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Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf StudyVideo and Text Based

Courses and Certificate Fees

Fees InformationsCertificate AvailabilityCertificate Providing Authority
INR 1000yesIIT Guwahati (IITG)

The fees for the course Quantum Hall Effects is :

Fees componentsAmount
Exam feesRs. 1,000

The Syllabus

  • Transport in mesoscopic systems
  • Historical introduction of Hall effect
  • Classical Hall effect
  • Discovery of Quantum Hall Effect (QHE)
  • Two dimensional electron gases (2 DEG)
  • Band diagrams

  • Hall Resistivity and Conductivity
  • Resistivity measurements
  • QHE and Metrology, quantization of resistivity, experimental plot of quantized resistivity
  • Hall and longitudinal resistivity, plateaus, Integer QHE (IQHE)

  • 2DEG in strong magnetic field
  • Solution of Schroedinger equation
  • Gauge invariance, Landau gauge
  • Landau levels degeneracy, quantum of flux
  • Shubnikov de Haas (SdH) oscillations

  • Laughlin’s argument
  • Corbino ring, Origin of the plateaux, effect of electric field, inclusion of spins of electrons
  • Role of disorder, edge states, topological insulator

  • Hall conductivity
  • Linear response theory, derivation of Kubo formula, choice of gauge potentials
  • Hall conductivity and Chern number

  • Topological considerations
  • Gauss-Bonnet theorem
  • Berry connection and Berry curvature
  • IQHE revisited in Graphene and 2D Dirac materials, quantization of the plateaus
  • Graphene nanoribbon.

  • Fractional Quantum Hall effect (FQHE)
  • QHE at non-integer filling fractions
  • Role of Coulomb interactions, Laughlin wave function
  • Symmetric gauge, 
  • Lowest Landau level, 
  • Fractional Statistics, Fractional charge, Anyons, Braiding statistics

  • Spin Hall effect
  • Spin Orbit coupling
  • Spin Hall effect, application to spintronics, real materials
  • HgTe-CdTe quantum wells

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