Condensed Matter Physics–I

Hartree-Fock Theory: The basic Hamiltonian in a solid: electronic and ionic parts, the adiabatic approximation;Single-particle approximation of the many-electron system; single product and determinantal wave functions, Occupation number representation; matrix elements of one and two-particle operators; The Hartree-Fock (H-F) method; the one electron H-F equation; exchange interaction and Fermi hole; Coulomb correlation; the H-F ground state energy.

Quasi electrons and Plasmons: The interacting electron gas; The coulomb interaction; The Hartree-Fock approximation for the electron gas; Exchange Hole; Screeming, Plasmons; Quasi-electrons; The dielectric constant of the electron gas.

Magnons Absence of magnetism in classical statistics; Origin of the exchange interaction; Direct exchange, superexchange, indirect exchange and itinerant exchange; Spin-waves in ferromagnets-magnons, spontaneous magnetization, thermodynamics of magnons; Spin waves in lattices with a basis-ferri- and antiferromagnetism; Measurement of magnon spectrum; Ordered magnetism of valence and conduction electrons, Stoner’s criterion for metallic ferromagnet.

Basics of DFT, Comparison with conventional wave function approach, Hohenberg-Kohn Theorem; Kohn-Sham Equation; Thomas-Fermi approximation and beyond: LDA and GGA; Application of DFT in a many body calculation and its reliability.

Free electron theory (qualitative idea), variation of density of states with energy, variation of density of state and band gap with size of crystal. Electron confinement in infinitely deep square well, confinement of two and one dimensional well, idea of quantum well structure, tunnelling through potential barrier, quantum dots, quantum wires, introduction to fullerenes and graphenes.