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M.Sc. (Physics) | Curriculum | Subject: Condensed Matter Physics II | Paper Code: 09020403

Curriculum

Subject: Condensed Matter Physics II

Paper Code: 09020403

S No. Topic Learning Objective Teaching Guidelines Methodology Time

(Hrs)

1 ·                        Motion of electrons in bands and the effective mass tensor

·                        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

The student will be able to learn semi classical treatment of motion of electrons in band, transport phenomena and the scattering of electrons in bands To cover the concepts of band structure, relaxation time, effective mass and scattering. Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

3

2 ·                        Electrical conductivity of metals

·                        Temperature dependence of resistivity and Matthiesen’s rule

The student will be able to discuss the conductivity of metals and the temperature dependence of metal resistivity To cover different methods to determine resistivity or conductivity Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

 

3

3 ·                        Thermoelectric effects, Thermopower

·                        Seebeck effect, Peltier effect, The Wiedemann-Franz law.

The student will be able to discuss phenomenon based of thermoelectricity and the laws associated with it. To cover definitions of Thermoelectricity, Seebeck effect and Peltier effect Black board teaching

 

Online lectures

 

Power point presentations

 

 

2

4 ·                     Nanostructures; Imaging techniques (principle)

·                     Electron microscopy (TEM, SEM)

·                     Optical microscopy, Scanning tunneling microscopy

·                     Atomic force microscopy

The students will be able to learn about electron microscopy techniques. To cover construction, working principle and application of particular technique. Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

 

5

5 ·                     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.

The student will learn about electronic structure and transport in 0D and 1Dsolid systems. To cover the concept of 0D and 1D structures, band structure and density of states of different structures. Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

 

 

 

7

6 ·                       The basic Hamiltonian in a solid: Electronic and ionic parts

·                       One-electron model

·                       The adiabatic approximation

The student will be able to learn about total energy in a solid and the effect of a perturbation on the system. ·                       To Cover the determination of Hamiltonian equation and one-electron model Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

3

7 ·                       The Hartree equations, Exchange: The Hartree-Fock approximation

·                       Hartree-Fock theory of free electrons- Ground state energy, exchange energy, correlation energy (only concept)

The student will be able to determine wave function and the energy of a quantum many-body system in a stationary state. To cover introduction to slater determinant and variational method in order to discuss the Hartree-Fock approximation Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

3

8 ·                       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).

The student will be able to calculate the effects of electric field screening by electrons in a solid To cover the difference between Thomas-Fermi and Lindhard theory of screening Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

 

 

4

9 ·                        Many-particle Schrodinger wave equation in first quantization

·                        The single-particle states as basis states

·                        Normalized symmetric and anti-symmetric wave functions

The student will be able to learn the wave mechanical description of many particle system in first quantization To cover the definitions of eigen values, wavefunctions and eigen states. Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

3

10 ·                        Second quantization: Transformation of Schrodinger equation to occupation number representation (both for bosons and fermions)

·                        Many-particle Hilbert space and creation and destruction operators

·                        Field operators, Second-quantized from of number density operator

·                        Application to degenerate electron gas

·                        First and second-quantized Hamiltonian operator

The student will be able to determine wave functions with Boson Symmetry and with Fermion Symmetry in the Occupation Number Representation. To cover the definitions of occupation number, density operator, bosons and fermions Black board teaching

 

Online lectures

 

Power point presentations

 

 

 

 

 

 

 

4

11 ·                        rs parameter, Ground-state energy in first-order perturbation theory

Contact with the Hartree-Fock result, Exchange energy.

The student will be able to determine Ground-state energy in first-order perturbation To cover contact with the Hartree-Fock result and Exchange energy. Black board teaching

 

Online lectures

 

Power point presentations

 

 

3

Books Recommended:

  1. Solid State Physics: An Introduction to Principles of Materials Science (4th Ed.) by H. Ibach andH. Luth
  2. Introduction to Solid State Physics (8th Ed.) by Charles Kittel
  3. Solid State Physics by Neil W. Ashcroft and N. David Mermin
  4. The Wave Mechanics of Electrons in Metals by Stanley Raimes
  5. Quantum Theory of Many-particle Systems by A. L. Fetter and J. D. Walecka
  6. Many-body Quantum Theory in Condensed Matter Physics by H. Bruus and K. Flensberg