Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad...

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Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based on Wen’s slides)

Transcript of Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad...

Page 1: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Holographic Models forHigh-Tc superconductors

Jiunn-Wei Chen (NTU)w/ Ying-Jer Kao, Debaprasad Maity,

Wen-Yu Wen and Chen-Pin Yeh

(talk largely based on Wen’s slides)

Page 2: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

R=8πGT Why bother to know about gravity?

Page 3: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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!

Page 4: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Some physical observations

Dilute Gas

S ~ V

Black hole

Bekenstein-Hawking: S ~AFluid/Solid

Horizon

Lesson 1 (Holographic Principle): In the strong coupling regime, field theory degrees of freedom

could have been repacked into gravity degrees of freedom

weakly interact strongly interact

(`tHooft,98)

Page 5: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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)

r

Imagine a string stretching in between, we obtain Coulomb potential for attractive force

Lesson 2 (AdS/CFT correspondence):Interaction could be encoded into geometry

(Witten,98)

(Maldacena,98)

IR

UV

V~1/|x-x’|

)( 2222

22 drxddtr

Lds

Page 6: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

More surprise to come

r

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)

Page 7: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Applied String Theory (3 yrs old)

for strongly coupled system• 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)

Page 8: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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

Page 9: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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)

Page 10: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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

Page 11: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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

Page 12: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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

Page 13: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Condensate

• φ field is in balance between two competing forces: gravitational attraction and electric repulsion.

Page 14: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

• 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

Page 15: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

)0( ,0

0

1,22,1

Page 16: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Tc[Hartnoll,Herzog,Horowitz, 08]

Bosonic condensation Fermionic condensation

strongly correlated?usual BCS ~ 3.5

Page 17: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

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

Page 18: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

• Goal #2: Fermionic spectral function of HTSC---measurable experimentally

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Page 20: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.
Page 21: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.
Page 22: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.
Page 23: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

More story…

Page 24: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.
Page 25: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

SummaryThe gap we found in the s-wave superconductor is “soft”.

p-wave superconductor appears to have a hard gap at zero temperature

Page 26: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Towards a holographic model of D-wave superconductors

• 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.

Page 27: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Prospects

• Gap • D-wave• phase diagrams; quantum critical point (Sachdev,

Liu, etc.) and insulator-superconductor phase transition (Takayanagi et al.)

• microscopic mechanism

Page 28: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

A practical thing to do

BCS-BECGraphene…

I should learn more condensed matter

Page 29: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

Thank You

Page 30: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

• 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

Page 31: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

• 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

Page 32: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.

• 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

Page 33: Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.