Thermoelectricity and Heat Transport in Graphene and Other 2D Nanomaterials

I. LOW-ENERGY ELECTRON EXCITATIONS IN GRAPHENE
1.1. Dirac equation for chiral fermions
1.2.1. Tight binding scheme
1.2.2. Density of electron states in graphene
1.3. Berry phase and topological singularity in graphene
1.4. Klein paradox and chiral tunnelling.

II. THERMAL TRANSPORT OF CHARGE CARRIERS
2.1. Components of the heat transport
2.2. Modelling of heat transport of charge carriers in graphene and carbon nanotube devices
2.3. Quantum confined Stark effect
2.4.  PT-invariance the Dirac Hamiltonian
2.5.  Heavy chiral fermions at zigzag edges of graphene stripe

III. PHONON TRANSPORT AND HEAT CONDUCTIVITY
3.1. Phonon modes in the two-dimensional graphene
3.2. Phonon spectra in graphene, and graphene nanoribbons
3.3. The phonon transport in two-dimensional crystals
3.4. Momentum diagram of phonon transport in graphene
3.5. Thermal conductivity due to phonons in graphene nanoribbons

IV. EXPERIMENTAL STUDY OF THE THERMAL TRANSPORT
4.1. Raman scattering
4.2. Role of the degrees of freedom
4.3. Molecular vibrations and infrared radiation
4.4. Various processes of light scattering
4.5. Stokes and anti-Stokes scattering
4.6. Raman scattering versus fluorescence
4.7. Selection rules for Raman scattering
4.8. Raman amplification and Stimulated Raman scattering
4.9. A requirement of the coherence
4.10. Practical applications
4.11. Higher-order Raman spectra
4.12. Raman spectroscopy of graphene
4.13. Kohn anomalies, double resonance, and D and G peaks
4.14. Deriving the electron–phonon coupling from Raman line width
4.15. Raman spectroscopy of graphene and graphene layers
4.16. Failure the adiabatic Born–Oppenheimer approximation and the Raman spectrum of doped graphene
4.17. Influence of the atomic and structural disorders
4.18. Graphene ribbons and edges

V. ROLE OF STRUCTURAL DEFECTS AND IMPERFECTIONS
5.1. Pseudospin conservation during the scattering of chiral fermions
5.2. Phonon drag effect
5.3. Screening by interacting electrons
5.4. Plasma oscillations
5.5. Plasma excitations in graphene
5.6. Electron-impurity scattering time in graphene
5.7. Scattering of phonons in a few-layer graphene

VI. MANY BODY EFFECTS IN GRAPHENE
6.1. Electron-electron interaction
6.2. Electron self-energy effects
6.3. Quasi-particle excitations
6.4. Numeric results
6.5. Excitons in graphene and in the other atomic monolayers
6.6. Wannier-Mott excitons
6.7. Excitonic states
6.8. Experimental observation of excitons in graphene and in the other atomic monolayers
6.9. Electron scattering on indirect excitons
6.10. Tomonaga–Luttinger liquid
6.11. Probing of intrinsic state of one-dimensional quantum well with a photon-assisted tunneling
6.12. The TLL tunneling density of states of a long quantum well
6.13. Identifying the charge and the spin boson energy levels
6.14. Useful relationships

IX. THERMOELECTRIC DEVICES BASED ON GRAPHENE AND OTHER ATOMIC MONOLAYERS
7.1. Thermoelectric phenomena on nanoscale
7.2. Performance and efficiency of the thermoelectric device
7.3. Quantum theory of electronic thermal transport
7.4. Electron transport and elastic collisions
7.5. Reversible Peltier effect in carbon nano-junctions
7.6. Thermoelectric figure of merit and Fourier law
7.6.1. The linear heat flow
7.6.2. The cooling power.
7.6.3. Seebeck coefficient.
7.6.4. Electron thermal conductivity.
7.6.5. Figure of merit.
7.7. Phonon Transport and Thermal Conductivity
7.7.1. Estimation of phonon thermal conductivity.
7.8. Recent experiments for measuring the thermal conductivity of graphene
7.9. Microscopic model of the thermoelectric effect
7.9.1. The electron Green function of infinite space.
7.9.2. The d.c. electric current.
7.9.3. The d.c. heat current.
7.9.4. Fourier Law.
7.9.5. The cooling efficiency of a gated stack of nanotubes.
7.9.6. Cooling Power.
7.10. Converting the heat into electricity by a graphene stripe with heavy chiral fermions
7.11. Blocking the phonon flow by multilayered electrodes
7.12. Molecular dynamics simulations
7.13. Non-equilibrium thermal injection
7.13.1. Transparency of the H/RR interface
7.16. Perspectives of Thermoelectric Research for Graphene

XI. OTHER ATOMIC MONOLAYERS
8.1. Heat transport in atomic monolayers
8.2. A few-layered materials
8.2.1. Hexagonal boron nitride (h-BN)
8.2.2. Transition metal dichalcogenides
8.2.3. Chalcogenides of group III, group IV and group V
8.2.4. Synthesis
8.2.5. Bottom-up fabrication
8.2.6. Electronic bandstructure of atomic monolayers
8.3. Electric transport in nanodevices
8.4. Electronic transport versus scattering mechanisms
8.5. TMDC thermoelectric devices
8.6. Perspectives of the TMDC transducers
8.7. Vibrational and optical properties of TMDCs
8.7.1. Transparent and flexible transducers
8.7.2. Photodetection and photovoltaics
8.7.3. Emission of light
8.8. The future thermolectric applications of 2D materials

Thermoelectricity and Heat Transport in Graphene and Other 2D Nanomaterials describes thermoelectric phenomena and thermal transport in graphene and other 2-dimentional nanomaterials and devices. Graphene, which is an example of an atomic monolayered material, has become the most important growth area in materials science research, stimulating an interest in other atomic monolayeric materials.

The book analyses flow management, measurement of the local temperature at the nanoscale level and thermoelectric transducers, with reference to both graphene and other 2D nanomaterials. The book covers in detail the mechanisms of thermoelectricity, thermal transport, interface phenomena, quantum dots, non-equilibrium states, scattering and dissipation, as well as coherent transport in low-dimensional junctions in graphene and its allotropes, transition metal dichalcogenides and boron nitride.

This book aims to show readers how to improve thermoelectric transducer efficiency in graphene and other nanomaterials. The book describes basic ingredients of such activity, allowing readers to gain a greater understanding of fundamental issues related to the heat transport and the thermoelectric phenomena of nanomaterials. It contains a thorough analysis and comparison between theory and experiments, complemented with a variety of practical examples.

• Shows readers how to improve the efficiency of heat transfer in graphene and other nanomaterials with analysis of different methodologies
• Includes fundamental information on the thermoelectric properties of graphene and other atomic monolayers, providing a valuable reference source for materials scientists and engineers
• Covers the important models of thermoelectric phenomena and thermal transport in the 2D nanomaterials and nanodevices, allowing readers to gain a greater understanding of the factors behind the efficiency of heat transport in a variety of nanomaterials

Materials scientists, solid state physicists and engineers working in the areas of carbon nanomaterials and seeking to increase their efficiency with a view to industrial application