q magnetic resonant mode neutron blind spots - high energies - high doping levels hole concentration

23 Resonant inelastic x-ray scattering (RIXS) Cu L 3 edge 3d xx 2 yy 2 3d 2 2 3zz rr 3d xz, 3d yz 3d xy 3p 3/2 3p 1/2 3s 2p 3/2 2p 1/2 2s 1s 1) Resonant absorption at the Cu L 3 edge 2p 6 3d 9 2p 5 3d 10 2) Spin-Orbit coupling of the core hole can cause a spin flip LL SS = LLLLLL zz + (LL + SS +LL SS + )/2 3) Optical decay of the core hole L. J. P. Ament et al., PRL 2009 M. W. Haverkort, PRL p 5 3d 10 2p 6 3d 9 *

24 RIXS theory RIXS from cuprates Haverkort, PRL 2010 charge spin RIXS can detect single-magnon excitations in crossed polarization similar to neutrons, but with different polarization factor

25 RIXS from La 2 CuO 4 dispersion of single-magnon excitations excellent agreement with neutrons Braicovich et al., PRL 2009, 2010

26 RIXS from doped cuprates Le Tacon et al. Nature Phys well defined paramagnon excitations at all doping levels

27 Spin excitations in doped cuprates magnon-like quasiparticle excitations observed at all doping levels energy-integrated spectral weight conserved upon doping Le Tacon et al. Nature Phys nearest-neighbor spin correlations almost independent of doping

28 Paramagnons in overdoped cuprates Plate et al. PRL 2005 Le Tacon et al., Nature Phys. 2011, PRB 2013 p ~ 0.27, T c = 6 K Vignolle et al. Nature 2008 well defined fermionic quasiparticles well defined paramagnon excitations short-range AF correlations challenge for theory

29 RIXS theory Quantum Monte Carlo calculations of 2D Hubbard model Jia, Devereaux et al. Nature Comm RIXS cross section proportional to spin-spin correlation even in doped cuprates persistence of paramagnon excitations reproduced ongoing discussion: Benjamin et al., PRL 2014; Minola et al., PRL 2015

30 Magnetic order and excitations in YBa 2 Cu 3 O 6+x temperature (K) universal spin fluctuations available for d-wave pairing electron paramagnon electron 100 SDW AFI SC hole concentration

31 Spin fluctuation mediated d-wave pairing complete bosonic spectral function of YBa 2 Cu 3 O 7 (T c = 90 K) no adjustable parameters solution of gap equation within t-j model with different momentum cutoffs _ + + _ Dahm et al., Nature Phys Le Tacon et al., Nature Phys _ + + _ simple mean-field models give reasonable estimates of T c

32 Spin fluctuation mediated d-wave pairing pair breaking pair forming in d-wave channel high doping levels excitations at q ~ (π,π) disappear reduction of T c Wakimoto et al. PRL 2007

33 Charge density wave resonant inelastic x-ray scattering on underdoped YBCO photon energy tuned to L-edge of planar Cu elastic scattering at q = (0,0.31) polarization dependence indicates charge correlations Ghiringhelli et al., Science 2012 Achkar et al., PRL 2012 Blanco-Canosa et al., PRL 2013, PRB 2014 consistent with NMR Wu et al., Nature 2011; Nature Com confirmed with hard x-rays Chang et al., Nature Phys. 2012; Blackburn et al., PRL 2013

34 Charge density wave real space periodic modulation of the conduction electron density momentum space opens gap at Fermi surface, competes with superconductivity q 1 Blanco-Canosa et al., PRL 2013 charge density wave

35 CDW temperature dependence YBa 2 Cu 3 O 6.6 maximum correlation length 16 a CDW nearly critical correlation length suppressed below T c CDW competes with superconductivity CDW fluctuations reduce T c Ghiringhelli et al., Science 2012 Achkar et al., PRL 2012 Blanco-Canosa et al., PRL 2013, PRB 2014

36 CDW doping dependence Blanco-Canosa et al. PRL 2013, PRB 2014 CDW wave vector qualitatively consistent with size of Fermi surface common to YBCO, Bi2201, Bi2212, Hg1201 different from La 2-x (Sr,Ba) x CuO 4 with coexisting spin & charge order

37 CDW and Fermi arcs pseudogap at antinodes Fermi arcs distance between Fermi arc tips matches CDW wave vector Comin et al., Science 2014

38 Doping dependence of CDW amplitude CDW amplitude maximum at p ~ 0.12 CDW vanishes for p ~ 0.08, 0.16 two quantum critical points? Blanco-Canosa et al. PRB 2014

39 Competing order in YBa 2 Cu 3 O 6+x temperature (K) incommensurate spin density wave incommensurate charge density wave QCP QCP quantum oscillations SDW CDW in high magnetic fields Fermi surface reconstruction AFI SC hole concentration

40 Magnetic field dependence Blanco-Canosa et al. PRL 2013, PRB 2014 moderate to high doping magnetic field weakens superconductivity enhances CDW correlations

41 Magnetic field dependence Grisonanche et al. Nature Comm Ramshaw et al. Science 2015 transport experiments in high magnetic fields superconducting dome splits into two domes, strong mass enhancement at centers centers coincide with CDW quantum critical points from x-rays role of quantum-critical CDW fluctuations for high-t c superconductivity???

42 CDW and superconductivity onset of CDW onset of superconducting fluctuations Blanco-Canosa et al., PRB 2014 Dubroka et al., PRL 2011 combined CDW & superconducting fluctuations in pseudogap regime

43 CDW-induced phonon anomalies T < T c T > T c giant phonon softening giant phonon linewidth highly anisotropic electron-phonon interaction favors CDW formation, not superconductivity in narrow range around CDW wavevector Le Tacon et al. Nature Phys. 2014

44 Summary & Outlook summary comprehensive map of unusual spin and charge correlations in cuprates static order competes with superconductivity key theoretical challenges understanding relative stability of SDW, CDW, SC states in 2D metals role of CDW correlations for high-temperature superconductivity prediction of higher-temperature superconductors outlook interfaces and superlattices higher-resolution RIXS dynamical control

45 Mercedes-Benz Museum Ludwigsburg Castle Spectroscopies of Novel Superconductors Stuttgart, Germany, June 19-24, MPI for Solid State Research University of Stuttgart