Advanced Condensed Matter Physics

Overview

The Course deals with the prerequisite material for studying advanced level research in Condensed Matter Physics. The course begins with a preliminary discussion on second quantization, followed by zero temperature and Matsubara Greens functions. Applications to Hubbard model, Kane Mele model and superconductivity are discussed.

Syllabus 8

Week 1 : Module 1
- Lec 1: Propagators I
- Lec 2: Propagators II
- Lec 3: Second quantization I
- Lec 4: Second quantization II
- Lec 5: Second quantized Hamiltonian
Week 2 : Module 2
- Lec 6: Tight Binding Hamiltonian, Hubbard model
- Lec 7: Magnetism
- Lec 8: Singlet and Triplet State: Magnetic Hamiltonian
Week 3 : Module 3
- Lec 9: Antiferromagnetism in Hubbard model
- Lec 10: Green's function and representations in quantum mechanics
- Lec 11: S matrix and free electron Green's function
Week 4 : Module 4
- Lec 12 : Wick's theorem and normal ordering
- Lec 13 : Green's function and Feynman diagrams
- Lec 14 : Feynman diagram
Week 5 : Module 5
- Lec 15 : Phonon Green's function and Hartree Fock approximation
- Lec 16 : Finite temperature Green's function and Matsubara frequencies
- Lec 17 : Dyson's equation and disorder in electronic systems
Week 6 : Module 6
- Lec 18 : Introduction to electrodynamics, Meissner effect
- Lec 19 : London penetration depth, Type I and II superconductors
- Lec 20 : Cooper's problem, BCS gap equation
Week 7 : Module 7
- Lec 21 : BCS theory, Transition temperature
- Lec 22 : Ginzburg Landau Theory, Coherence length and penetration depth
- Lec 23 : Quantum Hall Effect
Week 8 : Module 8
- Lec 24 : Spin Hall effect, 2D topological insulator
- Lec 25 : Bose-Einstein condensation
- Lec 26 : Kubo-Greenwood Formula

Advantages and disadvantages

Advantages

Taught by IIT and IISc professors, and it follows the Indian university syllabus closely.
All videos and assignments are free on NPTEL and SWAYAM.
The certificate is recognised by many Indian universities for credit transfer and by GATE aspirants.
Great for GATE and semester exam preparation.
From Indian Institute of Technology Guwahati, a well-regarded name.
Completely free.
Self-paced: start any time.
A clear syllabus (8 parts) you can see before you start.

Disadvantages

The certificate needs a proctored exam at a centre, which has a fee.
Recorded classroom lectures: thorough, but slower than made-for-online courses.
New runs start on fixed dates (January and July).
Learning is free, but the certificate costs money.

Some points apply to every course of this kind; see how we rank.

Free to learn

Free: Every video and assignment is free on NPTEL and SWAYAM. Enrol when the next run opens.
Certificate: Optional. It needs a proctored exam at a centre, which has a fee.