Venue: Emmy Noether Seminar Room
Class Timings: Tuesdays and Thursdays from 02:00 PM - 03:30 PM
First Meeting: 09 January 2025
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) Recap of free bosons and free fermion gas
(d) Recap of application symmetries in quantum systems
(e) Basic types of condensed matter experiments–
(i) Measuring thermodynamic properties
(ii) Measuring transport properties.
(iii) Scattering experiments and correlations.
(f) Recap of phase transitions and idea of spontaneous symmetry breaking
(g) Elements of second quantization
2. Topic 1 : Electrons in continuum(a) Jelium Model of electrons
(b) Drude and Somerfeld theory of electrons
(i) Ohm’s law and conductivity
(ii) Hall effect and Hall coefficient
(c) Boltzmann equation and idea of linear response(d) Coulomb interactions among electrons
(e) Hartree-Fock theory of interacting electrons and the idea of quasi-particles and their lifetime.
(f) Screening on interactions
(g) Landau Fermi liquids
(h) Idea of quasi-particle and single-particle lifetime vs. transport lifetime
(i) Landau Level and Integer Quantum Hall effect of a free electron gas in two dimensions
3. Topic 2 : Lattice(a) Crystallisation 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) Bloch theorem and Bloch states
(iv) Detecting phonons in inelastic scattering experiments
(v) Raman and Infrared spectroscopy
(vi) Anharmonic effects and thermal expansions
(g) Theory of elasticity
(h) Defect in crystalline solids
(h) Defect in crystalline solids
4. Topic 3 : Electrons in crystalline solids
(a) Electron orbitals
(i) Atomic orbitals and periodic table
(ii) Spin-Orbit coupling
(iii) Hund’s rules
(iv) Crystal fields
(i) Atomic orbitals and periodic table
(ii) Spin-Orbit coupling
(iii) Hund’s rules
(iv) Crystal fields
(b) Hopping of electrons on a lattice
(i) Tight-binding models
(ii) Role of symmetries
(iii) Electron band structure
(iv) Wanniner Orbitals
(v) Band Insulators, Band metals and semi metals
(vi) Fermi surfaces
(vii) Magnetic oscillations
(viii) Topological Band Insulators
(ix) Graphene
(x) Pierl’s substitution and Hofstadter Model
(i) Tight-binding models
(ii) Role of symmetries
(iii) Electron band structure
(iv) Wanniner Orbitals
(v) Band Insulators, Band metals and semi metals
(vi) Fermi surfaces
(vii) Magnetic oscillations
(viii) Topological Band Insulators
(ix) Graphene
(x) Pierl’s substitution and Hofstadter Model
(c) Semiclassical Dynamics of electrons
(d) Conductivity in metals
(e) Umpklapp scattering
(f) Electromagnetic response of electrons in a solid
(d) Conductivity in metals
(e) Umpklapp scattering
(f) Electromagnetic response of electrons in a solid
(i) Dielectric properties
(ii) Plasmons
(a) Origin of magnetism
(i) Recap of Dirac theory of spins and the non relativistic limit
(ii) Single spin in a magnetic field as a model of dilute paramagnet
(iii) Different contributions to magnetism in a material
(iv) Magnetic susceptibility
(v) Neutron scattering
(b) Magnetic insulators
(i) Spin model and their origin
(ii) Spin rotation symmetry breaking and magnetic orders– Ferromagnetism, Antiferromagnetism.
(iii) spin waves
(iv) Curie-Weiss Mean field theory (Ising Model)
(v) Toric code as example of topological order
6. Topic 5 : Superfluidity(i) Recap of Dirac theory of spins and the non relativistic limit
(ii) Single spin in a magnetic field as a model of dilute paramagnet
(iii) Different contributions to magnetism in a material
(iv) Magnetic susceptibility
(v) Neutron scattering
(b) Magnetic insulators
(i) Spin model and their origin
(ii) Spin rotation symmetry breaking and magnetic orders– Ferromagnetism, Antiferromagnetism.
(iii) spin waves
(iv) Curie-Weiss Mean field theory (Ising Model)
(v) Toric code as example of topological order
(a) Ultracold bosons
(b) Bose-Einstein condensate in ultracold atoms
(c) Idea of superfluidity and phase stiffness
(d) Different sound modes
(e) vortices
7. Topic 6 : Superconductivity(b) Bose-Einstein condensate in ultracold atoms
(c) Idea of superfluidity and phase stiffness
(d) Different sound modes
(e) vortices
(a) What is superconductivity ?
(b) Electron-phonon interactions and Cooper instability
(c) Cooper pairs
(d) Landau theory of superconductivity
(e) Electromagnetic response of a superconductor
(b) Electron-phonon interactions and Cooper instability
(c) Cooper pairs
(d) Landau theory of superconductivity
(e) Electromagnetic response of a superconductor
(i) Meissner effect
(ii) Josephson effect
Prerequisite:
Quantum Mechanics, Statistical Mechanics.
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 behaviour 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 (50%) : Typically one assignment every 2 weeks.
2. Mid Semester Exam (25%)
3. End Semester Exam (25%)
- Teacher: Subhro Bhattacharjee
Credit Score: 4