Condensed Matter Physics–I

Paper Code: 
PHY324(A)
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

Course Objectives:
1.   To teach the students about Fundamentals of many-electron system, Quasi electrons and Plasmons, spin- orbit and Spin-spin interaction, Density Functional Theory.
2.    To build up on the basic knowledge of nanomaterials and their properties.
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: describe the role of quantum effects in micro- and macro-scopic systems and explain significance of condensed matter physics.

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

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

CO83: improve formalism of the 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: 
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: 
UNIT II

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: 
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: 
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: 
UNIT V

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.

Essential Readings: 

1.    Stanly Raimes: Many Electron Theory; North Holland Publishing company Amsterdam-London
2.    O. Madelung: Introduction to Solid State Theory; Springer
3.    D.Pines and P. Nozier: The Theory of Quantum Liquids; Perseus Books Publishing LLC
4.    P.I. Taylor, A Quantum Approach to the Solid State, Prentice Hall.
5.    Wlater A. Harrison: Solid State Physics, Dover Publication (1980).
6.    Harald Ibach and Hans Luth: Solid State Physics: An introduction to Principles of Materials Science, Springer (2003).
7.    J.M. Ziman: Principles of the Theory of Solids; Cambridge.
8.    C. Kittel : Quantum Theory of Solids

 

References: 

1.    Edo M. Yussouf: Lecture Notes in Physics, No. 283, Electronic band structure and its Applications, Springer – Vertag (1987).
2.    N.H. March and M. Passinello: Collective Effects in Solids and Liquids.
3.    J.M. Ziman: Principles of the Theory of Solids; Cambridge
4.    C. Kittel : Quantum Theory of Solids.    
5.    Jorge Kohan off: Electronic Structure Calculations for Solids and Molecules, Cambridge (2006).
6.    D.J. Singh & Lars Nordstrom: Plane waves, Psedopotentials and the LAPW method 2nd Ed. (2006).
7.    User guide/manual of softwares: WIEN2K,VASP, Quantum Expresso, Abinito
8.    J.H.Fendler; Nanoparticles and Nanostructured Films: Preparation, Characterization and Application.
•    Michael J. O’Connell: Carbon Nanotubes: Properties and Applications, (CRC press, 2006).

E- CONTENTS:
1.    C. David Sherrill: An Introduction to Hartree-Fock Molecular Orbital Theory:http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/hf-intro.pdf.
2.    Rangarajan, G., Condensed Matter Physics, NPTEL Course Material, Department of Physics, Indian Institute of Technology Madras, https://nptel.ac.in/courses/115106061/.
3.    Wen, X-G., Physics of Solids I, MIT open course: https://ocw.mit.edu/courses/physics/8- 231-physics-of-solids-i-fall-2006/
4.    http://www.cse.clrc.ac.uk/cmg

 

Academic Year: 
2023-2024
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