Condensed Matter Physics – I

Paper Code: 
PHY 324(A)
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

  1. The student will be equipped with background knowledge to understand different types of materials and to take up research in Condensed Matter Physics.
  2. The student will be able to understand Fundamentals of many-electron System, Quasi electrons and Plasmons, spin- orbit and Spin-spin interaction, Density Functional Theory & Experimental techniques in nanotechnology.

Course outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

PAPER CODE

Paper Title

PHY 324(A)

 

 

Condensed Matter Physics – I

(Theory)

 

 

 

The students will be able to:

CO80: understand the role of quantum effects in micro- and macro-scopic systems and explain significance of condensed matter physics.

CO81: get the knowledge about the theory and procedures of Hartree Fock and Density functional theory for many-electron System

CO82: learn about the difference between Schrodinger’s picture and Heisenberg’s picture of interactions for a Many body problem

CO83: understand the formalism of spin- spin interaction and magnons

CO84: develop basic understanding of nanomaterials and learn their properties.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials,  Demonstration, Problem Solving

 

 

 

Learning activities for the students:

Self learning assignments, Effective questions,  Seminar presentation, Solving numerical.

Additional learning through online videos and MOOC courses

Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations

 

12.00
Unit I: 
Fundamentals of many-electron System: Hartree-Fock Theory:

The basic Hamiltonian in a solid: electronic and ionic parts, the adiabatic approximation; Single-particle approximation of the many-electron system; single product and determinantal wave functions, Occupation number representation; matrix elements of one and two-particle operators; The Hartree-Fock (H-F) method; the one electron H-F equation; exchange interaction and Fermi hole; Coulomb correlation; the H-F ground state energy.

 

12.00
Unit II: 
The interacting free-electron gas:

The interacting free-electron gas: Quasi electrons and Plasmons: The interacting electron gas; The coulomb interaction; The Hartree-Fock approximation for the electron gas; Exchange Hole; Screeming, Plasmons; Quasi-electrons; The dielectric constant of the electron gas.

 

12.00
Unit III: 
Spin-spin interaction:

Magnons Absence of magnetism in classical statistics; Origin of the exchange interaction; Direct exchange, super exchange, indirect exchange and itinerant exchange; Spin-waves inferromagnets-magnons, spontaneous magnetization, thermodynamics of magnons; Spin waves in lattices with a basis-ferri- and antiferromagnetism; Measurement of magnon spectrum; Ordered magnetism of valence and conduction electrons, Stoner’s criterion for metallic ferromagnet        

 

12.00
Unit IV: 
Density Functional Theory:

Basics of DFT, Comparison with conventional wave function approach, Hohenberg-Kohn Theorem; Kohn-Sham Equation; Thomas-Fermi approximation and beyond: LDA and GGA; Application of DFT in a many body calculation and its reliability.

 

12.00
Unit V: 
Experimental techniques :

Introduction of Nanomaterials: Free electron theory (qualitative idea), variation of density of states with energy, variation of density of state and band gap with size of crystal. Electron confinement in infinitely deep square well, confinement of two and one dimensional well, idea of quantum well structure, tunneling through potential barrier, quantum dots, quantum wires, introduction to fullerenes and graphenes.
 

References: 
  • Stanly Raimes: Many Electron Theory; North Holland Publishing company Amsterdam-London
  • O. Madelung: Introduction to Solid State Theory; Springer
  • D.Pines and P. Nozier: The Theory of Quantum Liquids; Perseus Books Publishing LLC
  • W.A. Harison : Pseudopotentials in the Theory of Metals, Benjamin
  • Norman Henry March, ‎W. H. Young, ‎S. Sampanthar- Many Body Problem; cambridge university press
  • P.I. Taylor, A Quantum Approach to the Solid State, Prentice Hall.
  • Ech. Steinhardt and Ostulond: Physics of quasi crystals.
  • Neil W. Aschoft & N. David Mermin : Solid State Physics, Harcourt Publishers (1976)
  • Gerald Burns: Solid State Physics, Academic Press (1985).
  • Wlater A. Harrison: Solid State Physics, Dover Publication (1980).
  • Harald Ibach and Hans Luth: Solid State Physics: An introduction to Principles of
  • Materials Science, Springer (2003).
  • F. Seitz and D.Tumbull (Eds.): Solid State Physics, Advances in research and
  • applications, supplement 3: A.A. Maraduddin, E.W. Montrol and G.H. Weiss: Theory of
  • lattice dynamics in harmonic approximation : Academic Press (1963).
  • 13. Callaway: Quantum Theory of Solids Part A & B, Academic Press (1974).
  • 14. M.P. Marder: Condensed Matter Physics, Wiley-Interscience (2000).
  • H.Ibach and H.Luth: An Introduction of Theory and Experiments- Solid State Physics, Narosa (1991).
  • Edo M. Yussouf: Lecture Notes in Physics, No. 283, Electronic band structure and its Applications, Springer – Vertag (1987).
  • D.Pines: Elementary Excitations in Solids; Perseus (1999)
  • N.H. March and M. Passinello: Collective Effects in Solids and Liquids.
  • J.M. Ziman: Principles of the Theory of Solids; Cambridge
  • C. Kittel : Quantum Theory of Solids                      
  • Richard M. Martin: Electronic Structure- Basic Theory and Practical Methods:
  • Cambridge (2004).
  • Jorge Kohanoff: Electronic Structure Calculations for Solids and Molecules, Cambridge (2006).
  • D.J. Singh & Lars Nordstrom: Plane waves, Psedopotentials and the LAPW method 2nd Ed. (2006).
  • User guide/manual of softwares: WIEN2K,VASP, Quantum Expresso, Abinit
  • J.H.Fendler; Nanoparticles and Nanostructured Films: Preparation, Characterization and Application

 

Academic Year: 
2021-2022
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