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Topological states of matter – from the quantum Hall effect to Majorana fermions

Topological states of matter – from the quantum Hall effect to Majorana fermions. Ady Stern (Weizmann). The quantum Hall effects – introduction Unavoidable conclusions. The quantum Hall effects. Introduction. ---------------------------------. I. B. +++++++++++++++.

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Topological states of matter – from the quantum Hall effect to Majorana fermions

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  1. Topological states of matter – from the quantum Hall effect to Majorana fermions Ady Stern (Weizmann) • The quantum Hall effects – introduction • Unavoidable conclusions

  2. The quantum Hall effects Introduction

  3. --------------------------------- I B +++++++++++++++ Landau level filling factor = density of electrons density of flux quanta The Hall effect Electrons in two dimensions Classically, Hall resistivity - longitudinal resistivity - unchanged by B. Quantum mechanically degenerate harmonic oscillator spectrum Landau levels

  4. The quantum Hall effect • zero longitudinal resistivity - no dissipation • quantized Hall resistivity to amazing precision • Integer quantum Hall effect - integer n • Fractional quantum Hall effect

  5. Single particle spectrum – highly degenerate Landau levels

  6. The original sample of the FQHE:

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