KUK - LMS

Syllabus

MODULE NO / UNIT	COURSE SYLLABUS CONTENTS OF MODULE	NOTES
Course Code: PHY 403A Course Name: Condensed Matter Physics-II
1	Electron Transport Phenomenon (12 hrs.) Motion of electrons in bands and the effective mass tensor (semi-classical treatment); Currents in bands and holes; Scattering of electrons in bands (elastic, inelastic and electron-electron scatterings); The Boltzmann equation, Relaxation time ansatz and linearized Boltzmann equation; Electrical conductivity of metals, Temperature dependence of resistivity and Matthiesen's rule; Thermoelectric effects, Thermopower, Seebeck effect, Peltier effect, Thomson effect, The Wiedemann-Franz law.
2	Nanostructures and Electron Transport (14 hrs.) Nanostructures; Imaging techniques for nanostructures (principle): Electron microscopy (TEM, SEM), Optical microscopy, Scanning tunneling microscopy, Atomic force microscopy; Electronic structure of 1D systems: 1D sub-bands, Van Hove singularities; 1D metals- Coulomb interactions and lattice couplings; Electrical transport in 1D: Conductance quantization and the Landauer formula, Two barriers in series- Resonant tunneling, Incoherent addition and Ohm's law, Coherence-Localization; Electronic structure of 0D systems (Quantum dots): Quantized energy levels, Semiconductor and metallic dots, Optical spectra, Discrete charge states and charging energy; Electrical transport in 0D- Coulomb blockade phenomenon.
3	Beyond the independent electron approximation (12 hrs.) The basic Hamiltonian in a solid: Electronic and ionic parts, The Born-Oppenheimer Approximation; The Hartree method, Connection with variational principle; Exchange: The Hartree-Fock approximation, Koopmans’ theorem; Application of Hartree and Hartree-Fock methods to homogeneous electron gas- One-electron energy, Band width, DOS, Effective mass, Ground-state energy, Exchange energy; Concept of correlation energy; Screening in a free electron gas: The dielectric function, Thomas-Fermi theory of screening, Calculation of Lindhard response function, Lindhard theory of screening, Friedel oscillations, Frequency dependent Lindhard screening (no derivation).
4	Many-particle physics: Second quantization formulation (14 hrs.) Many-particle systems; The Schrodinger equation in first quantization, Expansion of wave function in basis of single-particle wave functions, Symmetry of expansion coefficients, Normalized symmetric and anti-symmetric wave functions; Second quantization: Transformation of Schrodinger equation to occupation number representation for bosons and fermions, Many-particle Hilbert space, and creation and destruction operators, Second-quantized Hamiltonian; Fields, Hamiltonian and number-density operators in terms of field operators; Application to degenerate homogeneous electron gas: First and second-quantized Hamiltonian operators, rs parameter, Ground-state energy in first-order perturbation theory, Contact with the Hartree-Fock result, Exchange energy.