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 (semiclassical treatment)
 Currents in bands and holes
 Scattering of electrons in bands (elastic, inelastic and electronelectron 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 WiedemannFranz 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
 CoherenceLocalization; 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
 Oneelectron model
 The adiabatic approximation
 The Hartree equations, Exchange: The HartreeFock approximation
 HartreeFock theory of free electrons Ground state energy, exchange energy, correlation energy (only concept)
 Screening in a free electron gas: The Dielectric function
 ThomasFermi 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
 Manyparticle Schrodinger wave equation in first quantization
 The singleparticle states as basis states
 Normalized symmetric and antisymmetric wave functions
 Second quantization: Transformation of Schrodinger equation to occupation number representation (both for bosons and fermions)
 Manyparticle Hilbert space and creation and destruction operators
 Field operators, Secondquantized from of number density operator
 Application to degenerate electron gas
 First and secondquantized Hamiltonian operator
 rs parameter, Groundstate energy in firstorder perturbation theory
 Contact with the HartreeFock 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 Manyparticle Systems by A. L. Fetter and J. D. Walecka
6. Manybody Quantum Theory in Condensed Matter Physics by H. Bruus and K. Flensberg