High Tc superconductivity in cuprates: Determination of pairing interaction Han-Yong Choi / SKKU SNU Colloquium May 30 018
It all began with Discovered in 1911 by K Onnes. Liquid He in 1908. Nobel prize in Physics in 1913.
Super-conductivity. 1. Perfect-conductor r r ne J = σ E σ = τ E 0. * m Superconductivity. Perfect-diamagnet Meissner effect r r r B = µ 0H + M 0. London equation r ne J = m Thermodynamically stable new state of matter which needs an explanation. Gap: specific heat Order parameter r A. * / C ~ e T
BCS theory Pairing Bardeen-Cooper-Schrieffer 1957 c k c + + k 0 = V c c + + k k Phonon mediated effective interaction retarded attractive interaction pairing bound state of two electrons superconductivity. For repulsive interaction: Anisotropic pairing Gap tied to Fermi surface infinite conductivity
Symmetry of Pairing order Symmetry of c k c + + k Pairing two spin ½ fermions Total spin S=1 or 0. The total wavefunction must be antisymmetric orbital part must be symmetric for S=0 antisymm for S=1. L=0 s d 1 3 p f Cuprate SC: d-wave pairing Conventional SC: s-wave pairing
Bottle neck: low Tc Applications
High Tc SC H 3 S ~ 00 K YH 10 ~ 300 K 00 BCS Cu FeAs/ Hydrides FeSe Current atmosphere is unlike the pre-high Tc era. Because high Tc is still the unsolved problem and new materials keep being discovered. Higher is different
CuO planes Cuprates La Y Bi Hg Tl families simple clean ARPES Physical properties are controlled by doping. Bi Sr CaCu O 8+δ
Pairing interaction for cuprates ~30 years of intense research into the cuprates enormous progress & plethora of complexities/phases Some key issues however remain unresolved. What is the pairing interaction for the cuprates. the interaction exists above Tc to induce pairing it must explain AN PG as well. The d-sc PG AN must be understood in their totality. Theory of everything
Pseudo-gap & anomalous normal states Suppression of density of states around the Fermi energy above Tc. Fermi arc. T<Tc Tc<T<T* T>T* Fermi surface evolution Kondo et al Nature Comm. 015 T<Tc Tc<T<T pair T pair <T<T* T>T* Origins: Preformed pairs RVB competing orders nematicity Loop currents Mottness. Strange metal anomalous normal state: marginal Fermi liquid. How the PG and SM states are related with the high Tc superconductivity?
Bozovic et al. Nature 016 1 λ ne ndh eµ e s s 0 = µ * 0 = = kt * B Θ m m dh ε0d hc.
View on SC state
Leading proposals Resonating valence bond theory Anderson : no pairing boson Anti-ferromagnetic spin fluctuations Pines Scalapino Loop current Varma
Comparison of leading theories These all give rise to d-wave pairing φθ ~ cosθ. How to settle down? -- Like s-wave pairing we need dynamical information McMillan-Rowell analysis. θ dependence of the normal & pairing self-energies determined from the laser ARPES analysis. Bi Sr CaCu O 8+δ Bi1 AF RVB LC θ-dependene of φ ~ cosθ O O O -dependene of φ θ-dependene of Σ -dependene of Σ
Phonon mediated effective interaction Isotope effect T e ph c 1/ λ M α α = 1/. However Zr Ru HTS α 0 1. The interaction is still mediated by phonons but the BCS form for V is oversimplified.. The interaction is mediated by some other low-frequency mode of solid involving no lattice motion. It is very hard to prove or disprove it experimentally. de Gennes 1965. McMillan-Rowell 1965. Experimental input tunneling conductance boson spectrum. el-ph interaction confirmed.
McMillan-Rowell for HTS Density of states N = Re. α F Ζ. Eliashberg eq. s-wave SC: normal self-energy Σ and pairing self-energy φ have the same symmetry. d-wave SC: Σ has the full symm of the lattice & φ the d-wave symm. Both momentum and energy resolved information needed ARPES is ideally suited.
Implementation SKKU Jin Mo Bok HYC- IOP XJ Zhou Laser ARPES group- UCR CM Varma
UD89 angle=0 deg T=97 & 16 K. [ ] θ θ ν θ θ B k A f k M k I k I + = = r Laser ARPES Data on Bi1 UD89 Tc=89 K and OD8 Tc=8 K. 1 θ ξ θ Σ = k k G r
Spectral function. ~. ~ ~ Im 1 X X X G k G k A k + Σ = Σ + Σ + + Σ = = φ ξ ξ π
Normal & pairing self-energies impurities peak = b + 0
Intrinsic self-energy for cuprate SC Bok et al Quantitative determination of pairing interactions for hightemperature superconductivity in cuprates Science Adv 016. Φ ~cosθ trust upto E~ -0.15 ev. Can also determine whether the pairing glue is necessary for cuprate SC. Li & Dessau Nature Comm 018.
Eliashberg functions α F ε θ N ε θ P normal Eliashberg fun from pairing Eliashberg fun from % ε = ε θ / cos θ P P Σ θ φθ
AF fluctuations: frequency dependence Gull & Millis cluster DMFT of d Hubbard model PRB 015. Sakai & Imada PRL 016 arxiv 018.
AF fluctuations: Angle dependence The ARPES deduced freq & momentum dependence may not be reproduced by the AF fluctuations. π Σ θip = i p αf θθ i sgn ' ' β θ ' ip' π ip ' ip = % k r F i k r β ip' p ' % φ η α θθ ' η '. Central paradox : How can the same interaction gives rise to the mom isotropic normal properties and anisotropic d-wave pairing? θθ '
Resonating valence bond theory d-wave RVB of singlet pairs = PG. Doping renders the pairs more itinerant & SC emerges. Pairing boson unnecessary. Essential to determine the symmetry of the pseudo-gap order parameter & -dependence of φ. 1 Reφ k = 0 = ' Imφ ' + φ0. φ0 << Reφ0. π d k 0 ' No calculations of φ for RVB yet.
Loop current fluctuations Loop current order = PG. LC fluctuations give rise to the strange metal and SC states. The normal and pairing Eliashberg functions have the same freq dependence. The coupling vertex is different for the normal and pairing channels. = c c P N T ε ε 0 tanh ~ cos / ~ θ θ ε ε P P
Central paradox The normal and pairing channels have different coupling vertex. π Σ θ ip = i sgn p' α θ θ ' χ i β θ ' ip' ~ ~ π ip' r r φ ip = η k α θ θ ' χ i η k '. β ' θ θ ' ip' p r r α ~ k k ' ~ k F sin θ θ' ~ 1 cos θcos θ' [ ] Crucial to confirm ~ ε ε P = N
Summary To solve the high Tc problem we need theory of everything. PG order parameter? Its symmetry? Its fluctuations give rise to the strange metal & high Tc superconductivity? We can determine the intrinsic self-energies of the cuprate SC yet need to extend the energy range by factor of ~. Need the angle & freq dependence of the self-energies for each proposal. Find a model hamiltonian where AF/RVB/LC is present and calculate the self-energies. How to reconcile the complexities Bozovic results? Local pairs and fermions coexist? And p * and p end.