Concepts in Magnetism and Superconductivity

ABOUT THE COURSE:The course aims to introduce and work through the underlying concepts behind magnetism and superconductivity. Starting from an electron in a magnetic field, the magnetic response of a collection of atoms in a solid are all worked out. Magnetization and susceptibility in para and diamagnetic cases, their applications and excitations are discussed. Superconductivity: zero resistance, Meissner effect, perfect diamagnetism; BCS theory, energy gap, isotope effect and tunneling experiments worked out. Josephson junctions and their applications, qubits and quantum chips discussed. Novel high-TC superconductor introduced. The emphasis is on working things out from very simple physical concepts.INTENDED AUDIENCE:B Tech, BE, M Tech, ME, MSc, PhDPREREQUISITES:Modern physics and elementary quantum mechanics, basic ideas in condensed matter or solid-state physicsINDUSTRY SUPPORT:Microsoft, IBM, AT&T, Accenture, google quantum AI, Philips, DRDO, Intel, BEL, Infineon technologies, Samsung, LG, Silfab and such others

Week 1: The magnetic moment, Bohr magneton, canonical momentum, Bohr-van Leeuwen theorem. Magnetisation and susceptibility; an isolated atom in a magnetic field, dia, para and ferromagnetic susceptibilities. Ground state of ions – Hund’s rules. Van Vleck paramagnetism. Week 2:Magnetization of a collection of independent ions: Curie’s Law. Adiabatic demagnetization, Pauli paramagnetism. Ions in a solid: Crystal field, Orbital quenching, Jahn-Teller effect. Week 3:Magnetic resonance technique: NMR and ESR, Mossbauer. Long range order, magnetic interactions, relevant energy scales, dipolar interaction and origin of exchange: 2-electron system, singlet-triplet splitting-Spin Hamiltonian. Week 4:Direct exchange, super-exchange, indirect exchange and itinerant exchange. Magnetic impurity, spin-glass and RKKY interaction, magnetic multi-layers and the concept of GMR. Spin models, mean-field theory and exact solution of 1D Ising model. Week 5:Absence of LRO and Mermin-Wagner theorem, Ferromagnetic Heisenberg model, ground state and excitations; Antiferromagnetism and the concept of frustrated spin systems. Week 6:Absence of LRO and Mermin-Wagner theorem, Ferromagnetic Heisenberg model, ground state and excitations; Antiferromagnetism and the concept of frustrated spin systems. Week 7:BCS theory, energy gap, isotope effect, transition temperature, Specific Heat. Type-I, Type-II superconductors, Abrikosov vortices. Week 8:Quantum interference, Josephson effect, superconducting junctions, squid and its applications, qubits and quantum chips. Novel superconductors.