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Computational Quantum Nanoelectronics (lecture 2/4)

Mercredi 6 mai 2015 10:00 - Duree : 2 heures
Lieu : LPSC, room number 7 ground floor (53 rue des Martyrs across the street from Neel Institute)

Orateur : Xavier WAINTAL (INAC/SPSMS/GT)

4 x 2 hours on Wednesdays from 10h00-12H00 : April 29th, May 6th, 13th and 20th.

Quantum nanoelectronics deals with the physics of small (less than 1 micrometer), cold (tens of milliKelvin) objects connected to the macroscopic world through electrodes or gates. A central question at the core of this field is how quantum effects can be observed and/or manipulated through the macroscopic measuring apparatus – some would say despite the presence of the measuring apparatus. In this lectures, we will gradually enter this field with a balance between a discussion of what is observed experimentally (1/3), the theoretical concepts (1/3) and the practical knowledge needed to perform simple numerical computations of practical devices (1/3). The course is opened to anyone with a basic knowledge of quantum mechanics, statistical physics and condensed matter theory.
The numerical part of the lecture is based on the Kwant package (http://kwant-project.org). Kwant is based on the Python programming language which will be introduced in the lecture. No particular background in programming is needed (but it would not hurt).

A tentative (and rather optimistic) outline is :
1) The simplest quantum nanoelectronic system, the quantum point contact (QPC).

  • a. Some old and slightly less old experiments.
  • b. 2 central theoretical concepts : the scattering matrix S and the Landauer formula.
  • c. How to calculate the conductance of a QPC in just 15 lines of gentle code.
    2) Python : a swiss army knife for scientific programming.
  • a. Some propaganda about how scientific programming should be done
  • b. A half an hour tour of the language.
  • c. More propaganda : the Kwant package for quantum nanoelectronics
  • d. From continuum to lattice models – the Fermion doubling theorem
    3) Electronic interferometry : the Aharonov-Bohm effect
    a. Experimental findings b. The S matrix as a Feynman path integral c. How to get Ohm law from quantum mechanics ? d. Numerics
    4) The grand father of all topological insulators : the Quantum Hall Effect (QHE).
  • a. Experiments
  • b. From Landau levels to edge states
  • c. A first glimpse at topology : Berry phases and Chern numbers
  • d. Testing the topological protection with numerics.
    5) Mesoscopic superconductivity
  • a. An ultra short introduction to superconductivity
  • b. The Bogoliubov – De Gennes Hamiltonian
  • c. Andreev reflection & Andreev bound states
  • d. Topological insulators, Majorana fermions and braiding of non-abelian statistics
  • e. Seeing all that in simple numerics
    6) Behind the scene : what we use to scare experimentalists away.
  • a. Keldysh Formalism & its application to nanoelectronics (Wingreen Meir formalism).
  • b. From Green’s functions to Scattering matrices & Floquet theory
  • c. Selected applications to time-dependent phenomena.

Contact : xavier.waintal@cea.fr

Discipline évènement : (Physique)
Entité organisatrice : (Ecole Doctorale de Physique de Grenoble)
Nature évènement : (Ecole/cours) -
Nature évènement : (Séminaire)
Site de l'évènement : Polygone scientifique

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