PHYS 051 Thinnest Material In Nature: Graphene

Question 1

Valero N. Kotov

Answer 1

UVM
Date: 20 Oct, 2017
Time: 9:40am-10:10am

Question 2

Graphene

Answer 2

• Made of C atoms

Question 3

• Carbon forms lattices (solids), few structure

Answer 3

• Forms of bonding in carbon
  
  1. Sp^2: graphite
  2. Sp^3: diamond

Question 4

0-D

Answer 4

• Fullerenes / buckyballs
  Zero dimensional
• C20, C60, C540

Question 5

1-D

Answer 5

• Carbon nanotubes

Question 6

3-D

Answer 6

• 3D: Graphite
• Graphene: the mother of all: 2-D sheet > single sheet
• 1mm of graphite > 3 million layers of graphene stacked on top of one another
• Almost perfect carbon web only 1 atom thick

Question 7

Graphene characteristics

Answer 7

• 1st ever atomically thin material (2004)
• Thickness abt 0.1nm
• e- move in graphene as relativistic massless Dirac fermions (like neutrinos)
• E(p) = +-vp
• v = c/300
• E^2 = v^2p^2 + m^2v^4
• m = 0

Question 8

Graphene characteristics (cont)

Answer 8

- Normal conduction: Fermions
   E(p) = p^2/2m
- Graphene: Dirac fermions
   E(p) = +-vp
> Quantum mechanics: wave-particle duality particle wave

Question 9

Main features of graphene

Answer 9

• Atomically thin, high quality 2D material
• Controlled by electric field effect
• Massless Dirac quasiparticles propagate ballistically
• High mobility > 15,000cm^2/Vs; as high as 1,000,000cm^2/Vs in suspended graphene
• No gap (unlike common semi-conductors)

Question 10

Elastic properties: strong & soft material

Answer 10

• Young’s modulus E = 1TPa
• Also tends to: form wrinkles, ripples, fold
  > Flexible / stretchable / foldable electrons

Question 11

New field of 2D materials: van deer Waals heterostructures

Answer 11

• Graphene
• hBN
• MoS_2
• WSe_2

Question 12

Conclusions

Answer 12

• Graphene = first atomically thin material; e- propagate as relativistic particles
• Stretches, bends, wrinkles easily: electronic membrane
• Electron devices: screen, phones, solar panel, flexible electronics