Coming soon
Condensed Matter Physics
Paper Code:
PHY 144 (B)
Credits:
04
Contact Hours:
60.00
Max. Marks:
100.00
Objective:
This course will enable students to understand
• Structure of different crystals using X-ray diffraction
• Different theories for solving electron problems in metals
• Superconductivity
12.00
Unit I:
UNIT I
a) Crystal Structure
Periodic array of atoms – Lattice translation vectors. The basis and the crystal structure, primitive lattice cell, unit cell. Lattice symmetry operations – point groups and space groups. Fundamental types of lattices – two dimensional lattice types, three dimensional lattice types, crystal planes indexing. Simple crystal structures – sodium Chloride, Cesium Chloride, hexagonal closed packing , diamond, cubic zinc sulphide and hexagonal zinc sulphide structures, amorphous substances, glasses.
Use of X-ray diffraction for structure determination. Scanning electron and transmission electron microscopy.
b) Crystal diffraction and the reciprocal lattice
Bragg’s Law, Lave equations, reciprocal lattice – its properties, Bragg diffraction, condition in terms of reciprocal lattice vectors, brillouin zones, reciprocal lattice and brillouin zones of bcc, fcc, and hexagonal lattices, symmetry points of brillouin zones.
12.00
Unit II:
UNIT II
Free electron Model of Metals
Energy levels and density of orbitals in one dimension, effect of temperature on the Fermi- Dirac distribution function, free electron gas in three dimensions. Heat capacity of electron gas, electrical conductivity,. thermal conductivity of metals, Wiedmann- Franz law.
Introduction to Hartree and Hartree- Fock methods for solving a many electron problem in metals. Classical Hall effect, Integral quantum Hall effect, Fractional Quantum Hall effect.
12.00
Unit III:
UNIT III
Electron energy bands
Nearly free electron Model; origin of energy gap , the bloch theorem, Kronig-Penny model, wave equation of electron in a periodic potential, crystal momentum of an electron, reduced zone scheme; approximate solution near a zone boundary ; number of orbitals in a band, density of states; metals, insulators and semiconductors. Construction of Fermi surfaces, electrons, holes and open orbitals, effective mass of electrons in crystals.
12.00
Unit IV:
UNIT IV
a) The Pseudopotential Method
The approximations, orthogonalized plane wave method. The pseudopotential formulation, nonlocal and local pseudopotentials, separation of the pseudopotential. Selfconsistent screening of a local pseudopotential- Thomas Fermi method, Hartree Dielectric Screening function , Exchange and Correlation.
The diffraction model, Energy Eigen states, scattering, factorization of matrix elements– structure factor and form factors, evaluation of total energy.
b) Density functional Theory
Thomas-Fermi - Dirac approximation – example of a functional, the Hohenberg - Kohn theorems, formulation of density functional theory ,the Kohn-Sham equations, and advantages of density functional method; Extension of DFT to spin polarized systems. Exchange –correlation potential, Local Density Approximation, Introduction to time dependent density functional theory, local spin density approximation (LSDA), Generalized –gradient approximations, (GGAs).
12.00
Unit V:
UNIT V
a) Superconductivity
Occurrence of superconductivity, experimental observations, persistent currents, Effect of magnetic fields, Meissner effect, type I and type II superconductors, intermediate states, entropy and heat capacity, Energy gap, isotopic effect, thermal conductivity.
Theoretical explanations : London’s equations, penetrations depth, coherence length, cooper pairs, elements of BCS theory, flux quantization, Josephson effect, High Tc superconductors: MgB2 , Cuprate superconductors, Hubbard model.
b) Theoretical estimations of superconducting state parameters
Electron- phonon coupling strength (λ), Coloumb pseudopotential (μ), Eliashberg gap equations, Mc Millan’s formulation for Tc and isotope effect in low temperature superconductors. Interaction strength, estimation of superconducting state parameters for metallic superconductors and alloys.
Essential Readings:
1. Solid State Chemistry, D.K. Chakrabarty , New Age International Publishers
2. Introduction to Solid State Physics, Charles Kittel, John-Willey & Sons, New York, VIIth edition
3. Solid State Physics, N.W. Ashcroft & N.D. Mermim, Holt and Rinechart &Winston, International edition ,1996
4. Pseudopotentials in the Theory of Metals, W.A. Harmison, WA Benjanin, New York, 1966
5. D. Prines Elementary Excitations in solids, WA Benjanin, New York.
6. Electronic Structure Calculations for Solids and Molecules, Jorge Kohanoff: Theory and Computational Methods, Cambridge University Press, U.K., 2005.
References:
1. Solid State Chemistry & Its Applications, Anthony R. West, John-Willey & Sons, New York
2. H. Ehrenreich, F. Seitz and D. Turnbull(eds.) Solid State Physics ( Volzu Acadamic Press, New York 1970)
3. A Quantum Approach to Solid State, P.L. Taylor, Premier Hall, Englenwood Chifts, NJ 1970
4. Quantum Theory of Solids, C. Kittel, John-Willey & Sons, New York, 1987.
5. A Text Book of Solid State Physics, S. L. Kakani & C. Hemrajani, Sultan Chand and Sons, New Delhi, 1997.
6. Electronic Structure : Basic Theory & Practical Methods, Richard M. Martin, Cambridge University Press, U.K., 2005.
7. Characterization of Materials, John B. Watchman.
8. Principles of Condensed Matter Physics, Chalasriar and Lubensky .
9. Crystallography for solid state physics, Verma and Shrivastava.
10. Material Science and Engineering, V. Raghavan, (PHI 2007)
11. Fundamentals of Molecular Spectroscopy, Banwell.
12. Concepts of Modern Physics, A. Baiser.
Academic Year:
