plasmino in graphene at finite temperature?

Daqing Liu

Changzhou University, China

Outline

Collective Excitations in hot QCD Possible collective excitations in warm grap

hene Outlook

In QCD, about T>150Mev, there is a first phase transition (QCDPT). i.e.,

< 0;Tj¹q(x)q(0)j;0;T >=

(0; in quark gluon plasma phaseT > Tc

¡ (:23Gev)3: in hadron phaseT < Tc

L.S. Kisslinger and D. Das, arXiv:1411.3680

Two ways to get so high temperature

Early universe

Latent heat.

heavy ion collision, RHIC and LHC

q

k

k q

qPlasmon

In QGP, there are two collective excitations

q q p q

pPlasmino

Some literatures on plasmino

arXiv:1208.6386

arXiv:1109.0088

arXiv:hep-ph/0509339

Possilbe collective excitations in graphene

Possible collective excitations in warm graphene

Plasmon

1) F.H.L. Koppens, D.E. Chang and F.J.G. de Abajo, Graphene plasmonics: A platform for stron Light-matter interactions, Nano Lett. 11, 3370 (2011)

2) S.D. Sarma and E.H. Hwang, Collective modes of the massless Dirac plasma, Phys.Rev.Lett. 102, 206412 (2009)

3) Y. Liu, R.F. Willis, K.V. Emtsev and T. Seyller, Plasmon dispersion and damping in electrically isolated two-dimesenional charge sheets, Phs. Rev. B78 201403(R) (2008)

4) S.D. Sarma and Q. Li, Intrinsic plasmon in 2D Dirac materials, Phys. Rev. B. 87, 235418 (2013)

Propagators

Fermion

where

Potential

iSF (p0;p) = (p0+®¢p)[ ip02¡ p2 ¡ 2¼f+(p)±(p

02 ¡ p2)]

S0F¡ 1 =p0 ¡ ®¢p

Feynman diagram for carrier self-energy correction

q q p q

p

We also focus on the case q¿ q0;

As for the correction from temperature, there are two cases,

High temperature, Debye screening

Low temperature (The influence of T on V is neglected)

Phys. Rev. B 85, 085420 (2012)

Phys.Lett. B359 (1995) 148-154

§ = 18¼2Rd2pf+(p0)

(1-®¢p0=p0)V(q0+p0;p) ¡ (1+®¢p0=p0)V(q0 ¡ p0;p)

This is the main challenge of the topic. We set

To calculate the correction we introduce invariants

We have

and the domain of the integration

and

u= p;v= p0

px =q2+u2¡ v2

2q py = §p((q+u)2¡ v2)(v2¡ (q¡ u)2)

2q

，

dpxdpy = 4uvp((q+v)2¡ u2)(u2¡ (q¡ v)2)

q = (q;0)

v 2 (0;q);u 2 (q¡ v;q+v) v 2 (q;1 );u 2 (v ¡ q;v+q)

The scalar part, which is an odd function of ,q0

The self-energy correction can be divided into two parts,

a= ®scT 3¼q02 [i¼

3³(3)2jq0j +

2cqq02 (

7¼4T40q +3³(3))]

The spinor part, which is an even function of ,q0

¡ b®¢q

b= ®s¼[0:5

Tq ¡ 0:06

T 2q2 +

c2q2

q02 (0:35Tq +0:9

T 3q3 )]

aq0

c= ¼®sgs8

？

In RPA, the full carrier propagator is

S(0)¡ 1F =q0 ¡ ®¢q

S¡ 1F (q0;q) = (1¡ a)q0 ¡ (1¡ b)®¢q

The zero point is at

q02= (b¡ 1a¡ 1

)2q2 (1)

T=0.3

To simplify the discussion, we assume ®s =2:1; c=¼®sgs8

We have two solutions

T=0.5

q02 =4:T +0:1q+0:02q2

Tq01 =3:78T +0:43q¡ 0:02

q2

T

T=0.3. The fit curve is

3:78T +0:43q¡ 0:02q2

T+

T2

0:31T +91q

The difference between with 0.06 term and wothout 0.06 term

Outlook

Graphene: The TRUE bridge between high- and low-energy physics

The (anti-)plasmino states in graphene can help us to understand (anti-)plasmino in QGP and hot QCD.

Thanks for your attention