Electronic Theory of Solids

Week 1 : Free electron theory of metals, Fermi-Dirac distribution, Free electrons, boundary conditions, Density of levels in 1, 2 & 3 dimensions, Fermi momentum and Fermi energy, Connection between electron density and Fermi energy. 

Week 2 : Independent electron systems, degenerate fermi gas: Specific heat, semiclassical theory of transport, Drude theory and Hall effect. Electronic properties of solids: the two-atom solid, theory of electrons in an N-atom solid, linear combination of atomic orbitals – band formation

Week 3 : Periodic potential, Bloch's theorem, tight binding approximation. Brillouin zones for square, triangular, cubic lattices and energy bands in reduced zone scheme. 

Week 4 : Fermi surface in several cases, instabilities of the Fermi surface. Novel electronic structures: graphene and carbon nanotubes. Concept of symmetries and their relevance in emergent electronic properties, topological insulators.

Week 5 : Elementary concepts of low dimensional electron gas, quantum dot, 1D and 2D electron gas introduced. 2D electrons in a magnetic field, integer quantum hall effect. Spin filtering and magnetoresistance. Spintronics and its applications. Future directions in spin- or valley-tronics. 

Week 6 : Magnetism and its origin, magnetization and susceptibility, dia-, para- and ferro-magnetism. Larmour diamagnetism.

Week 7 : Hund’s rule and paramagnetism, Van Vleck paramagnetism, Curie’s law. Thermal properties of magnetic insulators, Pauli paramagnetism.

Week 8 : Magnetic interactions, two-electron system, spin-spin interactions – exchange interaction, direct, super and itinerant exchange. 

Week 9 : Magnetic order, Ising, XY and Heisenberg spin models, mean-field theory, ground states and thermodynamics.

Week 10 : Phenomenology of Superconductors, Superconductivity in metals and alloys, New Superconductors, Zero Resistance, Meissner Effect, London equation and two- fluid model. Attractive interaction, Cooper problem – instability of the Fermi surface, pair formation and binding energy. 

Week 11 : BCS theory, tunneling, SC gap and transition temperature. Sp. heat jump at Tc, coherence length and penetration depth: electrodynamics of superconductors, Type-I and II SC, vortices.

Week 12 : Quantum interference, Josephson effect, SC junctions, squid and its application. Novel superconductors.