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

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

A ngle R esolved P hoto E mission S pectroscopy A direct exp technique to observe distribution of electrons (single electron excitation)

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

AdS/CFT correspondence 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 φ O φ

Example 1: Spin-0 field

Example 2: Spin-1/2 field

Holographic non-fermi liquid Extremal charged AdS-BH always has AdS 2 as its near horizon geometry Dirac fermion probed in AdS 2 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

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

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

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

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

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

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

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

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

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

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

Numerical result Spin average spectral function is imaginary part of trace of retarded Green function ( Δ B =2Δ F =3 ) Chen-Kao-Wen, arXiv:

Peak Dip Hump

Dynamics of peak and hump Gap q<2.6 q>2.6 ω/k<1 ω/k<0.15 kFkF

More story…

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?