Venue and Class Timings: 11:30 - 13:00 on Tuesdays (Emmy Noether Seminar Room) and Fridays (Chern Lecture Hall)
First Meeting: 9 January 2026 (Friday) at 11:30 (Chern Lecture Hall)
Course Description:1. Topic 0 : Introduction to quantum condensed matter
(a) What is this course about ?
(b) Recap of the idea of identical quantum particles
(c) Elements of second quantization
(d) Recap of free bosons and free fermion gas
(e) Recap of application of symmetries in quantum systems
(f) Numerical exact diagonalization of quantum many-body Hamiltonians
(g) Recap of phase transitions and idea of spontaneous symmetry breaking
(h) Linear response and basic condensed matter experiments
(a) Hartree-Fock theory of interacting electrons
(b) Jellium Model of electrons
(c) Screening of Coulomb interactions
(d) Density functional theory
(e) Idea of quasi-particles and their lifetime
(f) Landau Fermi liquids
(g) Electromagnetic response of electrons
(i) Dielectric properties
(ii) Plasmons
(i) Dielectric properties
(ii) Plasmons
(h) Transport: Drude theory of electrons
(i) Ohm’s law and conductivity
(ii) Hall effect and Hall coefficient
(i) Boltzmann equation(i) Single-particle lifetime vs. transport lifetime
(j) Thermal conductivity and thermoelectric effects of electrons
(k) Landau Level and Integer Quantum Hall effect of a free electron gas in two dimensions
(a) Crystallization as spontaneous symmetry breaking
(b) Description of a crystal
(b) Description of a crystal
(i) Bravais lattice and description of crystal in real space
(ii) Reciprocal lattice and description of crystal in momentum space
(c) Aspects of finite space groups
(d) Experimental detection of crystal through X-ray diffraction
(e) Basics of Amorphous solids
(f) Lattice vibrations
(d) Experimental detection of crystal through X-ray diffraction
(e) Basics of Amorphous solids
(f) Lattice vibrations
(i) Phonons as goldstone modes
(ii) Harmonic theory of phonons
(iii) Phonon heat capacity
(iv) Anharmonic effects and thermal expansions
(v) Detecting phonons in inelastic scattering experiments
(vi) Raman and Infrared spectroscopy
4. Topic 3 : Electrons in crystalline solids
(a) Hopping of electrons on a lattice
(i) Bloch theorem and Bloch states
(ii) Tight-binding models
(iii) Role of symmetries
(iv) Electron band structure
(v) Wannier Orbitals
(vi) Band Insulators, Band metals and semi metals
(vii) Fermi surfaces
(viii) Magnetic oscillations
(ix) Graphene
(x) Peierls substitution and Hofstadter Model
(ii) Tight-binding models
(iii) Role of symmetries
(iv) Electron band structure
(v) Wannier Orbitals
(vi) Band Insulators, Band metals and semi metals
(vii) Fermi surfaces
(viii) Magnetic oscillations
(ix) Graphene
(x) Peierls substitution and Hofstadter Model
(xi) Berry curvature, Chern numbers, and topological band insulators
(b) Electron-phonon interactions
(c) Umklapp scattering
(c) Umklapp scattering
(d) Conductivity in metals
(e) Disorder and localization
(a) Sampling over distributions
(b) Discrete fields and Ising models
(b) Discrete fields and Ising models
(c) Continuous fields and hybrid Monte Carlo
(d) Fermions and the sign problem
6. Topic 5 : Superfluidity and Superconductivity(a) Bose-Einstein condensate
(b) Idea of superfluidity and phase stiffness
(c) Sound modes
(d) vortices
(b) Idea of superfluidity and phase stiffness
(c) Sound modes
(d) vortices
(e) What is superconductivity ?
(f) Electron-phonon interactions and Cooper instability
(g) Cooper pairs
(h) Landau theory of superconductivity
(i) Electromagnetic response of a superconductor
(f) Electron-phonon interactions and Cooper instability
(g) Cooper pairs
(h) Landau theory of superconductivity
(i) Electromagnetic response of a superconductor
(i) Meissner effect
(ii) Josephson effect
7. Advanced topic (if time permits) : non-Fermi liquids
Prerequisite:
Quantum Mechanics, Statistical Mechanics.
References: Modern Condensed Matter Physics by Girvin and Yang, Solid State Physics by Ashcroft and Mermin
Course Outcome:
- The course will provide the basics of many-body techniques to understand electronic phases starting from conventional metals, magnets and superconductors to unconventional ones such as topological insulators and quantum Hall systems.
- It will provide the important techniques and ideas of the very successful framework of modern condensed matter physics which is the cornerstone of our understanding of quantum many-body behavior in materials around us.
- It will provide a bridge of understanding properties of such materials starting from microscopic description of quantum materials to low energy field theories on one side and numerical calculations on the other-- both of which provide complementary insights to experiments and on such systems.
Grading:
1. Assignments (75%)
2. Class participation (25%)
- Teacher: Aavishkar Apoorva Patel
Credit Score: 4