## Projects

**These below are examples of projects our group can offer to Master and Bachelor students**

### Bachelor Projects

Several of the master projects listed above and described below can be adapted to be a bachelor project. Even more so, a solid background in math/physics/programming is required - please email your request to the relevant project proposer, mentioning your grades in all classes relevant.

### Master projects

The master projects that we offer require a solid background in maths, physics, and programming. Therefore, anyone interested should first follow Prof. Nicola Marzari's course on Quantum Simulations of Materials (MSE468, spring semester). If interested, please contact the responsible for the organisation of the projects Michele Simoncelli at least two weeks before the EPFL registration deadline, with a copy of your transcripts and a short description of your competences and interests. The projects listed below are also suitable for EPFL master students who will take the course “Research project in materials I” (10 credits). Be aware that all the master students are required to attend all the group meetings and recommended seminars, remote supervision is guaranteed in case of absence of places in the laboratory.

- Koopmans-compliant calculations on systems with analytical solutions
- Theoretical and computational study of cathode materials for eco-friendly rechargable batteries (Spring 2021)
- Develop an active-learning AiiDA lab application for the Materials Cloud
- Visualization plugins for the Materials Cloud platform
- Quantum dynamical effects in correlated materials
- Engineering defect centers for quantum computing
- Predicting screening parameters for fast Koopmans-compliant calculations

##### Koopmans-compliant calculations on systems with analytical solutions

Density functional theory (DFT) is a go-to method for predicting the structural and spectroscopic properties of materials and molecules computationally. However, DFT is only approximate, and standard formulations of DFT exhibit some notable shortcomings. Our group has been developing Koopmans-compliant (KC) functionals [1], an extension to DFT that is far better at predicting quasiparticle-related quantities such as ionization potentials and electron affinities.

We have already shown, via numerical calculations on real molecules, that KC functionals work well [2]. However, we have never tested them on simple systems where analytical solutions exist. Such systems are a dream for physicists: their simplicity, and the fact that we know the exact solution from the start, makes it much easier to interpret what is going on and diagnose any problems. In this project, the student will test KC functionals on systems with analytical solutions. This will involve a mix of mathematical derivations and numerical calculations, all in an effort to assess what KC functionals do well, and what they do poorly. The student's conclusions will help inform the ongoing development of KC functionals.

**Requirements**: a strong mathematical background is essential. This project will involve running calculations with Quantum Espresso and Mathematica on Linux machines, so prior familiarity with Mathematica and Linux would be useful, as would completion of MSE-423 and MSE-468 or equivalent.

[1] G. Borghi et al., Koopmans-compliant functionals and their performance against reference molecular data, Phys. Rev. B 90, 075135 (2014).

[2] N. Colonna et al., Koopmans-compliant functionals and potentials and their application to the GW100 test set, J. Chem. Theory Comput. 15, 1905 (2019).

Contact: Edward Linscott

##### Theoretical and computational study of cathode materials for eco-friendly rechargable batteries (Spring 2021)

**Requirements:** Prior to this project, the candidate must follow the two courses MSE-423 and MSE-468.

Description of the project:

Our society is currently making a big effort to undergo a transition to the climate-friendly ecosystem. Constant growing of the population is accompanied by needs in larger amounts of energy [1], which is currently being produced mainly by using oil, coal, natural gas, which are sources of huge CO2 emissions which lead to the global warming. This cannot be continued like that further because the consequences for our planet and for the humanity will be disastrous. In fact, many governments announced roadmaps for achieving carbon-free ecosystem by 2050 (Swiss Energy Strategy 2050, EU's Battery2030+ flagship). Therefore, all the traditional energy sources must be replaced by the renewable energy sources (solar, wind, hydro, etc.), but these are not stable, and hence we need efficient and eco-friendly ("green") battery technologies for storing large amounts of energy and use it later when there are large demands. This semester project is focused on the theoretical and computational investigation of batteries, more precisely of the positive electrodes ("cathodes") [2].

Cathode materials contain transition-metal compounds (TMCs) (see figure below, which is the crystal structure of LiFePO4 [3]), and from the theoretical point of view modelling of TMCs is very challenging due to the presence of strongly localized and partially filled d-type electrons. In this project the student will use Hubbard-corrected density-functional theory [4,5,6], which has proven to be successful for accurate modelling of TMCs. All calculations will be done using the Quantum ESPRESSO package, which is the most widely used open-source electronic-structure software for materials modelling at the atomistic scale [7,8]. For more information see this page.

[1] D. Larcher and J.-M. Tarascon, Nature Chem. 7, 19 (2014).

[2] L. Monconduit, L. Croguennec, R. Dedryvere, Book "Electrodes for Li-ion Batteries: Materials, Mechanics, and Performance", vol. 2, Wiley (2015).

[3] M. Cococcioni and N. Marzari, Phys. Rev. Materials 3, 033801 (2019).

[4] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991).

[5] V.L. Campo Jr. and M. Cococcioni, J. Phys.: Condens. Matter 22, 055602 (2010).

[6] I. Timrov, N. Marzari and M. Cococcioni, Phys. Rev. B 98, 085127 (2018).

[7] P. Giannozzi et al., J. Phys.: Condens. Matter 29, 465901 (2017).

[8] P. Giannozzi et al., J. Chem. Phys. 152, 154105 (2020).

This project requires the following skills:

- Good knowledge of quantum mechanics, density-functional theory
- Basic knowledge of Linux and bash scripting

Contact: Iurii Timrov

##### Develop an active-learning AiiDA lab application for the Materials Cloud

The Materials Cloud is a modern web platform built to support researchers in sharing data with other researchers as well as performing computational research directly on the platform. For example, researchers can use the platform to carry out structure optimization and band gap calculations and then publish their results to make it accessible for follow-up investigations.

In this project, the student will develop a new AiiDA lab application that enables researchers to use previously calculated results to determine which calculations/simulations to carry out next (active learning)[1-3]. The first stage of the project involves the identification of a suitable benchmark study and the research of pertinent machine learning algorithms. The student will then need to develop a design document for the application and start implementing a prototype implementation. The final stage is the implementation of a polished version of the app which will then be published on the Materials Cloud platform.

[1] Xue, Balachandran, Yuan, Hu, Qian, Dougherty, Lookman, PNAS, 113, 47 (2016).

[2] Balachandran, Prasanna, Young, Lookman, Rondinelli, Nat. Comm. 8, 1 (2017).

[3] Dai, Bruss, Glotzer, arXiv:1803.03296 [Cond-Mat, Physics:Physics], (March 2018).

The student should have a background in materials science and engineering, but is free in identifying the specific research focus suitable to their strengths and interests.

This project requires advanced software development experience with Python and basic experience with Jupyter notebooks.

Contact: Simon Adorf

##### Visualization plugins for the Materials Cloud platform

Our group has been developing AiiDA (www.aiida.net), a platform to automate simulation of materials, store results in a database, analyse the results and share them. Moreover, we develop Materials Cloud (www.materialscloud.org), a rich web interface to expose the AiiDA database and show research results, as well as to provide simulation tools to researchers. These projects require that the student is already expert with python, including its object-oriented programming features.

**Option 1**:
There is room for the students to choose a project to extend the functionalities to support researchers in the use of AiiDA via web interfaces, or to improve the web interface tools of Materials Cloud.

*These projects require experience with JavaScript, HTML, CSS.*

A non-exhaustive list of examples:

- New visualizer plugins of data in the database, or of specific physical properties: see e.g. http://materialscloud.org/tools/seekpath/ for crystal structures and Brillouin zones
- graph browsing, or Graphical Query Builder to look into the database
- advanced python tools to analyse calculation results

**Option 2**:

*These project requires experience with python and jupyter.*

Task: create interactive visualisations in python notebooks and/or as Materials Cloud tools (https://www.materialscloud.org/work/tools/options).

On possible example is the realisation of a tool that, given the Hamilonian parameters as obtained from a Wannier-Function calculation, can compute the interpolated band structure on the fly, and when zooming recalculates the band structure on the selected region, giving the illusion of an infinite-zoom capability. This project would help students in better understanding band structures, dealing with the interpolation of them from DFT calculations on denser grids using Wannier functions, and to put this knowledge together in a useful and advanced web tool.

Contact: Elsa Passaro,Valeria Granata, Giovanni Pizzi

##### Quantum dynamical effects in correlated materials

Electronic structure calculations are fundamental to understand several physical properties of materials. For many ground state quantities, like the density or the total energy, density functional theory (DFT) is the way to go. However, to reproduce spectra that are measured, e.g., in photoemission experiments, DFT shows its limits, and more advanced theories are needed.

In this project, the student will approach electronic structure calculations from a theoretical perspective and apply DFT to a prototypical material. In a second stage, the study of more refined properties will be pursued, with an emphasis on dynamical quantum effects.

The project involves the use of the open-source software Abinit on Linux machines. A prior basic knowledge of Linux and bash scripting is recommended, as well as the main concepts of quantum mechanics applied to computational solid state physics. For that, the two courses MSE-423 and MSE-468 are strongly recommended.

Contact: Marco Vanzini

##### Engineering defect centers for quantum computing

The advent of quantum computers would revolutionise the scientific world. Industrial giants like IBM, Microsoft and Google, and a bigger and bigger number of researchers, are involved in a race for developing the technology to build a big and fault tolerant quantum computer. Among the most promising qubit candidates, defect centers in semiconductors stand out for the extremely long coherence time at room temperature. Thanks to their optical properties, these systems can be used successfully also for quantum communication (encrypt messages thanks to the laws of quantum mechanics) and quantum sensing (measuring very small quantities due to the extreme sensitivity to perturbations).

In this project, the student will perform electronic structure calculations to discover new defect centres in semiconductors. The first step consists in investigating the stability of the defects and their capability of storing quantum information. In a second stage, the defects will be engineered in order to overcome the limitations emerged in the first analysis.

The project involves the use of the software Quantum ESPRESSO on Linux machines. A prior basic knowledge of Linux and bash scripting is recommended, as well as the main concepts of quantum mechanics applied to computational solid state physics. For that, the two courses MSE-423 and MSE-468 are strongly recommended. The knowledge of the theory of quantum information is NOT required.

Contact: Francesco Libbi

##### Predicting screening parameters for fast Koopmans-compliant calculations

Density functional theory (DFT) is a go-to method for predicting the structural and spectroscopic properties of materials and molecules computationally. However, standard formulations of DFT exhibit some notable shortcomings, including the fact that they do not comply with Koopmans theorem.

Our group has been developing Koopmans-compliant functionals [1], an extension to DFT that complies with Koopmans theorem, making it far better at predicting quasiparticle-related quantities such as ionization potentials and electron affinities [2]. However, these calculations are relatively complicated, especially because we must first calculate a lot of screening parameters.

In this project, the student will investigate how we can streamline these complicated calculations. Specifically, they will investigate (a) if screening parameters can be accurately predicted from other system properties that are easier to calculate and (b) if these screening parameter estimates give sufficiently accurate ionization potentials and electron affinities.

This project will involve running calculations with Quantum Espresso on Linux machines. For this reason, prior familiarity with Linux is essential, as is completion of MSE-423 and MSE-468 or equivalent. Familiarity with python is also strongly recommended.

[1] G. Borghi et al., Koopmans-compliant functionals and their performance against reference molecular data, Phys. Rev. B 90, 075135 (2014).

[2] N. Colonna et al., Koopmans-compliant functionals and potentials and their application to the GW100 test set, J. Chem. Theory Comput. 15, 1905 (2019).

Contact: Edward Linscott

##### Prediction of shear and layer-breathing modes for layered materials

When atoms oscillate in a layered material, composed by 2D layers, the low-energy part of the vibrational spectrum is characterised by two fundamental sets of normal-mode vibrations, where the layers oscillate as rigid units. These oscillations can be either parallel (shear modes) or perpendicular (layer-breathing modes) to each other.

We have already performed a study that, given the symmetry of the layered material, can predict these modes, typically plotted as a function of the number of layers in the multilayer, in what is called a "fan diagram". This method has also been implemented in an online tool on the Materials Cloud. Below you can find a screenshot for molybdenum disulphide.

The goal of this project is to:

- create a database of computed interlayer force-constant parameters for the known 2D materials, e.g. for all materials of our 2D database. This part will involve running simulations with Quantum ESPRESSO, using the AiiDA code to manage the simulation workflows;
- extend the online tool so that, for known materials, the force constants are taken from our computed database (rather than using random initial values)
- extending its applicability also to heterostructure formed by different layers, that are now routinely realised experimentally (now, the tool is able to predict frequencies only for multilayers composed of identical layers). This includes computing force constants for multiple pairs of layers, and for different angles between them.

Contact: Giovanni Pizzi