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M.Sc. (Physics) | Subject Condensed Matter Physics II | Paper Code 09020403

Subject: Condensed Matter Physics II

Paper Code: 09020403

Unit

Topic

Domain

Hours as per UGC

I

ELECTRON TRANSPORT PHENOMENON

  • Motion of electrons in bands and the effective mass tensor (semi-classical treatment)
  • Currents in bands and holes
  • Scattering of electrons in bands (elastic, inelastic and electron-electron scatterings)
  • The Boltzmann equation, Relaxation time ansatz and linearized Boltzmann equation
  • Electrical conductivity of metals
  • Temperature dependence of resistivity and Matthiesen’s rule
  • Thermoelectric effects, Thermopower
  • Seebeck effect, Peltier effect, The Wiedemann-Franz law.
 

 

Must Know

Desirable to Know

8

II

NANOSTRUCTURES AND ELECTRON TRANSPORT

  • Nanostructures; Imaging techniques (principle)
  • Electron microscopy (TEM, SEM)
  • Optical microscopy, Scanning tunneling microscopy
  • Atomic force microscopy
  • Electronic structure of 1D systems, 1D sub bands
  • Van Hove singularities; 1D metals- Coulomb interactions and lattice couplings
  • Electrical transport in 1D:Conductance quantization and the Landauer formula
  • Two barriers in series- Resonant tunneling Incoherent addition and Ohm’s law
  • Coherence-Localization; Electronic structure of 0D systems (Quantum dots)
  • Quantized energy levels, Semiconductor and metallic dots
  • Optical spectra, Discrete charge states and charging energy
  • Electrical transport in 0D- Coulomb blockade phenomenon.
 

 

Desirable to Know

Must Know

Must Know

12

III

BEYOND THE INDEPENDENT ELECTRON APPROXIMATION

  • The basic Hamiltonian in a solid: Electronic and ionic parts
  • One-electron model
  • The adiabatic approximation
  • The Hartree equations, Exchange: The Hartree-Fock approximation
  • Hartree-Fock theory of free electrons- Ground state energy, exchange energy, correlation energy (only concept)
  • Screening in a free electron gas: The Dielectric function
  • Thomas-Fermi theory of screening
  • Calculation of Lindhard response function
  • Lindhard theory of screening, Friedel oscillations
  • Frequency dependent Lindhard screening (no derivation).
 

 

 

 

 

 

Must Know

10

IV

MANY PARTICLE PHYSICS: SECOND QUANTIZATION FORMULATION

  • Many-particle Schrodinger wave equation in first quantization
  • The single-particle states as basis states
  • Normalized symmetric and anti-symmetric wave functions
  • Second quantization: Transformation of Schrodinger equation to occupation number representation (both for bosons and fermions)
  • Many-particle Hilbert space and creation and destruction operators
  • Field operators, Second-quantized from of number density operator
  • Application to degenerate electron gas
  • First and second-quantized Hamiltonian operator
  • rs parameter, Ground-state energy in first-order perturbation theory
  • Contact with the Hartree-Fock result, Exchange energy.
 

 

Must Know

 

Nice to Know

 

Must Know

 

10

Books Recommended:
1. Solid State Physics: An Introduction to Principles of Materials Science (4th Ed.) by H. Ibach andH. Luth
2. Introduction to Solid State Physics (8th Ed.) by Charles Kittel
3. Solid State Physics by Neil W. Ashcroft and N. David Mermin
4. The Wave Mechanics of Electrons in Metals by Stanley Raimes
5. Quantum Theory of Many-particle Systems by A. L. Fetter and J. D. Walecka
6. Many-body Quantum Theory in Condensed Matter Physics by H. Bruus and K. Flensberg