 I'm new to the Vanie community, so it's been really beneficial for me both to participate in the summer school and in this week. A bit about my background. I did a PhD at the Technical University of Denmark with my, the main supervisor Casten Jacobsen and co-supervisor Christian Thuysen, which made me familiar faces. And I did it with collaboration with Synopsis Denmark, and I worked on electronic transport in these 2D transition methodical co-connected transistors. Now I'm a postdoc at the Southern University of Denmark with Professor Joel Cox and in the group of Aska Mortens. So, the idea behind all of this project was that we would like to do feasible time dependent simulations of extreme nonlinear optical phenomena in nanostructure systems, which means nano ribbons nano islands, twisted layers stack layers so basically systems with large supercells. And how to do this in an efficient way. So I had the idea to use vanarization because then we can really toggle the effective system size we can go in and say how many bands do we really need in order to describe our system. And we also can get sparse Hamiltonians which can help with the memory of these large systems. So why don't we just use perturbation theory, which is the go to method we for these response calculations. Well it's because we want to look at the extreme nonlinear effects and that's this means we goes to, to large orders in electronic field. So, in linear response you can get the linear response function relatively easily. If you go to second order now you have, I think, at most 18 terms of some tensor if you go further just sort of blows up. And furthermore we need quite intense electric fields for these things so saying that it's a small perturbation is also perhaps a bit of a stretch. So that's why we are going beyond perturbation theory and actually just do a direct time dependent simulations. The current project looks at high harmonic generation in 2D nano rhythms and just a brief introduction to high harmonic generation because I think there's perhaps not a lot of people was aware of this phenomenon I didn't know it before I started working with it. I can sort of explain it through this three step model, which is really for high harmonic generation in the gas phase. And in the solid state of course it's more complicated but this sort of conveys the idea. So if you have a very strong electric field. So if you perturb your potential and an electron can sort of be tunneled away from the nuclei. And then when you have the face of the field changing it sort of gets driven back and forth, and at some point it will be collide with the nuclei and it will emit some radiation which then is emitted at these integer numbers of the impinge in field frequency. And what Professor Joe Cox has been working a lot on is looking at this effect in the graphene in different graphene nano ribbons nano islands, and has shown that when you have these confined systems, which have some well defined plasmonic resonance, then having the field exactly at the frequency of this plasmonic resonance really enhances this high harmonic generation. So that's what we were would like to investigate in other materials and other configurations as well. And what we look at for quantifying this effect is the dipole acceleration squared. And this is because it's proportional to the far field power spectrum and basically this resolves this feature very nicely. We looked at graphene and phosphoryne nano ribbons. Both of these have nicely tunable plasmonic resonances so when you either chemically or electrostatically dope them you can really change the precision of your plasmonic resonance and they also have strong light matter interaction. In the case of graphene we know that we have this plasmon assisted high harmonic generation. And it's also a nice benchmarking system because you can look at this very simple type binding model which we've also looked at sometimes during the school I think where you just have a news neighbor hopping. And then you can can look at your result compared to that. And phosphoryne is very nice because it's semiconductor with high carrier mobility and some simulations on extended system has shown that it has potential to actually outperform graphene when it comes to high harmonic generation. So this is our framework. I had to come up with a name. I didn't have a name before I went here this week but I feel like everyone has a name for their coach. I've made up a name maybe it will change but for now I call it X nor for extreme non optical extreme non linear optical response. The framework is basically that we do DFT ground state calculations using the deeper package. Then we do a binary station with 90 to get the system in the binary basis set. Then I use the deep hole once more to get the cool arm interaction between my near orbitals. I feed it into the X nor code, which then solves this equation of motion to get the induced dipole in frequency domain and then I can look at linear and non linear response. And right now we have two types of pulses, we can input the first is this very brief delta pulse which is just like a small spark which then sort of excites the entire frequency range and the output will then be the linear response where we can look at the absorption spectra and and really localize these plasmonic resonances. And the other is a Gaussian pulse where you have a full width have met maximum of 100 fence of seconds and you have the time dependent simulations to get your, your harmonic spectra. So now moved to some results. Here are a comparison between three different will basically actually four different kinds of descriptions of the group in nano rhythm. This is a 2.5 nano meter rhythm with six act termination. And so the green model is this newest neighbor type binding model and you see that it sort of captures the feature close to the family level but you don't have this asymmetry around the family level and you don't have any particular state, obviously, in this case, then we have a binary station just using one orbital for atom where the initial projections is the PC also and then we get the correct behavior around the family level. And we also have a more sophisticated model where we also get some of this spaghetti both above and below these PC bands. And then below I show you the linear response where I changed the, the family level position to see how the linear response changes with doping and we see this very nice tune ability we have in graphene. So we don't have any difference between electron and hold doping in the type binding model. The two money models. I agree relatively well there is some difference when going to high doping levels. I'm going to compare here to a dft RPA calculation and for electron doping it's, it's quite similar for hold doping there are some features from the dft here which our model doesn't capture. Then I looked at the plasma and hands harmonic generation. Again using the three different models here. And basically, what I show here is the scale is this type of acceleration. And the x axis we have the, the frequency of the field, and then we have the frequency of the immediate variation here. And on top we have this linear response so here we have a plus money resonance here, and we see somehow that there is some high harmonic generation but really it's definitely most clear in the case of the more advanced model where we have bands also besides these simple PC also bands. And of course it makes sense because when you have these very high harmonics, then you really do go and excite bands very far away from the family level so it is something which requires you to go to somehow sophisticated models but I think what we have here seems to be reasonable. Then I have some results for phosphoryl. So now we have a band structure with a gap and single. No actually I think there's two states here. We have six act terminated ribbons and armchair terminated ribbons. And for the six egg I have one which is 2.5 nanometers and one which is five nanometers wide. And again we have looked at the linear response with different doping levels. And I have a DFT calculation for reference which now seems to don't know if you can see this I think it's a bit light on this screen. So I shall have to trust me that there's actually a really nice agreement now between these two. This is slightly more sophisticated in the way that now I have four orbitals per atom, because in phosphoryl we have a very strong SP hybridization so you really can't get around with going with less than that. And again we see that there is nice tune ability of these plus monic resonances. So then I would like to look at the tune ability of the high harmonic generation. And this is the high harmonic generation spectrum for the six second armchair ribbon, the short ones. And it's just to show how the spectrum looks like you can't really see the difference with doping here because it's just on top of each other. But here I've looked at the intensity of the third, the fifth and the seventh harmonic with different doping levels here. And for this six sec. Wow, it's really can you see the third harmonic I can't. Okay, I'm sorry. It's too light on this screen. Okay anyway, it's really flat. And that's also what the, the plus money expect to show so there's, there's not a lot of tune ability for this six egg ribbon. With the, which is not as wide but with a go to over here to the right I have the longer ribbon the five nanometer ribbon and here I get not a specific tune abilities are not that just if I increase the doping I get higher money generation but I have some doping levels which is preferable and basically hold open is slightly better than electron doping. I'm sure I have a more consistent sort of behavior here that if I increase the whole doping I will increase the intensity of the high harmonic generation. So I took sort of the best doping level for these three nano ribbons and then I looked at how, how much I actually get enhancement from this place, placement resonance. So this is the same plots as I showed for graphene. And basically, what we have here for the, the short six egg ribbon is really that you don't have this clear plus money question and this is really just sort of a lot of small peak so you don't get specifically large enhancement. But for the armchair ribbon you have a more specific peak and you get a nice enhancement and if you then increase the length of the six egg ribbon. Now you start to really have these prominent peaks again and you get very nice enhancement at this placement frequency. So this sort of shows that the systems I'm working with is actually perhaps slightly too small to really get into these effects so I would like to go to larger systems. And we are pushing to get to five and 10 nanometers and this is possible just takes a bit more time it's a bit more cumbersome to get everything running. So, to summarize, I've made this new code it's based on maximally localized money functions and we can calculate these extreme non linear effects. If we benchmark against response calculations from DFT we get quite nice agreement. I have used this to look at high harmonic generation, especially in phosphorine and the ribbons where it hasn't been investigated that much before. And we see that hold open seems to show the strongest high harmonic signal and we can actually enhance the signal with these plus money resonances and we can tune. Also, the, the effect both by the size of the ribbon and the dopey level. That's all. Thanks. Thank you for my stock so we have time for questions. Again, if you're on zoom you can write the question in the chat, or unmute yourself. And if you're here just raise your hand. Very nice work. And I have a technical question about how you somehow van your eyes your calculation. Do you. Do you import the Hamiltonian only, or also the position matrix elements. Also the position. Okay, yeah. So my question is, because I, we can, I can show you the paper that I have in mind later, but there was a paper I think the first author is silver three years ago, where, yeah, where they show that this position matrix elements were off diagonal position which elements were quite important for higher money generation in their van your eyes scheme for help us I think in real time. So I was just wondering if you if you make some comparison. No, no, but that would be very interesting to do that. Next. Thank you very much. I have a question on the graphene where you showed you have a model with one, one with three orbitals per atom, and you have some differences in your results. Yeah, exactly on the on the left, let's say. Do you know why there's differences because you have missing bands, or is because the shape of the bands or the many functions is different. It's because I have missing bands, because the shapes are pretty well replicated by the money models. Other questions. Okay, so if not, we thank our speaker again. Thank you.