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PHY669: Nano Physics II 4 CH (L60+T20) Nature of the course: Theory Full Marks: 100 Pass Marks: 50 Course Description:

This course aims at providing students with basic knowledge and skill in theoretical as well as experimental aspects of Nano Physics.

Course Objectives:

To acquaint student with the theoretical and experimental methods in Nano Physics.

To prepare them in developing skill to pursue further study and research in the field of physics.

Course Content: Electronic Transport in Mesoscopic systems

1. Preliminary concepts: [10 hours]

1.1 2-Dimensional electron gas,

1.2 Effective mass, Density of states,

1.3 Characteristic lengths,

1.4 Low field magnetoresistance,

1.5 High field magnetoresistance,

1.6 Transverse modes,

1.7 Drift velocity or Fermi velocity.

2. Conductance from Transmission: [15 hours]

2.1 Resistance of a ballistic conductor,

2.2 Landauer formula,

2.3 Where is the Resistance,

2.4 What does a voltage probe measure?

2.5 Non-zero temperature and bias,

2.6 Exclusion principle,

2.7 Use of Landauer-Buetticker formula.

3. Transmission function, S-matrix and Green’s functions: [15 hours]

3.1 Transmission function and S-matrix,

3.2 Combining S-matrices,

3.3 Green’s functions,

3.4 S-matrix and Green’s functions,

3.5 Tight-binding model,

3.6 Self-energy,

3.7 Relation to other formalism,

3.8 Feynman paths.

4. Quantum Hall effect: [5 hours]

4.1 Origin of zero resistance,

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4.2 Effect of backscattering.

5. Localizations and Fluctuations: [7 hours]

5.1 Localization length,

5.2 Weak localization,

5.3 Effect of magnetic field,

5.4 Conductance fluctuations,

5.5 Diagrammatic perturbation theory.

6. Double barrier tunneling: [8 hours]

6.1 Coherent resonant tunneling,

6.2 Effect of scattering,

6.3 Single electron tunneling.

Textbook:

1. Datta S. – Electronic Transport in Mesoscopic systems, Cambridge University Press,

Cambridge (2003).

Reference Books

1. Mitin V. V., Kochelap V. A. and Strocio M. A. – Introduction to nanoelectronics, Cambridge

University Press, Cambridge (2008).

2. Davies J.H. – The physics of low dimensional semiconductors, Cambridge University

Press, Cambridge (2005).