Superconducting state of correlated metals Richard Hlubina 1,2 and - - PowerPoint PPT Presentation

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Superconducting state of correlated metals Richard Hlubina 1,2 and - - PowerPoint PPT Presentation

Jan 02, 2024 48 likes •411 views

Superconducting state of correlated metals Richard Hlubina 1,2 and Juraj Mrz 1,3 1 Comenius University, Bratislava 2 SISSA Trieste, Italy 3 IBL Software Engineering, Bratislava PRB 67, 174518 (2003), PRB 69, 104501 (2004) PRB 70, 144529 (2004),

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Superconducting state of correlated metals

Richard Hlubina1,2 and Juraj Mráz1,3

1 Comenius University, Bratislava 2 SISSA Trieste, Italy 3 IBL Software Engineering, Bratislava

PRB 67, 174518 (2003), PRB 69, 104501 (2004) PRB 70, 144529 (2004), PRB 72, (2005), and unpublished

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Outline

  • 1. Motivation
  • 2. Systematic corrections to the mean field theory

in the p-p and p-h channels Applications:

  • 3. Superconducting phase diagram of the t-t’ Hubbard model

d-wave region: bilayer p-wave region: Sr2RuO4

  • 4. Van Hove density: p-p vs. p-h competition
  • 5. Retardation effects
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Our program

Hypothesis: supercond. in cuprates = giant Kohn-Luttinger effect Strategy: approach from overdoped side; search for new features Byproduct: application to Sr2RuO4

  • 1. What are the distinguishing features of the

superconducting state of doped Mott insulators?

pairing symmetry………………………d-wave also at weak coupling! particle-hole asymmetry…………? reduced phase stiffness…………Josephson effect (RH, Hvar ‘02) frequency dependence of Δ……difference w.r.t. phonons? ???

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  • 2. Systematic corrections

to the mean field theory

Particle-particle channel Particle-hole channel at q=(π,π) Particle-hole channel at q=0

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  • 1. split the Hamiltonian

Kinetic energy

  • 2. canonical transformation
  • 3. resulting Hamiltonian

where LARGE! SMALL! (can be treated by mean field)

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BCS channel Density wave channel Landau channel

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Density wave channel

Order parameters Variational energy where particle-particle susc.

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Gap functions SDW case: 4-vector 4x4 matrix eigenvalues unitary state: gap equation: (unitary states)

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Classification of symmetry breaking solutions

Channel: BCS, density wave, Landau Spin sector: singlet,triplet Orbital sector (2D square lattice): s, d, dxy, g, p Charge density wave channel: Spin density wave channel: (“axial” states)

(Hankevych,Wegner, EPJ ’03)

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  • 3. Superconducting phase diagram
  • f the t-t’ Hubbard model
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Sr2RuO4

(U infinitesimal)

cuprates ρ t’/t

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Transition temperatures for singlet and triplet pairing

t’/t=0.35, U=6t, 512x512

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Triplet-singlet mixing

ρ

0.6 0.645

Mixed phase pure p-wave pure dxy-wave

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Mixed phase – correlation functions

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  • 4. Competition between particle-particle

and particle-hole instabilities at the Van Hove density

ρ t’/t

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t’/t=0.0, Van Hove density, 128x128

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s-SDW d-SC, d-SDW, d-CDW Gap functions for U=3t t’/t=0, ρ=1, 128x128 p-CDW

Degenerate states (Hankevych, Wegner)

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t’/t=0.05, Van Hove density, 128x128

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t’/t=0.10, Van Hove density,128x128

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t’/t=0.20, Van Hove density, 128x128

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ρ t’/t

Van Hove phase diagram, U=3t

SD W SC

(absent in mean field!)

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  • 5. Retardation effects
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Hubbard-Holstein model

Scattering terms

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Eliminate scattering terms: Effective interaction in the Cooper channel:

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D/t=0.4, ω0/t=0.2, Γ/t=0.02 2D2/ ω0=1.6t

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Gap function

U=0 U=3t

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Gap function along (0,0) to (π,π)

Fermi surface momentum gap

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Cooper pair wavefunction

U=0 U=6t

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Cooper pair wavefunction

el.-el. distance

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Conclusions

  • methodology:
  • simple ‘variational’ method allowing comparison of different

symmetry breaking patterns on the same footing

  • applications:
  • fully microscopic model for the Tc enhancement on a bilayer
  • t-t’ Hubbard model: a possible canonical model for p-wave

superconductivity in Sr2RuO4

  • correlation effects:
  • additional structure due to Hubbard U in Δ(ω) of the Holstein

model

  • retardation effects in the d-wave sector: work in progress
  • bservability of the structure??