Gatedefined Nanowire Quantum Dot
Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gatedefined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/condmat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wraparound' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a sourcedrain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>
Dear Jonathan, There is one physical ingredient which is not yet included in Kwant and that is crucial for the type of calculation that you want to deal with: Coulomb blockade. We are working on it but it is not straightforward. Kwant can help you to build the geometry and give you the corresponding Hamiltonian, but you will need to do something with the electrostatic interaction to proceed. If your dot is nearly isolated (tunneling regime), then this is rather straightforward, you can use a master equation approach. In the general case, it is an open problem. Best regards, Xavier
Le 4 avr. 2017 à 11:35, Jonathan Fields <jonathanfields80@outlook.com> a écrit :
Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gatedefined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/condmat/0609463 <https://arxiv.org/abs/condmat/0609463>. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package.
At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea?
My problem is that if one does this, then I run into the problem of how to model the 'half wraparound' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates.
On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png <https://i.imgur.com/WZC983c.png> as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot.
I haven't been able to confirm this as I am not yet sure how one can apply a sourcedrain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way.
The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently?
Kind regards Jonathan
Dear Xavier, Has there been any progress in Kwant's ability to model Coulomb blockade since this post? It's something that I'd be interested in modelling, in a similar setup to the one described by Jonathan. All the best, Michael
Dear Michael, Nothing has been released yet. If you just want to do Coulomb blockade, I would go for Master/Lindblad equation and for that you can use e.g. the qutip solver (https://qutip.org <https://qutip.org/>) or even write your own. (First construct the quantum dot empirically and calculate the parameters of the master/Lindblad equation with Kwant. Second use qutip to solve the latter). If you want a realistic model that treats the electrostatic properly (i.e. the input is just the geometry of the gates + some material parameters), then you have to wait a bit for the PESCADO package that is a few months away from its first release (you will still need a master equation solver eventually). If you want the full thing (i.e. with Kondo effect) then the best method we have at the moment is by far this: https://arxiv.org/abs/2207.06135 <https://arxiv.org/abs/2207.06135> but we’re still a long way from releasing an open source code (The core of the algorithm, the « tensor cross interpolation " part will be released soon though, the package will be called Xfactorization or xfac). Best regards, Xavier
Le 15 sept. 2022 à 14:51, michael.hynes.18@ucl.ac.uk a écrit :
Dear Xavier,
Has there been any progress in Kwant's ability to model Coulomb blockade since this post? It's something that I'd be interested in modelling, in a similar setup to the one described by Jonathan.
All the best, Michael
Thank you for your advice Xavier. I will look into using qutip alongside kwant for now, and keep an eye out for your release of xfac/Xfactorization. Best wishes, Michael
participants (4)

Jonathan Fields

Michael Hynes

michael.hynes.18＠ucl.ac.uk

Xavier Waintal