‘Connecting the nodes’ in the knowledge graph: Renormalization

One of the things that excites me about learning is the process of creating connections between different things. I believe, this is also the process of learning that is persistent throughout our lives, and in my opinion it can be as powerful as the process of learning in our childhood.

I therefore decided to start writing down notions that I read and which connect to notions I had read before. It’s funny how this can also be converted into a ‘computational’ network, and observe how clusters are formed between its nodes. The difference is that here I will not be connecting words between them, but rather presenting the same word, with the same conceptual meaning, used in different sub-domains in physics. Maybe the most appropriate measure here is when the network would ‘break down’. That is, when the meaning between different uses will change completely.

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The Finite Elements Method convergence survival guide

Ok, people, let’s face it. Many of us had no idea about the maths behind Finite Elements Method (FEM) simulations when we initially started using them. And most of us have felt that horrible feeling when we repeatedly saw the message ‘No convergence’ instead of a nice output. What is horrible about it is that, unless you or your group develops the software, you probably have no idea where to start looking for fixing the problem.

I heard from a lot of people in my field (electronics) that they have felt discouraged with FEM and did not even want to touch it. But I’m here to tell you that there is hope! I decided to write this guide after almost 10 years of using this type of software (on and off), first for nanoelectonics and then for semiconducting quantum technologies. It might be that the issue is actually more important in the latter, because of the differences in magnitude (or the scale of things) between classical and quantum effects (yes, not everything is quantum in quantum TCAD). But this is a user’s and not developer’s guide, so I will also keep it math-and code-free.

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3D and 2D reciprocal lattice vectors (Python example)

When I started using Density Functional Theory and, even more, when trying to re-create its results in a meaningful piece of material, like a nanoribbon or a nanowire, a lot of the problems came during geometry creation. This is natural, as DFT is a theory to derive quantities like eigenenergies, in a crystal lattice with periodicity. But when trying to switch to a model that is finite in one or more directions, you have to start a sort of mix and match procedure.

During this time (and assuming you are not the one who writes the software), visualizing vectors is maybe the less useful thing to do. Still, there are cases where you need it in order to get a better understanding of things, like visualizing Weyl points.

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Extracting pinch-off and threshold voltages in quantum transistors

Many times I needed to extract threshold voltages from experimental results. I remember in my PhD days, this was quite a debate, and we could generally agree there is no optimum way of doing it. The problem mostly lied in that you are not exactly sure in which part of the plot the current starts to flow, or the channel is depleted. In room temperature transistors, this was mainly due to the intermediate region of thermal population of the bands. In quantum transistors, we are playing in the low temperature field and most of the time dopants are thought to be frozen.

What is really certain is that all voltages that you compare against will need to be extracted using the same method.

Since what we are interested in is changes in the curvature of the plot, we expect to play around with derivatives a lot. But for this, there is the extra problem that experimental results can be very noisy. Once you take the derivative, you introduce further noise, that goes even worse in the second derivative (see figure below).

Characteristics of a transistor with 2 pinch-off positions in the classical regime. First derivative (blue plot) shows pronounced amount of noise.
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On the universality of Landau theories

There is a lot of buzz going on about topological materials and the quantum Hall effect these days that mark the 40 years since its discovery. If you know a few things about topological materials, you will definitely know that the theory behind them is about a macroscopic mechanism that originates from microscopic (quantum) effects.

There is a similar class of problems, maybe less famous at the present time, namely that of polarization in materials, which has its own counterpart “The modern theory of polarization” that was developed in the ’90s. What these two have in common is exactly the emergence of macroscopic phenomena from microscopic ones.

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Vector potential with an angle to the periodic direction

One of the most difficult aspects in Tight Binding models is the incorporation of the magnetic field. And that is because a lot of the things that exist in simple analytical expressions in quantum mechanics, change when we are talking about a Tight Binding model, and especially one derived from First Principles using Density Functional Theory as that discussed here.

One of the problems that could emerge is that there exists an angle \theta between the periodic direction and the direction the magnetic field is applied. This differs from the case of the Peierls phase, defined as,

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Interview on ΒΗΜΑ Science

Our work at CEA in collaboration with CNRS has been published on the printed version of the Greek newspaper ΒΗΜΑ. I am happy that the project I am currently working on and the way it connects to the work I was doing at Aristotle University of Thessaloniki have gained publicity.

You can find it on-line here (requires subscription):

https://www.tovima.gr/printed_post/i-kvantiki-yperoxilfsta-skaria/?fbclid=IwAR1NnkS8YSNVDYs7OCHQnAqsIAOJZHKqVZsb6GhZgxGi2HrCfWMbBDqz4v8

Marie Curie fellowship

I am happy to announce that today was the first day of my journey as a Marie Skłodowska Curie fellow, funded by the European Union. My project is titled “A predicting platform for designing semiconductor quantum devices” (PRESQUE) and I will be working at CEA Grenoble for this, under the supervision of Xavier Waintal.

This project has the ambitious goal of making computational predictions for semiconductor-based quantum transistor devices a reality, since for this to happen, a lot of different physics need to be incorporated into one model. Luckily, the group of Dr. Waintal has done a great work in developing the software Kwant, including different modules that can work to this aim.

If we manage to have one such computational model, then this can signify that we are able to accelerate the procedure of searching for the optimum device configuration, and ultimately getting closer to the quest of the holy grail, that is, quantum advantage.

It will be a lot of work, and lots of interesting problems to solve, so there is bound to be some corollary technical intricacies, which you can follow in this blog, along with other updates on the project.

 

Matrix elements of the momentum operator in Quantum Espresso

Last week I was trying to find what the format of the filp file is for Quantum Espresso that produced by bands.x with the appropriate variable set, and which contains the matrix elements of the momentum operator between valence and conduction bands.

As I couldn’t find any documentation on is format, or any .gnu files to plot it, I thought it would be faster for me to go through the code, and indeed it was quite easy to figure out what was being printed, so I thought I would post this here too.

I will also upload a python notebook that converts them into .csv file, as soon as I double check that it is working properly. Continue reading