Ads/cft and double monolayer semimetals

Feb 9, Namshik Kim (NK) Exciton Condensate in Holographic Double Monolayer Semimetals
Exciton Condensate
in Holographic Double Monolayer Semimetals

List of Publications
• D3-D5 Holography with Flux - Grignani Gianluca, Gordon Semenoff, NK,  
Phys.Lett. B715 (2012)
• D7-anti-D7 bilayer: holographic dynamical symmetry breaking  
- Grignani Gianluca, Gordon Semenoff, NK, Phys.Lett. B (2013)
• Holographic D3-probe-D5 Model of a Double Layer Dirac Semimetal 
-Gianluca Grignani, Andrea Marini, Gordon Semenoff, NK, JHEP 1412 (2014) 091
• Exciton Condensation in a Holographic Double Monolayer Semimetal 
-Gianluca Grignani, Andrea Marini, Gordon Semenoff, NK Phys.Lett. B (2015)
• Flavor-symmetry Breaking with Charged Probes 
-J. Davis, NK, JHEP 1206 (2012) 064

• Study some models of strongly  
coupled 2+1 D quantum field  
theories with double monolayer  
using string theory.
M.Franz et al. (08)
+ + +
- - -
Motivation

• Study some models of strongly  
coupled 2+1 D quantum field  
theories with double monolayer  
using string theory.
• Quantum coherence  
between the layers
• Inter-layer exciton condensate 
(boson)
M.Franz et al. (08)
+ + +
- - -
Motivation

Motivation
MacDonald et al. 2008
• Inter-layer exciton condensate is conjectured to occur in double
monolayer graphene, maybe even at room temperature, with
meaningful applications in electronics (room temperature superfluid) 
• In spite of this optimism, inter-layer coherence is not yet seen in
double monolayer graphene
• Most recent searches down to nano-scale separation of monolayers
sees strong Coulomb drag force but no condensate yet.
Geim, Novoselov et al. 2012

• Interlayer condensate has been seen in cold atom analogs and in  
transient states of conventional semiconductor hetero-structures  
(at low temperatures and high magnetic fields) 
Utsunomiya et al, Nature 2008
• Theoretical analyses are difficult since they are in the strong coupling
regime
• Study some model defect field theories which are exactly solvable in the
strong coupling limit  
(AdS/CFT application)
Motivation

Gravity / Quantum theory

Holographic duality
DUAL!

• Defect quantum field theory in 2+1 D
• N=4 supersymmetric Yang-Mills theory  
lives in the 3+1-dimensional bulk
• U(1) charged fields on defect,  
interaction mediated by N=4 gauge fields  
in bulk, V(r)~1/r (similar to Coulomb)
• Graphene interacts by exchanging photons in bulk,  
whereas model interactions exchange N=4 SYM  
gluons, and truncate to planar limit
• Weak coupling limit should have an interlayer condensate when charges
of monolayers are balanced
e+
e
N = 4 SY M
DFT
t, x, y
z
The model ( field theory)
e

• Large N D3-branes at low energy limit cause the AdS background
geometry, and we consider probe D7 and D5 branes embedded on
the background geometry (No backreaction limit)
• D7 brane model resembles graphene in that it has relativistic
fermions on defect
• D5 brane has supermultiplet of fermions+scalars on defect, SUSY
broken by magnetic field, low energy physics governed by fermions -
Intra-layer condensate tends to form
The model ( gravitational theory)
S.J. Rey 2009
Karch, Katz 2002

maximally
symmetric
The dual model for probe D5

maximally
symmetric
less symmetric
C.Johnson et al. 2009

maximally
symmetric
less symmetric
Quantum Hall ferromagnetism (Zhou, Semenoff, 2011)
(Kristjansen, Semenoff, 2013)

maximally
symmetric
less symmetric
less symmetric
with B, Q, (F)
D.T.Son et al 2010
Semenoff, NK 2012

The dual model for probe D5 (double layer)
• We model the double monolayer by a D brane-anti D brane pair.
maximally symmetric less symmetric

Review on probe D-branes
• Large N D3-branes at low energy limit cause the AdS background
geometry, and we consider probe D7 and D5 branes embedded on
the background geometry (No backreaction limit)
• D7 brane model resembles graphene in that it has relativistic
fermions on defect
• D5 brane has supermultiplet of fermions+scalars on defect, SUSY
broken by magnetic field, low energy physics governed by
fermions

• The exciton transition occurs when the branes join
B, Q N.Evans, K.Y. Kim 2013
Semenoff, NK 2014

Results
• It is known, at weak coupling, the inter-layer electron-hole
interaction is much stronger if the electron Fermi surface in
one layer and the hole Fermi surface in the other layer are
nested
• Weak coupling interlayer condensate exists for small range of
charge densities near perfect nesting 
 
 
 
 
 
M.Franz et al. (08)

Results
• It is known, at weak coupling, the inter-layer electron-hole
interaction is much stronger if the electron Fermi surface in
one layer and the hole Fermi surface in the other layer are
nested
• Weak coupling interlayer condensate exists for small range of
charge densities near perfect nesting
• However, we find: at strong coupling, inter-layer
condensate occurs ONLY if charge densities are
balanced(=nested)
• Moving away from nesting destroys gap
M.Franz et al. 2008
Semenoff, NK, Grignani, Marini. 2014, 15

Results : Phase diagram for nested probe D5

Review : Phases
maximally symmetric intra
inter/intra or inter
B, Q

Results : Phase diagram for nested probe D5
• For balanced charge densities, an inter-layer condensate can form for
any value of the inter-layer separation
• For charge neutral layers (q=0), an inter-layer condensate can form only
when the separation is small enough ( L less then 1.357)

Results
• We find that when there is more than one species of fermions,
nesting can occur spontaneously.  
• Perfect nesting is hard to achieve in the lab — maybe it
happens spontaneously - need more work here
• Pseudospin of multi-layer condensed systems breaks some of
the internal symmetry of the D branes (case of Intra-layer
condensate)
Semenoff, NK, Grignani, Marini. 2014, 15

Results
• One of the geometrical solution of our model can be
computed analytically and exhibit the low momentum
structure that is expected when global symmetries are
spontaneously broken.
• For example, U(1) X U(1) -> U(1) symmetry breaking pattern
leads an insulator channel and a superfluid channel.
• These correlation functions have poles attributable to infinite
towers of vector mesons with equally spaced masses.
Semenoff, NK, Grignani 2013

Thank you

EF
Appendix : energy band and Fermi energy
E
~k
Metal semiconductor insulator
gapless thin gap gapful
conduction band
valence band

EF
Appendix : energy band
E
~k
Metal semiconductor insulator
gapless thin gap gapful
conduction band
valence band

Appendix : Hamiltonian of graphene

E
~k
E = ~c ~k
E = ~vg
~kEF
↵ =
1
4⇡✏0
e2
~c
↵g =
1
4⇡✏0
e2
~vg
=
c
vg
↵
Appendix : semimetal and graphene
⇠ 300↵
valence band
conduction band

Appendix : current-current correlation functions

Appendix : Free energy and phase transition

Ads/cft and double monolayer semimetals

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