 I'm when maybe some of you were already listening at conferences. We remember the bell outside, the real bell, but you can. OK, so Adio is back, so I can now start. OK, let's move to this last session of the conference. And I'm not going to say much about what they are going to talk now, but I'm going to talk a little about them. So the first speaker in this session of 2D materials is Suying Quack, and she comes from the National University of Singapore. She did her graduate studies in Singapore and then went to the US when she had her PhD thesis with Imsimius Caxiras from Harvard and Steve Louie from California, from the UCB, her thesis is in Harvard. And then for postdoc, she went to our dear Jeff Neaton. So she was there with Jeff for the postdoc. And she started with surface science, basically, and using DFT, GW, and plane waves. And then she moved to electronic transport, looking at a single molecule junction. And she has several very nice papers that we can find on the web about these studies. And then now she's back at National University of Singapore and back to surface and to thermically thin materials, 2D materials. And she has now a nice group of young people and working mostly on the electronic structure of low-dimensional materials for predicting experimentally observable quantities, which is, I mean, we still have a link with the experimentalists. This is really important to explain phenomena and to predict and also implementing in-house codes to compute Raman spectra, for example, resonant Raman, and developing new approximate easier just to get back to the old discussion, could it make it easier instead of with more computers, whereas, OK, I don't see Nicola. So approximate methods for energy level, alignment at surfaces that we know is really very difficult to do with our methods. It's very difficult. And now today she's going to talk about screening of quasi-particle excitations by atomically thin surfaces. So we are back to the molecule surface and thin surfaces. And the next speaker is Carlo Pinedoli. He did his laureate and PhD work in Modena with Carlo Bertoni and Rosa, PhD with Rosa di Felici, looking mostly at molecule surface interaction, first at chlorine in gallium arsenide and also how does the surface of gallium nitride grows. This was his PhD. And he used this, well, DFTGW, Plain Ways, also Kinetic Monte Carlo. He has a lot of work about it. And then his postdoc was in Zurich with Vandandreoni. And then he moved to dielectric properties of half-news silicates. But now he's back to molecule surface interactions. And he's now at the Swiss Federal Laboratory for Materials Science and Technology, meaning AMPA. That's how we say. And when I say molecule surface, molecule is now as 1D carbon-based graphene nanoribon. So it's not just a simple molecule. And now he has also very nice papers with the group with looking at nanowires. I have this formation of ultranarography nanoribons and nanografin. And he's looking at, he has this collaboration with experimentalists at AMPA. And for fabrication of characterization of carbon-based 1D nanostructures. And so now he's going to talk about on-surface synthesis of graphene nanoribons from a computational perspective. And I'll pass to Sue Hwing. And we start the session. OK, thank you very much, Merylia, for the introduction. And first of all, I'd like to say I'm so happy to be here in Triester. I've heard about the workshops here. But this is the first time I am here. And I'd like to thank the organisers and as well as the scientific advisory committee for giving me this opportunity. So today I'm going to tell you about some of our recent work on electronic screening by atomically thin substrates. So you have heard Professor Mazari's talk on 2D-layered materials and just to add that they come in a wide variety and with different properties. So you can play Lego with these materials. You can stack them and get new properties. And nowadays in experiments, you can control the stacking sequence and even sometimes the stacking angles. Now to twist this a little bit, there is a rather old field of organic electronics as well. And if you combine the organic electronics field with the 2D materials field, you could also have flexible devices with potentially interesting properties, such as the schematics that I've shown here. And these have also been realised experimentally in recent years. So the physical property that I'm going to be interested in looking at in today's talk is the energy level alignment at the interface. So energy level alignment is very important because it determines the energy barriers for electron transport. And the question that we want to ask is what is the energy level alignment at the organic 2D material interface? Just some background. Yesterday, a few speakers talked about the image charge screening method developed by Jeff Eaton. And I'll just give some physics about that. So basically, it is very difficult to compute the energy level alignment of large systems. And quite more than 10 years ago now, Jeff came up with this method where he approximates the quasi-particle levels using this two-step method. So first, we consider the DFT level alignment, which is wrong because the gap is too small, first of all. So we correct that small gap using gas-phase self-energy corrections. This is the gap of the molecule in the gas-phase. However, because of the presence of the metal substrate and the fact that the Homo and Lumo are actually the levels that you get from photoemission or inverse photoemission. So when you measure these quantities, you actually create a charged particle, a quasi-particle in the material. And this charge gets screened when you have a metal substrate. So the screening of the charge would, for example, if you imagine the Homo, you remove the electron and you get a hole. So the screening of the hole would stabilize the final state. And this would reduce the amount of energy that you need to get the electron out. So as a result, the Homo level is moving up. And similarly, the stabilization of the added electron will stabilize the Lumo. And together, you see that this reduces the band gap. And for a small molecule on the metal substrates, we can approximate this effect using classical electrostatics. So this is the polarization integral, which is the value of the self-energy from screening. And we can approximate the quantity here delta W, which is a change in screen coulomb potential due to the substrate. By this quantity, V screen RR, which I define to be the screening potential from the substrate, due to a charge perturbation at R. And the response is also felt at R, where R is the position at the molecule. So you remove the electron forming a hole, for example, and you feel the effect at the same position. So this is the kind of screening effect that you'd be feeling for a simple system like this. And then we can approximate this using classical image charge screening. And it can be generalized to semiconductors with dielectric constant. So the image charge approach is only valid in certain situations. Typically, the molecule has to interact weekly with the substrate. There should not be charge transfer, because then you get dynamical screening effects. And polarizably, the molecule should be much smaller than that of the substrate. And finally, you have the approximation which I just mentioned in the previous slide. And we were motivated by this experiment done in NUS, where we had PTCDA molecules, which is this molecule here, which assembles in a herringbone structure on different substrates. And we want to ask, to what extent does the 2D material tungsten disenionite, which is a semiconductor, participate in screening the PTCDA graphite interface? And how does the PTCDA gap change due to this monolayer? So here is the outline of my talk. In the first part of my talk, I'll talk about applying the image charge approach to this system. And this is published work in ACS Nano. Then in part 2, you'll find that in part 1, we were not quite satisfied with what happened. So in part 2, I will go further to talk about getting level alignment from the RPA electrostatic screening potential instead of the image charge approach. And this actually gives us additional insights into electronic screening by 2D materials in general, and also the screening of charge in priorities beneath 2D materials. Finally, in part 3, I will talk about how we are now able to get level alignment from GW that is adapted to large interface systems, such as the one that you saw in the previous slide. And we also apply it to PTCDA on silver, which is a prototypical system where you have charge transfer. OK, so that's the first part of my talk. So these are some nice STM images that we'll obtain. And you can see the Homo and the Lumo here. And they are done on different substrates. And the nice thing is that the pattern is the same for all the substrates. And this is the result. So this is the STS results, getting some spectroscopy. And this is what we calculate. And it actually looks not bad, much better than DFT. OK, so with DFT, you'll get the same rather small gap on all substrates. And with the image charge approach, you'll get substrate-dependent Homo-Lumo gaps. And screening effects reduce the gap by about more than 1EV. OK, and to what extent does the WSE2 monolayer screen? Well, the easiest way to look at that was to remove the tungsten disenlight layer, which we did, and keeping the graphite there. And that effectively increases the distance from graphite and gives a calculated gap that is much larger than any of the measured gaps. OK, this shows us that the tungsten disenlight layer, although being atomically thin, participates significantly in screening the effect of excitations. And you can see that in another way, this is the change in the electrostatic potential when we apply an electric field. And here in tungsten disenlight, you can see that the field is significantly screened. OK, but if we look more closely at the numbers in the table, you can see that there is a quantitative discrepancy. And they could be due to several effects. One is the neglect of molecular polarizability in these rather large molecules. And the graphite actually does not screen as well as a metal. And also the improper treatment of screening from tungsten disenlight. OK, in particular for a 2D material, what is the appropriate dielectric constant to be used in the image charge model? OK, so this brings us to part two. So instead of using the image charge approach here with this approximation, we decided that we would just compute v screen the quantity I talked about directly from AppInitio GW calculations on the 2D material. Actually, essentially, we do a RPA calculation of the dielectric matrix and then compute v screen. So before I go to the results, you might ask just intuitively, how does a suspended 2D material screen excitation above it? And in some approaches, it is common to take an effective dielectric constant, especially in engineering, and it's quite effective to do that, to consider the average dielectric constant that you have from different parts of the system. And here with lots of vacuum space, that kind of approach should give an effective dielectric constant of about one, which means it doesn't screen much at all. And if you go back to the history on the literature of 2D materials, one of the most interesting things about 2D materials was the large exotherm binding energies in these systems compared to in 3D. And this is precisely related to the fact that you have much weaker screening within the 2D materials compared to within 3D materials. So what we find is that the screening of excitations adjacent to 2D materials is actually non-trivial. For example, the homo-lumogap for benzene on monolayer hexagonal boron nitrite is 8.4EV, while that for gas-phase benzene is 10.6EV. And similarly, for what we have done on black phosphorus and hexagonal boron nitrite, we find that HPN can reduce the quasi-particle gap in black phosphorus in the exciton binding energy by as much as 11%. And this, to note that monolayer hexagonal boron nitrite is a very wide band gap material. So we thought that there's something interesting there. And OK, so I'm going to talk about the methodology. We said that we're going to have v-screen computed in this way. So we do this using the codes that are implemented already in Berkeley GW using plane wave basis sets and non-conserving pseudo-potentials. And of course, we need a slept column truncation cut-off. So here are results that we have comparing the homo-lumo gap for benzene on different 2D material substrates computed with GW and with the approximate method where I used an variant of the image charge approach but with v-screen that I compute directly. So the comparison is not bad. You can see that the 3 by 3 cell which we use for all these may be a little bit small. And when we use a 4 by 4 cell, we get actually better agreement. But what this tells us is, first of all, that you actually have an approximate way to tell what kind of renormalization, gap renormalization you have without actually doing the whole interface calculation and simply just doing the substrate calculation. And you can do this for a variety of different small molecules. The second thing that it tells us is that v-screen RR, which I have defined, captures the effects of screening from the 2D material quite well. So we want to study this quantity a little bit more. And we have studied it for a range of different 2D material substrates that cover a wide range of quasiparticle gaps and they are found in red. Okay, and we find quite a good linear relationship between the quantity that we compute and the quasiparticle gap of the 2D material. And interestingly, for the 3D materials that we compute, we, these are like more than 20 of our angstroms for the slab tight, they actually have the same linear relation. So this tells us that atomically thin materials screen the point charge perturbation adjacent to them just as well as a 3D substrate with a similar quasiparticle gap, which is quite different from the contrasting screening within the 2D and 3D materials that I talked about before. So I will not show the details in this talk, but we can actually compute the induced charge due to the excitations and show that this is consistent with the fact that most of the induced charge is at the surface within two to three angstroms. So this is because screening is essentially a surface effect. Now, another important aspect of screening from 2D materials was the discovery that thin film hexagonal boron nitride was an excellent substrate, the substrate of choice for graphene. It was found that if you put graphene on hexagonal boron nitride, you reduce dramatically the charge, the number of charged puddles that you have and you improve the mobility in graphene. So this again suggests some kind of a non-trivial screening from hexagonal boron nitride, despite its large band gap. And experimentally, people have tried to study this more fundamentally using electrostatic force microscopy experiments where basically what is measured is VS, which is a difference in surface potential between the top and the bottom of the slab. And they do measurements for different thicknesses and get thickness-dependent screening properties of 2D materials. So here I emphasize that the charged impurities are beneath the 2D material substrate. They are on SiO2. And then you imagine that graphene is on top and you want to know how well does the 2D material substrate screen out the effect of charged impurities beneath the substrate for something that is on top. Okay. So we can, using our methods, also model these experiments, using, and we use this formula here where we get the V screen at the top minus the V screen from the bottom. And then we average over in plane coordinates. And we were quite surprised that when we did that, we actually got rather good qualitative agreement between theory and experiment for three different papers here. Quantitatively, we did not expect to get exact agreement because it was already discussed in the papers that there's charged impurities that absorb base. And so they actually thought that what we saw was not actually an intrinsic property of the material. But what we find here is that the qualitative agreement is quite remarkable, which was nice. And here I want to talk a little bit more about hexagonal boron nitride. So in this paper in Nanolattes, they concluded based on DFT calculations of dielectric constants, as well as fits to a 3D, the red 1, 3D non-linear Thomas Fermi model. It was suggested that the experimental data point for one layer HBN is an outlier and it is due to increased charge transfer from an underlying water film. But according to what we have simulated, we do not think that the one layer data point is an outlier, but rather that it is part of the intrinsic property of HBN. So going back to how that hexagonal boron nitride was a substrate of choice to screen out charged impurities, we have this plot here of the delta V screen, V screen at the top minus V screen at the bottom, the magnitude of that, and compare MOS2 and boron nitride. And here you see that boron nitride, if they are similar, then according to this line here, boron nitride should be somewhere here, or very small. The delta V screen should be very small, which means it doesn't screen very well. But we find that for its large quasi-particle gap, boron nitride actually screens charged impurities under it rather well. Okay, so this is consistent with the use of boron nitride as an excellent wide-band gap dielectric substrate. Okay, so the summary of part two is that we have proposed a new methodology to compute the level alignment at small molecule 2D material interfaces where you do not need the large interface calculation. And along the way, we found that atomically thin 2D materials can screen a point charge perturbation adjacent to it, just as well as 3D substrates with the similar quasi-particle gaps because screening is a surface effect. And so the implications of that are you can use 2D materials as effective, atomically thin dielectrics. We also compare our results with electrostatic force microscopy experiments, and we show that, you know what they observe, at least the qualitative trends are really related to the intrinsic screening properties of 2D materials. And we also explain why layered hexagonal boron nitride is an excellent, or at least we show that layered hexagonal boron nitride is an excellent wide-band gap dielectric. Okay, now finally in the last part of my talk, I will talk about level alignment from GW adapted to large interface systems. So the parts one and two, actually the methods are quite simple and powerful. There are some restrictions, like as I had mentioned before. And just to repeat the molecule as an indirect, weakly with the substrate, charge transfer should be negligible, polarizability of molecules should be small. And well, as we have heard from yesterday's talks, GW is generally able to predict quasi-particle levels well and overcome the limitations that I listed in the previous slide. But the difficulty here is that it's actually very difficult to perform GW calculations on large interface systems such as PTCDA on substrates. And for example, when we use the Berkeley GW code, the bottleneck that we face is the memory requirements, even for benzene on MOS2, we have a memory requirement of seven terabytes. And this is largely related to the inversion of the static RPA dielectric matrix of the interface. So just to give some background for GW calculations, so the different parts of the calculations that we have, we approximate the self-energy using the GW approximation. And here we use the Berkeley GW code and the one-shot GW not approximation. So the steps are, the first step is to get a DFT mean field calculation of the Coen-Sham Eigen values and wave functions. And then to calculate the dielectric matrix, the static RPA dielectric matrix. And as was mentioned yesterday, this involves the computation of chi, which is ordered n to the four. And so memory requirement there is also large. And then the last part, which I call the sigma calculation, which requires a computation of sigma using the dynamically screen Coulomb interaction which you derive from this inverse dielectric matrix. Okay, so because of the huge cost of GW calculations, in the past there have been approximate GW calculations that have been proposed for interface systems. And primarily they are applied applicable to weakly coupled van der Waals hetero structures. So here I list the two examples. So the first example attributed to Christian Pegasen is called the G Delta W method, where you compute a change in screen Coulomb interaction after you form the van der Waals hetero structure. And then you compute sigma step, which is a self energy step for the individual layer, so not the hetero structure. Okay, and then the dielectric function for the hetero structure is evaluated by combining that of individual component layers in their unit cells. The second method, which was done by Professor Louis Berkeley, is what I call the add chi method. So they compute the chi matrix for individual component layers in the supercell structure, then they add the polarizabilities of these different component layers to get an approximation to the polarizability of the hetero structure. And then they compute sigma for the individual layer using the approximated chi. So here we propose a different method, our approach, which I call X-A-F-G-W for interfaces, is as follows. Step one, we have what we call an expand chi method. In step two, we have an add chi. And step three, we do full sigma, meaning sigma for the full interface. Okay, so in expand chi, we calculate the chi matrix for smaller unit cells for each component of the interface. So typically, if you have seen the PTCDA and WSE2 interface, there are many, many WSE2 unit cells in there. So what we can do is to calculate the chi matrix for those smaller cells and then expand that by unfolding to the larger cell. Then in step two, we add chi, okay, for different parts of the interface and we get the approximate chi for the interface. And in step three, we compute sigma using the chi matrix of the interface and the full wave functions of the interface. So the first step will reduce the memory requirement and computational cost for chi in large m by n cells by a factor of m to the four, which is a considerable savings. In step two, we add chi, this we can show to be a good approximation even for hybridized interfaces. And finally, for full sigma, this enables us to treat dynamical screening effects and wave function hybridization in contrast to all the previous approximations. And our approach is built upon the Berkeley GW code with a plane wave basis. So to just give some results, PTCDA on WSE2, in this slide, I showed the gamma point result. Here you can see that the homo state is only 48% on the molecule with so strong hybridization. Using our method, we get a gamma point gap of 4.1 EV. If we do not do full sigma, meaning we do the sigma calculation with PTCDA wave functions only, we get 3.5 electron volts. If we use the v-screen method from part two, we get 2.5 electron volts. And the experimental homo-lumo gap for this metric system on graphite is 3.7 EV. And since graphite would screen out, to reduce the gap even further, these would definitely not work. Okay, here on this slide, I showed the homo-lumo gap that has been obtained from the projected density of states. And these are our results. So here in today's talk, I have not yet done the full sigma with graphite, but only full sigma for PTCDA and WSE2. And this is the result that we get, which is in good agreement with experiment. And just to note that we have used a 28 electrons pseudo-potential for tungsten. So totally we have a 782 occupied bands here and a huge cell size, and we still are able to do that. Okay, and finally, my last slide results. PTCDA on silver is a huge system. Yeah, it's a prototypical system with large charge transfer where dynamical screening effects are important. Okay, I have a total of 2,850 electrons from silver atoms. Okay, here are our results. The XAFGW, we get, I consider very good agreement with the experiment and you can see the lumo is partially filled. So in summary, this methodology allows us to compute the GW quasi-particle energies for large interface systems using a plane wave basis. So the components of the interface can be molecules, semiconductors, or metals. And we include dynamical screening effects. And lastly, I'd like to acknowledge the people who did the work. My PhD student, Yuxie Zheng, Postdoc Yifeng Chen and Postdoc Kian Nuri, student Nicholas Ching and Postdoc Feng Yuanxian. And they are here in these slides and I acknowledge funding from National Research Foundation and Ministry of Education. Thank you very much for your attention.