Relativistic and Proximity Effect in Graphene Materials (II)

Malek Zareyan

Advanced School on Recent Progress in Condensed IPM, 7-8 TIR 1391 The Nobel Prize in Physics 2010

Andre Geim Konstantin Novoselov

The Nobel Prize in Physics 2010 was awarded jointly to Andre Geim and Konstantin Novoselov "for groundbreaking experiments regarding the two-dimensional material graphene"

6/28/2012 2 Graphene

6/28/2012 3 Graphene

TEAM image of graphene

6/28/2012 4 Graphene Electronic Structure

n

EF Dirac point D p

ε (k) = ±v k

At low energies electrons as massless Dirac fermions with a pseudospin chirality Relativistic Fermions in Condensed Matter!!!

[Novesolov et al, Nature 438, 197 (2005); Zhang et al, Nature 438, 201 (2005); …]

6/28/2012 5 Era of Dirac Materials

[Nature 483, 302–305 (2012)].

6/28/2012 6 6/28/2012 7 6/28/2012 8 6/28/2012 9 Sub-lattice pseudo-spin chirality

|A>= Α = Β Α Α |B>= Β = Β Β Α k ϕk

Α

|k>=|A>+exp(iϕk)|B>

Chirality links direction of pseudospin to momentum direction

6/28/2012 10 Graphene Electronic Structure

n E Dirac point D F p

ε (k) = ±v k ψ K   A  K   ψ    uˆ = B σ ⋅ p 0     K '    ψ H = vF    , H u = ε u  A  0 −σˆ ⋅ p  K '    ψ B 

[Novesolov et al, Nature 438, 197 (2005); Zhang et al, Nature 438, 201 (2005); …] Electron (n) and Hole (p)-doped graphene

  1 ∂ε (k ) v =   ∂k ˆ n Electron-Like v ˆ = k σ ⋅kˆ = +1 EF DiracΑ point D p

Hole-Like v ˆ = − k ˆ : a hole moves Α in opposite direction of its momentum σ ⋅kˆ = −1 ε (k) = ±v k

6/28/2012 12 Klein tunnelling

Reflection-less Klein tunnelling of normally incident chiral electrons through an electrical p-n barrier

EF<0

EF>0 ve ve

pe pe

n graphene p graphene

[M. I. Katsnelson et al., Nat. Phys.(2006); Cheianov and Fal’ko PRB (2006);…..]

6/28/2012 13 Klein tunnelling

[M. I. Katsnelson, K. S. Novesolov A. K. Geim, Nature Phys. 2, 620 (2006);…..]

6/28/2012 14 Klein tunnelling is a negative refraction process

EF<0 EF>0 n p pe pe

ve ve

6/28/2012 15 Proximity induced superconductivity and spin-polarization in graphene Ti/Al (10/70nm) superconducting bilayer (Tc~1.3 K) on top of graphene sheet

High quality graphene FS structures seems feasible

[N. Tomboros et al (van Wees group), Nature 448, 571(2007)] [Also Hill et al, (2006); Ohishi et al (2007),Shiraishi [Heersche et al, Nature 446, 56-59 (2007);… ] talk; Jozas et al, PRL (2008);….] 6/28/2012 16 6/28/2012 17 6/28/2012 18 Spin Chiral Graphene : Eex > EF

n p

ky EF

kx Carriers with different spins are of different electron- and hole-like

6/28/2012 19 h>EF

FG h SG ε/∆=1 ε / ∆ =1 2

ε/∆=0

e

Exchange field-induced enhancement of Andreev conductance: Ferromagnetic ordering amplifies superconductivity!!!

6/28/2012 20 Theory of superconductivity in graphene

[N. Tomboros et al (van Wees group), Nature 448, 571(2007)] [Also Hill et al, (2006); Ohishi et al (2007),Shiraishi [Heersche et al, Nature 446, 56-59 (2007);… ] talk; Jozas et al, PRL (2008);….] 6/28/2012 21 Local pairing interaction: orbital part s-wave (symmetric)

Bernal Stacking: Pseudospin part is anti-symmetric

Pauli exclusion principle: Spin-Triplet State

Pair wave function: s-wave Spin-Triplet state!!!!

Partial pairing: gapless property: exotic thermodynamics

6/28/2012 22 Temperature-induced condensation! Entropy of S (ordered) state can be higher than the N (less ordered) state!

6/28/2012 23 matter

6/28/2012 24 Quark matter

6/28/2012 25 Color superconductivity in QCD

State of matter at highest densities and low temperatures

Interlayer pairing in graphene may simulate color superconducting phase of quark matter

6/28/2012 26 Variety of pairing pattern between

6/28/2012 27 Interlayer superconductivity in Trilayer graphene

ABA stacking ABC stacking

[M. V. Hosseini and M. Z., submitted (2012).]

6/28/2012 28 Conclusion

• Characteristics of Relativistic Quantum Physics affect Ferromagnetism and Superconductivity in a Fundamental Way:

- Spin Chiral Material

- Exchange Field Induced Enhanceme of Spin-Singlet Superconductivity

- Spin Lens

- s-Wave Spin-Triplet Superconductivity

- Temperature Induced Condensation

- Superconducting State with an Entropy Higher than the Normal State

6/28/2012 29 Acknowledgment to the Founders of IASBS

The 20th Anniversary of IASBS

6/28/2012 30