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Quantum Hall Effect

Quantum Hall Effect. Instructor: Prof. Saurabh Basu, Department of Physics, IIT Guwahati. The Quantum Hall Effect is undoubtedly the greatest discovery in material science in the last century. The quantized Hall plateaus shows the occurrence of quantum effects at macroscopic scales and sets the standard of resistance from a lab experiment on a dirty two dimensional electron gas. The Hall effect is used in magnetic field sensors that are present in a large number of devices. It has already earned 3 nobel prizes, one each of Integer Quantum Hall effect (1985), Fractional Quantum Hall effect (1998) and its connections with topology (2016). The course will introduce from scratch the behavior of electrons at low temperatures and large magnetic fields, formation of Landau levels, Quantization of Hall plateaus from a physical perspective and hence derive Kubo formula. The connections with topology are shown via computing the Chern number. Moreover the fractional quantum Hall effect is introduced with a brief description of fractional statistics and Anyons. Finally the course introduces Spin Hall effect and its relevance to the field of spintronics. (from nptel.ac.in)

Lecture 21 - Plasma Analogy


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Lecture 01 - Conductance in Nanostructures
Lecture 02 - S-Matrix, Reflection and Transmission
Lecture 03 - Introduction to Classical and Quantum Hall Effect
Lecture 04 - Quantum Hall Effect
Lecture 05 - Landau Levels
Lecture 06 - Degeneracy of Landau Levels
Lecture 07 - Shubnikov de Haas Oscillations
Lecture 08 - Kubo Formula
Lecture 09 - Symmetric Gauge
Lecture 10 - Tight Binding Model, Hofstadter Butterfly
Lecture 11 - Topological Invariant, Chern Number
Lecture 12 - Electronic Structure of Graphene
Lecture 13 - Low Energy Dispersion
Lecture 14 - Dirac Hamiltonian, Hofstadter Butterfly
Lecture 15 - QHE, Landau Levels
Lecture 16 - Properties of Spin Angular Momentum, Spin Hall Effect
Lecture 17 - Quantum Spin Hall Insulator, Kane-Mele Model
Lecture 18 - Kane-Mele Model
Lecture 19 - Landau Gauge in Fractional Quantum Hall Effect
Lecture 20 - Laughlin States, Properties
Lecture 21 - Plasma Analogy
Lecture 22 - Composite Fermions, Hierarchy