Physics of graphene described by Dirac equation

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

General description of crystal. Tight-binding model of graphene and its approximation in terms of Dirac equation.Transport of Dirac fermions in graphene in presence of external fields and related phenomena. Bilayer graphene, its description and properties in the external magnetic field. Carbon nanotubes, their classification. Basic description of graphene nanoribbons,boundary conditions and energy. Dirac fermions in curved space, fullerenes. Other Dirac materials.

Requirements:

Syllabus of lectures:

- Basic description of crystals, Bloch theorem, covalent bonds, tight-binding model

- Emergence of Dirac equation in physics of graphene

- Transport properties in magnetic field

- Landau levels

- quantum Hall effect

- Transport properties in electric field

- Klein tunneling, super-Klein tunneling

- circular quantum dots

- Optical absorbtion

- Minimal conductivity

- bilayer graphene, 4x4 Dirac Hamiltonian, effective model 2x2 model

- Landau levels in bilayer graphene

- carbon nanotubes, their classification (metalic,or semiconducting), basic electronic properties (spectrum, absence of backscattering on impurities)

- graphene nanoribbons, general boundary conditions for terminated lattice, special cases: nanoribbons with zigzag, armchair, infinite-mass (MIT) boundary conditions and their spectra

- Dirac fermions in curved space fullerenes

- Other Dirac materials. Dirac fermions in Lieb and Dice lattices, systems with tilted Dirac cones

Syllabus of tutorials:

Study Objective:

Study materials:

Povinná literatura:

[1] M. I. Katsnelson, The Physics of Graphene, Cambridge University Press, 2020

Doporučená literatura:

[1] M. I. Katsnelson, The Physics of Graphene, Cambridge University Press, 2020

[2] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009)

[3] G. Grosso, G. Parravicini, Solid State Physics, Academic Press (2014), second edition

[4] T.O. Wehling, A.M. Black-Schaffer and A.V. Balatsky, Dirac materials, Advances in Physics 63, 176, (2014)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Inženýrství pevných látek (elective course)
• Matematická fyzika (elective course)
• Kvantové technologie (elective course)
• Solid State Engineering (elective course)