Fundamentals of Condensed Matter Physics

Contents
Preface
Part I Basic concepts: electrons and phonons
	1 Concept of a solid: qualitative introduction and overview
		1.1 Classification of solids
		1.2 A first model of a solid: interacting atoms
		1.3 A second model: elementary excitations
		1.4 Elementary excitations associated with solids and liquids
		1.5 External probes
		1.6 Dispersion curves
		1.7 Graphical representation of elementary excitations and probe particles
		1.8 Interactions among particles
	2 Electrons in crystals
		2.1 General Hamiltonian
		2.2 The Born–Oppenheimer adiabatic approximation
		2.3 The mean-field approximation
		2.4 The periodic potential approximation
		2.5 Translational symmetry, periodicity, and lattices
	3 Electronic energy bands
		3.1 Free electron model
		3.2 Symmetries and energy bands
		3.3 Nearly-free electron model
		3.4 Tight-binding model
		3.5 Electron (or hole) velocity in a band and the f-sum rule
		3.6 Periodic boundary conditions and summing over band states
		3.7 Energy bands for materials
	4 Lattice vibrations and phonons
		4.1 Lattice vibrations
		4.2 Second quantization and phonons
		4.3 Response functions: heat capacity
		4.4 Density of states
		4.5 Critical points and van Hove singularities
	Part I Problems
Part II Electron interactions, dynamics, and responses
	5 Electron dynamics in crystals
		5.1 Effective Hamiltonian and Wannier functions
		5.2 Electron dynamics in the effective Hamiltonian approach
		5.3 Shallow impurity states in semiconductors
		5.4 Motion in external fields
		5.5 Effective mass tensor
		5.6 Equations of motion, Berry phase, and Berry curvature
	6 Many-electron interactions: the homogeneous interacting electron gas and beyond
		6.1 The homogeneous interacting electron gas or jellium model
		6.2 Hartree–Fock treatment of the interacting electron gas
		6.3 Ground-state energy: Hartree–Fock and beyond
		6.4 Electron density and pair-correlation functions
		6.5 g(r, r′) of the interacting electron gas
		6.6 The exchange-correlation hole
		6.7 The exchange-correlation energy
	7 Density functional theory (DFT)
		7.1 The ground state and density functional formalism
		7.2 The Kohn–Sham equations
		7.3 Ab initio pseudopotentials and density functional theory
		7.4 Some applications of DFT to electronic, structural, vibrational, and related ground-state properties
	8 The dielectric function for solids
		8.1 Linear response theory
		8.2 Self-consistent field framework
		8.3 The RPA dielectric function within DFT
		8.4 The homogeneous electron gas
		8.5 Some simple applications
		8.6 Some other properties of the dielectric function
	Part II Problems
Part III Optical and transport phenomena
	9 Electronic transitions and optical properties of solids
		9.1 Response functions
		9.2 The Drude model for metals
		9.3 The transverse dielectric function
		9.4 Interband optical transitions in semiconductors and insulators
		9.5 Electron–hole interaction and exciton effects
	10 Electron–phonon interactions
		10.1 The rigid-ion model
		10.2 Electron–phonon matrix elements for metals, insulators, and semiconductors
		10.3 Polarons
	11 Dynamics of crystal electrons in a magnetic field
		11.1 Free electrons in a uniform magnetic field and Landau levels
		11.2 Crystal electrons in a static B-field
		11.3 Effective mass and real-space orbits
		11.4 Quantum oscillations: periodicity in 1/Band the de Haas–van Alphen effect in metals
	12 Fundamentals of transport phenomena in solids
		12.1 Elementary treatment of magnetoresistance and the Hall effect
		12.2 The integer quantum Hall effect
		12.3 The Boltzmann equation formalism and transport in real materials
		12.4 Electrical and thermal transport with the linearized Boltzmann equation
	Part III Problems
Part IV Many-body effects, superconductivity, magnetism, and lower-dimensional systems
	13 Using many-body techniques
		13.1 General formalism
		13.2 Interacting Green’s functions
		13.3 Feynman diagrams and many-body perturbation theory techniques
	14 Superconductivity
		14.1 Brief discussion of the experimental background
		14.2 Theories of superconductivity
		14.3 Superconducting quasiparticle tunneling
		14.4 Spectroscopies of superconductors
		14.5 More general solutions of the BCS gap equation
		14.6 Field theoretical methods and BCS theory
	15 Magnetism
		15.1 Background
		15.2 Diamagnetism
		15.3 Paramagnetism
		15.4 Ferromagnetism and antiferromagnetism
		15.5 Magnetism in metals
		15.6 Magnetic impurities and local correlation effects
	16 Reduced-dimensional systems and nanostructures
		16.1 Density of states and optical properties
		16.2 Ballistic transport and quantization of conductance
		16.3 The Landauer formula
		16.4 Weak coupling and the Coulomb blockade
		16.5 Graphene, carbon nanotubes, and graphene nanostructures
		16.6 Other quasi-2D materials
	Part IV Problems
References
Index