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Electronic Theory of Solids

By Prof. Arghya Taraphder   |   IIT Kharagpur
Learners enrolled: 253
The course aims to introduce electronic properties of solids starting from a very simple example: the two-atom solid. Building on this, it develops the theory of electrons in an N- atom solid – the band concept and its application to electrical and thermal properties in solids. The novel electronic concepts related to graphene and carbon nanotubes are discussed. Concept of symmetries and their relevance in emergent electronic properties are also outlined.Magnetism of solids is introduced. Different types of magnetic states and their origin are outlined. Magnetisation and susceptibility in para and diamagnetic cases, their measurements and calculations in simple cases discussed. Concept of magnetic long range order is presented with examples. A magnetic Hamiltonian is described and solved in simple cases. Idea of mean-field theory outlined. Basic concepts of superconductivity are introduced with historical developments. The Cooper problem and BCS theory are worked out. Electrodynamics and applications of super conductivity discussed. Elementary concepts of low dimensional electron gas, quantum dot, 1D and 2D electron gas introduced. Basics of Quantum Hall effect discussed. Spin filtering and magnetoresistance introduced. Spintronics and its applications outlined. Future directions in spin- or valley- tronics discussed.

INTENDED AUDIENCE : Physics, Chemistry, Material Science, Electronics, Electrical engineering, Nano-science and Nano-Technology
PREREQUISITES : Elementary quantum mechanics.
INDUSTRY SUPPORT : Physics, Chemistry, Material Science, Electronics, Electrical engineering, Nano-science and Nano-Technology
Summary
Course Status : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 24 Jan 2022
End Date : 15 Apr 2022
Exam Date : 23 Apr 2022 IST
Category :
  • Physics
Credit Points : 3
Level : Undergraduate/Postgraduate



Course layout

Week 1 : Free electron theory of metals, Fermi-Dirac distribution, Free electrons, boundary conditions, Density of levels in 1, 2 & 3 dimensions, Fermi momentum and Fermi energy, Connection between electron density and Fermi energy.
Week 2 : Independent electron systems, degenerate fermi gas: Specific heat, semiclassical theory of transport, Drude theory and Hall effect. Electronic properties of solids: the two-atom solid, theory of electrons in an N-atom solid, linear combination of atomic orbitals – band formation
Week 3 : Periodic potential, Bloch's theorem, tight binding approximation. Brillouin zones for square, triangular, cubic lattices and energy bands in reduced zone scheme.
Week 4 : Fermi surface in several cases, instabilities of the Fermi surface. Novel electronic structures: graphene and carbon nanotubes. Concept of symmetries and their relevance in emergent electronic properties, topological insulators.
Week 5 : Elementary concepts of low dimensional electron gas, quantum dot, 1D and 2D electron gas introduced. 2D electrons in a magnetic field, integer quantum hall effect. Spin filtering and magnetoresistance. Spintronics and its applications. Future directions in spin- or valley-tronics.
Week 6 : Magnetism and its origin, magnetization and susceptibility, dia-, para- and ferro-magnetism. Larmour diamagnetism.
Week 7 : Hund’s rule and paramagnetism, Van Vleck paramagnetism, Curie’s law. Thermal properties of magnetic insulators, Pauli paramagnetism.
Week 8 : Magnetic interactions, two-electron system, spin-spin interactions – exchange interaction, direct, super and itinerant exchange.
Week 9 : Magnetic order, Ising, XY and Heisenberg spin models, mean-field theory, ground states and thermodynamics.
Week 10 : Phenomenology of Superconductors, Superconductivity in metals and alloys, New Superconductors, Zero Resistance, Meissner Effect, London equation and two- fluid model. Attractive interaction, Cooper problem – instability of the Fermi surface, pair formation and binding energy.
Week 11 : BCS theory, tunneling, SC gap and transition temperature. Sp. heat jump at Tc, coherence length and penetration depth: electrodynamics of superconductors, Type-I and II SC, vortices.
Week 12 : Quantum interference, Josephson effect, SC junctions, squid and its application. Novel superconductors.

Books and references

Solid State Physics by N W Ashcroft and N D Mermin,Atoms to Solids by S Datta, Condensed Matter Physics by M Marder, Advanced Solid State Physics, Ed. 2 by Phillip
Phillips.

Instructor bio

Prof. Arghya Taraphder

IIT Kharagpur
Professor and former HoD, Dept of Physics and Centre for Theoretical Studies, IIT Kharagpur
PhD: IISc Bangalore 1991
PhD guidance: 7 completed 1 submitted
Postdoctoral Associate in the Condensed Matter Physics Group, Rutgers University, USA: Aug. 1991 - Jan. 1993
Visiting Scientist, NEC Research Institute, Princeton, USA: Aug. 1991 - Jan. 1993
Visiting Scientist, LEPES, CNRS, Grenoble, France: Feb. 1993 – July 1994
Visiting Professor, Michigan State University, July 1999
Visiting Professor, University of Neuchatel, Switzerland
Visiting Professor, Michigan State University, Feb. 2001-Apr.
2001
Visiting Associate, ICTP, Trieste Italy, May 2001-July 2001 Visiting Professor, Michigan State University, May 2001- July 2001
Visiting Professor, Humboldt University, Berlin, May 2003 Visiting Associate, ICTP, Trieste Italy, June 2003-Aug 2003 Visiting Professor, University of Neuchatel, Switzerland, Aug-Sep 2003
Visiting Professor, ICMM, CSIC, Madrid, Spain Oct. 2003- Sep. 2004
Guest Scientist, Max Planck Institute for Physics of Complex Systems, Dresden, Germany, Oct. 2004 - Dec. 2004
Guest Scientist, Max Planck Institute for Physics of Complex Systems, Dresden, Germany, May 2005 - July 2005
Guest Scientist, Max Planck Institute for Physics of Complex Systems, Dresden, Germany, May 2006 - July 2006
Guest Scientist, Max Planck Institute for Physics of Complex Systems, Dresden, Germany, May 2007 - July 2007
Guest Scientist, Max Planck Institute for Physics of Complex Systems, Dresden, Germany, Jan 2008 - April 2008
Guest Scientist, Max Planck Institute for Physics of Complex Systems, Dresden, Germany, May 2009 – July 2009
Guest Scientist, Max Planck Institute for Physics of Complex Systems, Dresden, Germany, May 2010 – July 2010
Visiting Professor, Michigan State University, June 2013- July 2013
Visiting Professor, University of Witswatersrand, Johannesburg, Aug 2014
Academia Sinica Foreign Expert, Yangchen Institute of Technology, China, Dec. 2014, June 2015
Research Interests:
Problems in Condensed-Matter Physics -- Correlated and disordered electronic systems, Phase transitions, Statistical mechanics including biological and other complex systems.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 April 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team


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