■ Introduction: QCD and graphene

■ Charge carriers in graphene and effective field

theory

■ Calculations on the hypercubic lattice

■ Calculations on hexagonal lattice

Charge-Carrier Transport in Graphene

P.V. Buividovich, O.V. Pavlovsky, M.V. Ulybyshev, E.V. Luschevskaya, M.A. Zubkov, V.V. Braguta, M.I. Polikarpov

ArXiv:1204.0921; ArXiv:1206.0619

Workshop on QCD in strong magnetic fields

12-16 November 2012, Trento, Italy

■ Introduction: QCD and graphene

■ Charge carriers in graphene and effective field

theory

■ Calculations on the hypercubic lattice

■ Calculations on hexagonal lattice

Charge-Carrier Transport in Graphene

P.V. Buividovich, O.V. Pavlovsky, M.V. Ulybyshev, E.V. Luschevskaya, M.A. Zubkov, V.V. Braguta, M.I. Polikarpov

ArXiv:1204.0921; ArXiv:1206.0619

Workshop on QCD in strong magnetic fields

12-16 November 2012, Trento, Italy

■ Introduction: QCD and graphene

■ Charge carriers in graphene and effective field

theory

■ Calculations on the hypercubic lattice

■ Calculations on hexagonal lattice

Charge-Carrier Transport in Graphene

P.V. Buividovich, O.V. Pavlovsky, M.V. Ulybyshev, E.V. Luschevskaya, M.A. Zubkov, V.V. Braguta, M.I. Polikarpov

ArXiv:1204.0921; ArXiv:1206.0619

Workshop on QCD in strong magnetic fields

12-16 November 2012, Trento, Italy

■ Introduction: QCD and graphene

■ Charge carriers in graphene and effective field

theory

■ Calculations on the hypercubic lattice

■ Calculations on hexagonal lattice

Charge-Carrier Transport in Graphene

P.V. Buividovich, O.V. Pavlovsky, M.V. Ulybyshev, E.V. Luschevskaya, M.A. Zubkov, V.V. Braguta, M.I. Polikarpov

ArXiv:1204.0921; ArXiv:1206.0619

Workshop on QCD in strong magnetic fields

12-16 November 2012, Trento, Italy

■ Introduction: QCD and graphene

■ Charge carriers in graphene and effective field

theory

■ Calculations on the hypercubic lattice

■ Calculations on hexagonal lattice

Charge-Carrier Transport in Graphene intight binding model

P.V. Buividovich, O.V. Pavlovsky, M.V. Ulybyshev, E.V. Luschevskaya, M.A. Zubkov, V.V. Braguta, M.I. Polikarpov

ArXiv:1204.0921; ArXiv:1206.0619

Workshop on QCD in strong magnetic fields

12-16 November 2012, Trento, Italy

QCD and Graphene

Carbon atom

Elementary structure

Some allotropes of carbon: a) diamond; b) graphite; c)lonsdaleite; d–f)

fullerenes (C60, C540, C70); g) amorphous carbon; h) carbon nanotube.

Fullerene (Buckminsterfullerene) C60

Richard Buckminster Fuller

1895 -1983

The Montreal Biosphère by

Buckminster Fuller, 1967

Fullerene C540

Richard Buckminster Fuller

1895 -1983

The Montreal Biosphère by

Buckminster Fuller, 1967

Nanotube

Graphene

The Nobel Prize in Physics for 2010 was awarded to

Andre Geim and Konstantin Novoselov

"for groundbreaking experiments regarding the

two-dimensional material graphene”

2

Nonrelativistic particle

2

mvE

2 4 2 2

Relativistic particle

E m c p c

2 4 2 2

Relativistic particle

Massless particle

E m c p c

E cp

2 4 2 2Relativistic particle

Massless particle

Graphene ; ;300

F F

E m c p c

E cp

cE v p v

2 4 2 2Relativistic particle

Massless particle

Graphene ; ;300

300 2.16 1

1.11 0.06 Pure graphene is the insulator!

F F

g

crit

g g

E m c p c

E cp

cE v p v

Hexagonal lattice = Triangle lattice + Triangle lattice

On such lattice nonrelativistic electrons are

“equivalent” to massless four component Dirac

fermions moving with

the effective charge is:

;300

F

cv

300 2.16 1g

Graphene lattice and Brillouin zone

Wallace, P. R. (1947). "The Band Theory of

Graphite". Physical Review 71 (9): 622.

Semenoff, G. W. (1984). "Condensed-

Matter Simulation of a Three-Dimensional

Anomaly". Physical Review Letters 53 (26):

2449.

2

1g g

Graphene on substrate

g

g

Graphene in the dielectric media

substrate

graphene

2if ( 1.11) graphene is the conductor

1

crit

g g

We can vary the effective coupling in graphene!

1.“Massless” four component Dirac fermions

2.Fermi velocity is

3.The effective charge is

4. We can vary the effective

charge if we vary the dielectric

permittivity of the substrate

Effective theory of charge carriers in

graphene

/ 300Fv c

300 2.16 1g

2

1g g

300 g

Fv

we can neglect Ai;

Effective field theory for graphene

After transformation

(2+1)D fermions

(3+1)D Coulomb

2

1g g

On substrate

Simulation of the effective graphene theory

Approach 1, hypercubic lattice

(2+1)D fermions

(3+1)D Coulomb

J. E. Drut, T. A. Lahde, and E. Tolo (2009-2011)

P.V. Buividovich, O.V. Pavlovsky, M.V. Ulybyshev, E.V. Luschevskaya, M.A.

Zubkov, V.V. Braguta, M.I. Polikarpov (2012)

W. Armour, S. Hands, and C. Strouthos (2008-2011)

Simulation of the effective graphene theory

Approach 2, 2D hexagonal lattice and

rectangular lattice in z and time dimensions R. Brower, C. Rebbi, and D. Schaich (2011-2012)

P.V. Buividovich, M.I.P. (2012)

H H Htb I

^ ^ ^

Approach 2, 2D hexagonal lattice, Hamiltonian

H H Htb I

^ ^ ^

Approach 2, 2D hexagonal lattice, Hamiltonian

Coulomb

interaction

Lattice

geometry

H H Htb I

^ ^ ^

Approach 2, 2D hexagonal lattice, Hamiltonian

Coulomb

interaction

Lattice

geometry

YXYX aa ,',', }ˆ,ˆ{

H H Htb I

^ ^ ^

Approach 2, 2D hexagonal lattice, Hamiltonian

300F

cv

H H Htb I

^ ^ ^

Approach 2, 2D hexagonal lattice, Hamiltonian

Coulomb

interaction

H H Htb I

^ ^ ^

Approach 2, 2D hexagonal lattice, Hamiltonian

Fermion condensate as a function

of substrate dielectric permittivity

Approach 1 Approach 2

Hypercubic lattice Hexagonal lattice

Conductivity as a function of

substrate dielectric permittivity

Approach 1 Approach 2

Hypercubic lattice Hexagonal lattice

substrate

graphene

HH

H

Graphene changes its properties when an external magnetic field

is applied, we can numerically simulate all that

Perpendicular magnetic field

Fermion condensate as the function

of substrate dielectric permittivity at

finite magnetic field

Substrate dielectric permittivity

- Magnetic field phase diagram

Approach 1 (preliminary)

???

???

Magnetic field

Finite temperature

Impurities

2-3-4 layers

Conductivity

Viscosity – Entropy

Optical properties

Critical indices

Conductivity of nanotube

What can be done in

the field theory approach

n

FE v

substrate

graphene

HH

H

Graphene changes its properties when an external magnetic field

is applied, we can numerically simulate all that

Parallel magnetic field (Aleiner, Kharzeev, Tsvelik 2007)

Ferromagnetic substrate

graphene

magnetic head

Trajectory of the magnetic head

Along the trajectory of the magnetic head graphene becomes

the conductor!

We can draw (construct) chips! All that we can simulate on

computers

Mobius carbon is a topological insulator?

ArXiv: 0906.1634

2R

Dependence of conductivity on the

radius of nanotube and

on magnetic field

B

Graphyne Competition for Graphene: Graphynes with

Direction-Dependent Dirac Cones

Daniel Malko, Christian Neiss, FrancescVines,

and Andreas Gorling

PRL 108, 086804(2012)

PHYSICAL REVIEW LETTERS

24 FEBRUARY 2012

Discussion Sessions

Tuesday 13 November 16:30 - …

Gerald Dunne and Yoshimasa Hidaka

Landau-level structure in QCD. Questions: To what extent is the Landau-level

picture applicable in QCD as an interacting theory? Is the LLL approximation valid

for strong magnetic fields, and does physics reduce to a 1+1 dimensional theory

here? If so, does the Mermin-Wagner theorem become effective? Is this visible in

the Dirac eigenmodes?

Wednesday 14 November 16:30 - …

Andreas Schmitt and Ingo Kirsch

Introduction to the ads/qft approach and comparison to lattice. Questions: Is there

any input from the lattice side, that could be used to fix certain free parameters of

the holographic approach, and what are the observables that we can compare?

Discussion Sessions

Thursday 15 November 16:30 - …

Dmitri Kharzeev and Vladimir Skokov

Chiral magnetic effect. Questions: Is there consensus about CME signatures in

experimental results from heavy ion colliders? What are the possible

interpretations of these data? What are the motivated theoretical suggestions for

ALICE to measure from the CME-interested community (becoming especially

actual after ALICE upgrade)? Is it resonable to look at higher order sin-harmonics

and their correlators? Is it reasonable to study their averages not over set of all

event but over some subsets?

Friday 16 November

09:00 - 09:40 Edward Shuryak

QCD topology near and above T_c

09:40 - 10:20 Discussion session

Maxim Chernodub, Yoshimasa Hidaka, Arata Yamamoto

Superconducting vacuum in strong magnetic field, does it exist or not?

10:20 - 10:40 Coffee break

10:40 - 11:20 Final discussion

All participants of the workshop

Talk of Eduardo Fraga => Wednesday