Home - Open Positions - KNIT project - Research interests - Publications - Various links -

- 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.

NEW NEW NEW NEW NEW NEW NEW

The Knit project has not been maintained for some years now as an new - better - project was being developped. Please go to the web site of the Kwant project here . Kwant can do everything that KNIT does and much more. You will find that Kwant has a much simpler interface (very close the mathematics), is much faster and way easier to install.

NEW NEW NEW NEW NEW NEW NEW

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.

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:

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.

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)

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.

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.

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.

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).