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
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