Holographic Superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Yu-Sheng Liu, Debaprasad Maity,...
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Transcript of Holographic Superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Yu-Sheng Liu, Debaprasad Maity,...
Holographic Superconductors
Jiunn-Wei Chen (NTU)w/ Ying-Jer Kao, Yu-Sheng Liu, Debaprasad Maity,
Wen-Yu Wen and Chen-Pin Yeh
(talk largely based on Wen’s slides)
Can this Universe a giant hologram?
Black hole entropy scales as the surface of the horizon.
Information upper bound scales as the surface of the system as well?
AdS/CFT Correspondence (Maldacena, 98)
• 4 dim gauge field theory (SYM) is equivalent to a 10 dim (AdS_5 x S_5) string theory--- a holography and a strong-weak interaction dual!
Some observations
Operator O(x) of dimension Δ<O(x)O(x’)> = |x-x’|-2Δ
x
x’
Flat D-dimensional CFTConformal symmetry SO(D,2)
(D+1)-dimensional anti-de SitterIsometry SO(D,2)
(□-m2)Φ(x,r)=0m2 = Δ(Δ-D)
z
Imagine a string stretching in between, we obtain Coulomb potential for attractive force
Lesson (AdS/CFT correspondence):Interaction could be encoded into geometry
(Witten,98)
(Maldacena,98)
IR
UV
V~1/|x-x’|
)( 2222
22 dzxddtz
Lds
More surprise to come
z
Gravity:
(Soft/hard) cut-off induces confinement
Field Theory:
Modify InfraRed physics
Linear potential for long string
Lesson 3 (AdS/ ? correspondence):Interesting physics could appear while away from AdS/CFT
The proof? Top down vs. bottom up
(Karch-Katz-Son-Stephanov,06)
Applied String Theory: strongly coupled system with approximate scaling symmetry
• Quark Gluon Plasma (RHIC)Drag forceJet Quenchingη/s
• QCDConfinement/deconfinementGluon scatteringBaryon/Hadron
• Quantum critical point• Superfluidity• High-Tc superconductivity
(1911 discovered, 1950 GL, 1957 BCS, 1986 HTSC)
Today’s goals
• Goal #1A minimum gravity model for HTSC
• Goal #2Fermionic spectral function of HTSC
• Goal #3
From S-wave to D-wave SC’s
Superconductors
• BCS theory: electron-electron pairing through phonon exchange; not enough for HTSC
• Ginzburg-Landau theory: low energy effective theory; breaking the (local) U(1) symmetry spontaneously---massive EM fields (Higgs mechanism)
Holographic Superconductors
• Minimum model:Breaking the U(1) symmetry spontaneously [local
U(1) in the “bulk”, global U(1) at the boundary]
• Essential ingredients:Finite temperature TChemical potential μCondensate φ (same quantum number as a fermion pair)
(3+1) Gravity model
(2+1) HTSC
Finite temperature• TH~ horizon size, large black hole is stable • HTSC is in thermal equilibrium with black hole at
Hawking temperature TH
T=0 Small T Large T
Hawking radiation
Finite chemical potential• Place electric field along radius direction, particles
with opposite charges will accumulate on boundary and horizon, giving a charged balck hole
• Voltage established between them can be interpretated as chemical potential (q)μ,which is the work done by moving a unit charge from horizon to boundary.
﹢﹢
﹢﹢
﹢
﹢
﹣﹣
﹣
﹣
﹣﹣
Er
Condensate
• φ field is in balance between two competing forces: gravitational attraction and electric repulsion.
• When black hole is too heavy (high T), φ will fall into the horizon. (normal state)
• When black hole is not so heavy (low T), φ safely stays outside the horizon and forms a condensate. (superconducting state)
Hairy black holeNo hair
SC phaseN phase
=φ
Tc[Hartnoll,Herzog,Horowitz, 08]
Bosonic condensation Fermionic condensation
strongly correlated?usual BCS ~ 3.5
SummaryThe gap we found in the s-wave superconductor is “soft”.
p-wave superconductor appears to have a hard gap at zero temperature
Towards a holographic model of D-wave superconductors
(JWC, Kao, Maity, Wen, Yeh)• At the boundary (field theory side), we need a
symmetric traceless 2nd rank tensor to form the condensate.
• In the bulk, we higged a symmetric traceless 2nd rank tensor.
• However, we have more components than we want and some of them are unstable---a remaining problem
• Condensate vs T and DC, AC conductivitives worked out nicely.
Prospects
• Fermi arcs: in the pseugap phase not SC phase • D-wave: stability (a hard problem)• phase diagrams; quantum critical point (Sachdev,
Liu, etc.) and insulator-superconductor phase transition (Takayanagi et al.)
• microscopic mechanism
• Ginzburg-Landau feels curvature from AdS-BH• AdS-BH metrics receives no back reaction from GL
sector. (probe limit)
AdS-BH
GL
T increases with BH mass
Abelian Higgs model in AdS black holea.k.a hairy black hole solution
Mass term has no explicit T dependenceV has no other higher order term
A: abelian gauge field U(1)φ: Higgs
• State-Operator correspondence:
x
AdS bulk
Boundary QFT
Operator of dimension Δ
Scalar field (Higgs) with mass m
21
21)(rr
r
22)3( Lm
• Time component gauge potential encodes the message of chemical potential and charge density at the boundary
rrr FE 0
AdS Bulk
Boundary QFT
r
r)(
),()( 0 rxAr