Develops the one-particle formalism within Hartree–Fock and density functional frameworks,and examines validity bounds. The effects of exchange and correlation are also discussed, bringing out the idea of an exchange hole for fermions.

Explains the effect of dimensionality on electronic susceptibilities, including nesting effects. It describes the onset of instabilities, as manifest in the Peierls phenomenon, and delineates their emergent order parameters. It also introduces the idea of a Kohn anomaly, and derives the giant Kohn anomaly as a consequence of the one-dimensional Peierls instability.

Introduces the concept of Cooper pairing and develops a diagramatic approach to the Cooper instability. The BCS Hamiltonian is then constructed and solved with the aid of the Bogoliubov–Valatin transformation. Nambu–Gorkov formalism is introduced, and the Gor'kov anomalous Green function constructed. The Ginzburg–Landau formulation is derived from microscopic theory using the coherent-state partition function and the HS transformation. Detailed account of the Ginzburg–Landau perspective of superconductivity is given, ending with a derivation of the Meissner effect and an explanation of the Anderson–Higgs mechanism.

Reveals limitations of noninteracting fermion formulation. The chapter also introduces Landau’s Fermi liquid parameters and the conceptual basis of quasiparticles. Some suscptibilities are derived. Microscopic justification is explained.

Treats the Bose-Einstein condensation, and explains superfluidity from the Bogoliubov and Ginzburg-Landau perspectives. It also describes the concept of spontaneous symmetry breaking and Goldstone modes.

Develops the formalism of electron–phonon interaction within the Matsubara framework.

Presents relevant aspects of topology, such as homeomorphism, fiber and vector bundles, connection and curvature, parallel transport, and holonomy, and ends with establishing the relevance of topology to physics.

Dirac materials and Dirac fermions are presented. Graphene, with its Dirac points and cones, and the Dirac fermion Hamiltonian in the vicinity of the K-points are described. Time-reversal symmetry-breaking Chern insulators, with special focus on Haldane’s model, are presented. The quantum spin Hall effect, as manifest in the graphene-like model of Kane–Mele, with strong spin–orbit (SO) coupling, is outlined. A detailed description of Weyl semimetals is given.

Outlines the different methods of electronic band calculations with detailed presentation of the pseudopotential and tight-binding methods, including Harrison’s matrix element scaling.

Presents a Hartree–Fock perturbative treatment of the interacting electron gas within the jellium model and highlights its drawbacks. It also introduces the concept of the random phase approximation.

Covers ferromagnetic and antiferromagnetic insulators, describing the nature of their respective ground states and deriving their spin-wave excitation spectra with the aid of the Holstein–Primakoff transformation.

Develops the many-body one-particle Green function, and explains its physical interpretation in terms of the spectral function, self-energy, and quasiparticle. lifetime. Its application in angle-resolved photoemission spectroscopy is presented in detail. The time-evolution operator in the interaction picture is derived, and time-ordering and adiabatic switching-on are introduced as precursor tools to construct the Feynman–Dyson many-body perturbation theory. A detailed account of Wick’s theorem, normal ordering, and contractions is outlined. Feynman diagrams are constructed, and the emergence of the infinite Dyson series from irreducible diagrams is outlined. Two-particle Green function and the particle-hole excitation spectra are developed. Diagramatic application of RPA for interacting systems is described. The finite-temperature Matsubara Green function is introduced and developed, together with its Fourier series representation and the evaluation of Matsubara sums.

Presents a detailed account of phonons, lattice dynamics and experimental techniques for measuring phonon dispersions. It derives the electron-phonon coupling in terms of symmetry-adapted (or normal) mode coordinates. The electronic contributions to phonon energies are developed in terms of the density-density response function. The developed expressions are then pedagogically used to construct phenomenological models for phonons in semiconductors and insulators "pseudocharge models”. The different experimental probes used in measuring the static and dynamic structure factors of solids are introduced.

Describes Berry’s phase, connection, and curvature, and derives the Chern topological number. It presents two pedagogically important but distinct examples: a two-level system, with its concomitant “magnetic monopole," and the molecular Aharonov–Bohm effect, where the interplay between the quantum electronic andionic motions leads to fascinating topological manifestations.

Presents a short review of the historical development of topology in condensed matter physics.