Home - Open Positions - KNIT project - Research interests - Publications - Various links - Xavier Waintal, CEA Grenoble (DSM/INAC/SPSMS)

THE KNIT PROJECT

KNIT is a library that implements a fast and versatile algorithm to calculate local and global transport properties in mesoscopic quantum systems. Within the non equilibrium Green function formalism (NEGF), KNIT applies a generalized recursive Green function technique to tackle multiterminal devices with arbitrary geometries. It is fully equivalent to the Landauer-Buttiker Scattering formalism. KNIT main functionality is written in C++ and wrapped into Python, providing a simple and flexible interface to develop your own new systems and/or calculate new physical observables. KNIT is an open source project which is freelly available to the scientific community. We merely ask you to quote the main KNIT paper (see below) in the publications where KNIT was used. The principal ressources for the KNIT project are:

The main scientific paper (the one that should be quoted) where the KNIT algorithm is described is: K. Kazymyrenko and X. Waintal "Knitting algorithm for calculating Green functions in quantum systems" Phys. Rev. B 77, 115119 (2008). The pdf file for this paper is also available here.
The KNIT documentation can be found here (64 pages pdf file), it is far from perfect, but it exists. Although we did make an effort to cover most aspects of KNIT, one still has to dig into the source code from time to time. Unfortunately, in most cases, I won't have time to help you.
Last, the full source code of the project, including the examples, tutorial and documentation is available here (you need to fill in your name and accept the license term before downloading the file).
NOTE: New release on March 01, 2011: It provides a new, much more stable, routine for calculating the lead self energies. The change should be transparent for the user except in the case of, say graphene, (non inversible V matrix) where one does not have to use ugly tricks anymore.

Below I put a few examples of actual calculations that have been performed with KNIT either in my group or outside. If you have nice calculations done with Knit, you can send me some material (typically one figure, a small text and the links to the references) and I will be happy to add it to the gallery below.

Inputs and outputs of KNIT

A very simple example

Below is a very simple yet non trivial example of the calculation of the conductance of a "L" shaped conductor. The 20 lines python script wich constitutes our input file reads:

An image of the system can be readily produced to check that it looks as it should, it look like this (before we add the lead on the left and after on the right):

Last, at the end of the script, the script perform the calculation of the conductance of the system an print it on the screen as a function of the (Fermi) energy:

Electronic Machzender interferometer in the quantum Hall regime

Here, we show a calculation of an electronic Mach-Zehnder interferometer in the quantum Hall regime where the 2D gas is modeled by a simple scalar tight-biding model on a square lattice. The first figure (a) illustrates the local current intensity when a bias voltage is applied to lead 0 and the other contacts are grounded (1.2 million sites, blue colors corresponds to no current and red to maximum current). One can observes the edge channel which is split by a first quantum point contact ("beam splitter") and then recombined by the second one.

The second figure (b) shows the differential conductance between lead 0 and lead 3 as a function of the number of flux quanta through the hole. One finds the usual (cosine) interference pattern.

See Phys. Rev. B 77, 115119 (2008) for more on this issue.

HgTe/HgCdTe topological insulator

The following figure shows a calculation of a "H" shaped sample made out of a p-n junction of a topological insulator (HgTe/HgCdTe heterostrustures) in presence of a strong magnetic field. The plot shows a strong magneto-conductance as a function of a parallel magnetic field along the x and y directions ("Datta-Das" transistor). A tight-binding model with 4 orbitals per sites is used in this calculation.

Calculation done in the group of Carlo Beenakker in Leiden. A. R. Akhmerov, C. W. Groth, J. Tworzydlo and C. W. J. Beenakker “Switching of electrical current by spin precession in the first Landau level of an inverted-gap semiconductor” Phys. Rev. B 80, 195320 (2009)

Anomalous Quantum Hall effect in graphene

This is a calculation of the Quantum Hall effect in a graphene Hall bar (with zigzag nanoribbons). The Hall conductance and longitudinal resistance are plotted as a function of inverse magnetic field (a) and carrier density (b) in presence of a small disordered potential (10% of the hopping matrix elements). The anomalous quantum Hall effect specific of graphene is nicely recovered. The inset of (b) shows a zoom of the transition between plateaus. Figure (c) shows the local current intensity when current is injected from both contact 1 and 4 which allows to study the edge channels.

See Phys. Rev. B 77, 115119 (2008) for more on this issue.

Spin accumulation in a Cu-Py-Cu-Py-Cu magnetic nanopillar

This figure shows the spin accumulation profile of a magnetic nanopillar (spin valve) made of the following stack: Copper (5 nm), Permalloy (20 nm), Copper (5 nm), Permalloy (20 nm) and Copper (5nm). The symbols correspond to the calculations done using KNIT with a spin dependent tight-binding model (the error bar corresponds to the average over different symbols) while the dashed line corresponds to a Random Matrix Theory aproach.

Magnetic focussing and Cross Andreev Reflection (CAR)

This calculation shows Cross Andreev Reflection magnified by magnetic focussing. The tight-biding model includes an electron/hole grading to account for superconductivity.

Calculation done in the group of Arne Brataas, Trondheim. "Focused Crossed Andreev Reflection", Havard Haugen, Arne Brataas, Xavier Waintal and Gerrit E. W. Bauer, arXiv:1007.4653.

Cross Andreev Reflection (CAR) in graphene

Other calculations of CAR were done in a graphene "Y" shaped sample connected to 2 normal and 1 superconducting electrode.

Also in the group of Arne Brataas, Trondheim. "Crossed Andreev reflection versus electron transfer in three-terminal graphene devices", Havard Haugen, Daniel Huertas-Hernando, Arne Brataas, and Xavier Waintal Phys. Rev. B 81, 174523 (2010).

Local density of states in a graphene cross