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Spectral function in Holographic superconductor

Spectral function in Holographic superconductor. Wen-Yu Wen (NTU) Taiwan String Theory Workshop 2010. Hightlight. Bi2Sr2CaCu2O8 +δ. H HTSC. Chen-Kao-Wen, arXiv:0911.2821. Norman, et al, Phys. Rev. Lett. 79. A ngle R esolved P hoto E mission S pectroscopy.

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Spectral function in Holographic superconductor

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  1. Spectral function in Holographic superconductor Wen-Yu Wen (NTU) Taiwan String Theory Workshop 2010

  2. Hightlight Bi2Sr2CaCu2O8+δ HHTSC Chen-Kao-Wen, arXiv:0911.2821 Norman, et al, Phys. Rev. Lett. 79

  3. Angle Resolved PhotoEmission Spectroscopy A direct exp technique to observe distribution of electrons (single electron excitation)

  4. Spectral function v.s.Retarded Green function Spectral function: Density of states:

  5. AdS/CFT correspondence φ • Consider a correspondence pair (O, ) • Retarded Green function of operator O can be seen as reflection coefficient of by imposing in-falling boundary condition at horizon. φ O φ

  6. Example 1:Spin-0 field

  7. Example 2:Spin-1/2 field

  8. Holographic non-fermi liquid • Extremal charged AdS-BH always has AdS2 as its near horizon geometry • Dirac fermion probed in AdS2 might be related to the non-fermi liquid at quantum critical point. (Sung-Sik Lee, Hong Liu, etc.) • What if a new phase appears before critical point is reached? Normal Phase SC Phase QC Point

  9. Holographic superconductor • To build a gravity model for HTSC ? ○ a phenomenological model: Ginzburg-Landau type ? a microscopic model: BCS type • Essential ingredients: Finite temperature T Chemical potential μ Condensate φ (3+1) Gravity model (2+1) HTSC

  10. Abelian Higgs model in AdS black holea.k.a hairy black hole solution • Ginzburg-Landau feels curvature from AdS-BH • AdS-BH metrics receives no back reaction from GL sector in probe limit AdS-BH T increases with BH mass GL A: abelian gauge field U(1) φ: Higgs Mass term has no explicit T dependence V has no other higher order term

  11. instability BH in flat space BH in AdS space Charged AdS-BH 0 Boundary Horizon

  12. State-Operator correspondence: Scalar field (Higgs) with mass m AdS bulk x Boundary QFT Operator of dimension Δ

  13. Time component gauge potential encodes the message of chemical potential and charge density at the boundary AdS Bulk Boundary QFT

  14. GR problem: Solving equation of motion for GL with given boundary conditions at horizon and infinity. Existence of two solutions implies a second order phase transition between them. Multiple solutions due to nonlinearity

  15. Tc[Hartnoll,Herzog,Horowitz, 08] Bosonic condensation Fermionic condensation strongly correlated? usual BCS ~ 3.5

  16. Hc [Nakano,Wen,Phys.Rev.D78 (08)]

  17. Holographic superconducting vacuum • Operational definition:continue lowering temperature below Tc, where condensate forms, untill it reaches absolute zero • Thanks to condensate, it has to be different from trivial vacuum, and different from nontrivial vacuum of extremal charged black hole AdS vacuum Final state of SSBH AdS + condensate Final state of cBH + Higgs Extremal AdS-RN Final state of RNBH

  18. Through backreaction, our geometry now encodes the information of condensate, which mostly deforms IR physics. [Horowitz-Roberts,09] HTSC in SC vacuum

  19. Numerical result • Spin average spectral function is imaginary part of trace of retarded Green function (ΔB=2ΔF=3) Chen-Kao-Wen, arXiv:0911.2821

  20. Peak Hump Dip

  21. q<2.6 • Dynamics of peak and hump ω/k<0.15 kF q>2.6 Gap ω/k<1

  22. More story…

  23. Prospects • A hard gap solution exists for s-wave HSC only by introducing Majorana coupling for the probed fermion. Any better/smarter way? • Will a probed fermion in p-wave HSC also show a hard gap? • Can we realize d-wave HSC, which is closer to High-Tc SC?

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