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Table of contents
Notations
Introduction
1 Electrons and phonons in 2D materials
1.1 Two-dimensional materials
1.2 Electrons and phonons in two dimensions
1.2.1 2D non-interacting electron gas in fixed ions
1.2.2 2D electron gas: electron-electron interactions
1.2.3 2D phonons
1.2.4 Electron-phonon interactions
1.3 Simulation challenges
2 Electron-phonon interactions in graphene
2.1 Electrons and phonons models
2.1.1 Dirac Hamiltonian for electrons
2.1.2 Phonons
2.2 Electron-phonon coupling matrix elements
2.2.1 Coupling to canonical phonon modes at
2.2.2 Coupling to DFT phonon modes at
2.2.3 Coupling to inter-valley A01 mode at K
3 Ab initio calculations of EPC in graphene
3.1 EPC parameters at finite phonon momentum from DFPT
3.2 EPC in the tight-binding model
3.3 EPC at zero momentum from static strain method
3.3.1 Acoustic EPC and strain-induced potentials
3.3.2 Calculation of strain-induced potentials at the DFT level
3.3.3 EPC parameters at the GW level
4 Static screening in 2D
4.1 Static dielectric function
4.1.1 Three-dimensional materials
4.1.2 2D materials
4.1.3 2D-periodic materials with finite thickness
4.1.4 2D materials periodically repeated in the third dimension
4.2 Static screening properties of graphene
4.2.1 Analytical and semi-numerical solutions
4.2.2 DFPT LDA solution
4.3 Results in graphene
4.3.1 Importance of cutting off the Coulomb interactions
4.3.2 Comparison of analytical and LDA methods: band structure effects
4.3.3 Estimation of the screened deformation potential
5 DFT/DFPT for 2D materials in the FET setup
5.1 Description of a 2D material doped in the FET setup
5.2 Treatment of the periodic images
5.2.1 Inadequacy of 3D PBC
5.2.2 Isolate the layers with 2D Coulomb cutoff
5.3 Implementation
5.3.1 KS Potential
5.3.2 Total Energy
5.3.3 Forces
5.3.4 Phonons and EPC
5.4 Results in graphene
5.4.1 Finite frequency for ZA phonons at
5.4.2 Screening
5.4.3 Finite coupling to out-of-plane phonons
6 Phonon-limited resistivity of graphene
6.1 Boltzmann transport theory
6.2 EPC included in the transport model
6.3 Results
6.4 Approximated solutions
6.4.1 Semi-analytical approximated solution
6.4.2 Additivity of resistivities
Conclusion
Appendices
A Computational Methods
B EPC in TB model
C Analytical susceptibility
D 2D Coulomb cutoff at G = 0
E Boltzmann transport equation
Résumé en français
Bibliography
