Extracting pinch-off and threshold voltages

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. But 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 theory

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):


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

Nearest neighbour hoppings in TBModels for kwant

TBModels is a python module that belongs to the Z2Pack toolkit, and can be used to constructuct Tight Binding models to be used with Kwant software for transport calculations using the Landauer-Buttinker formula.

When deriving Hamiltonian matrices from first principles with Wannier90 for kwant, TBmodels will restore all the hoppings between adjacent unit cells. This can be proven very time-consuming both when preparing and solving systems with lots of atoms. Often, only nearest neighbor (nn) interactions are needed, especially if next-nearest neighbor (nnn) etc. decay considerably that can be safely ignored.

For example, in my system, WFs 4 and 2 are neighbors. When looking at the Wannier_hr.dat file, I see the following:

0 0 0 4 2 -1.287933 0.000000


0 1 0 4 2 0.056218 0.000000


0 2 0 4 2 0.004991 -0.000000


0 3 0 4 2 0.008744 -0.000000


0 4 0 4 2 -0.004063 -0.000000

The first three numbers signify the unit cell, which is [0,0,0] in the home, [0,1,0] one hop in the y direction, [0,2,0] two hops in the y direction etc. The next numbers are the WFs (namely 4 and 2) and the last term is the hopping term. In my system, there is no repetition in the z direction, and so only x and y are important. z stays 0.

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Teaching in the age of doing

Ever since I was really young I hated classrooms. Throughout my life, I’ve spent a great portion of my time thinking about how lecturing should be done and always had crazy, innovative ideas. But I was also afraid that they would not be effective. So, then I started thinking how a society would be like that supports this type of teaching. But then I was afraid that it’s not worth it, since I would not be able to change the whole of it!

Fast forward 15 years later and boom! I’m the lecturer! And after spending some time observing people that I admire for their patience (how they talk, their ideas, how they teach) I realise that there is absolutely no reason to be scared! The ‘preparation’ was really long and the ideas are many, but now it is time to act on them, and I can’t help but being excited for what is coming!

So there, start small. Like this:

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