## 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 thesis projects

The master projects that we offer require a solid background in maths, physics, and programming. Therefore, anyone interested should first follow the course on Quantum Simulations of Materials (MSE468, spring semester, taught either by Prof. Nicola Marzari or Dr. Giovanni Pizzi). If interested, please contact the responsible for the organisation of the projects Nicephore Bonnet 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) [https://edu.epfl.ch/studyplan/en/master/materials-science-and-engineering/coursebook/research-project-in-materials-i-MSE-490]. 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.

- Thermal transport in mixed-valence thermoelectric skutterudites
- Accelerating structure optimizations using perturbative post-processing
- Topology in 1D and Majorana fermions: the case of exfoliable one-dimensional Ag
_{2}Se_{2} - Mechanical properties of novel exfoliable one-dimensional materials
- Developing an analytical model to describe the rattling motion in thermoelectric cage-like structured compounds
- Phonon-mediated heat transport in graphene and hexagonal boron nitride
- High-throughput screening of high thermal conductivity materials for efficient thermal management
- Theoretical and computational study of cathode materials for eco-friendly rechargable batteries
- Visualization plugins for the Materials Cloud platform

##### Thermal transport in mixed-valence thermoelectric skutterudites

Thermoelectric (TE) materials can realize direct conversion between heat and electricity, which is environment friendly and improves the usage efficiency of solar energy [1]. The conversion efficiency of thermoelectric materials can be evaluated by the dimensionless figure of merit, ZT = (S^{2}σT)/(κ_{e}+κ_{l}), where S is the Seebeck coefficient, σ is the electric conductivity, T is the absolute temperature, and κ_{e} and κ_{l} are the electrical and lattice thermal conductivity, respectively. For most semiconductors, the κ_{l} usually dominates thermal conductivity. To obtain high ZT materials, it is necessary to enhance the electrical conductivity (σ) and reduce thermal conductivity (κ=κ_{e}+κ_{l}) simultaneously. The free move of electrons or holes in the regular crystal lattice increases the power factor, while atoms vibrating with larger atomic displacement and different frequency in comparison to the neighboring ones lead to more phonon–phonon scattering lowering the lattice thermal conductivity [2].

Cage-like TE materials have a rigid sub-lattice responsible for the electrical conductivity and large empty cages. When the cages are filled with heavy atoms, these atoms, weakly bound to the cage, can vibrate inside (“rattling”) with a strong amplitude of vibration. These vibrations are optical phonons (coherent vibrations) mainly without dispersion (localized character) and with a weak energy which strongly interfere with acoustic phonons to decrease the thermal conductivity [3].

Skutterudites are studied as a low cost TE and have a chemical composition of RM_{4}X_{12}, where R is the rattler, M is a transition metal and X is a metalloid or XV group element. In some of these materials, like the heavy fermion compound SmOs_{4}Sb_{12}, the rattler can be found in a mixed-valence configuration [4], opening wide possibilities to improve thermoelectric performances. In this project, the student will first characterize the ground state of the system by using the state-of-the-art DFT+Hubbard theory [5,6,7] in order to correctly predict the oxidation states of M and R atoms. Then, the student will perform thermal conductivity calculations to investigate how the mixed-valence character of the rattler affects thermal transport [8].

This study aims at broadening the understanding of the fundamental physical role of the rattler and proposing an appropriate protocol to engineer skutteruidites to achieve excellent thermoelectric performances by exploiting filler atoms with different oxidation states.

**Requirements**: Knowledge of quantum mechanics in condensed matter and solid-state physics (MSE 423 and MSE 468 or equivalent are strongly recommended). Basic knowledge of Linux and bash/python scripting.

Contact: Enrico Di Lucente

[1] T. M. Tritt, "Holey and unholey semiconductors", Science, 283.5403, (1999).

[2] Li Jielan et al. "High-Throughput Screening of Rattling-Induced Ultralow Lattice Thermal Conductivity in Semiconductors." Journal of the American Chemical Society 144.10 (2022).

[3] E. Di Lucente, M. Simoncelli and N. Marzari, "Crossover from Boltzmann to Wigner thermal transport in thermoelectric skutterudites", arXiv preprint arXiv:2303.07019, (2023).

[4] A. Yamasaki et al., "Coexistence of strongly mixed-valence and heavy-fermion character in SmOs_{4}Sb_{12} studied by soft-and hard-X-ray spectroscopy. Physical Review Letters, 98(15), (2007).

[5] V.I. Anisimov, J. Zaanen and O.K. Andersen, "Band theory and Mott insulators: Hubbard U instead of Stoner I", Physical Review B 44(943), (1991).

[6] I. Timrov, N. Marzari and M. Cococcioni, "Hubbard parameters from density-functional perturbation theory", Physical Review B 98(8), (2018).

[7] I. Timrov, N. Marzari and M. Cococcioni, "Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations", Physical Review B 103(4), (2021).

[8] T. Pandey et al., "Ultralow thermal conductivity and high thermoelectric figure of merit in mixed valence In_{5}X_{5}Br (X=S,Se) compounds", Journal of Materials Chemistry A, 8(27), (2020).

##### Accelerating structure optimizations using perturbative post-processing

High-throughput studies, where thousands to tens of thousands of materials are simulated, are a powerful tool for broadening our knowledge of materials properties and discovering new and interesting functional materials. A key step in many of these studies is structure optimization, in which an approximate arrangement of atoms in a crystal is optimized to the most stable configuration.

Since each iterative step of the associated with this optimization is roughly as expensive as a single-point calculation of ground state energy, atomic structure optimization accounts for a substantial amount of computational time in high-throughput workflows. Additionally, the obtained minimal-energy geometry can be highly dependent on the chosen numerical parameters for the calculation, such as the basis set cutoff. Therefore, a good compromise between the error of a too small cutoff and a too slow (but accurate) structure optimization needs to be found.

Along this direction, mathematical research has provided a number of new tools in the past years to (a) estimate the numerical error due to basis set discretizations and (b) correct for this error using post-processing techniques. For the force as the key quantity of interest in structure optimizations, a promising perturbative approach has emerged recently [1]. A preliminary implementation of this force-refinement strategy is already available in the density-functional toolkit (DFTK, [2]), a Julia-based code which enables joint research of both mathematicians and scientists performing first-principle materials simulations.

Here at THEOS, we develop AiiDA [3], a software framework written in python which simplifies and automates workflows for high-throughput studies. By integrating DFTK with AiiDA, we want to both test the force refinement approach on a broader range of systems and unlock this cheaper route to structure optimizations for broader use.

**Requirements**: Strong programming skills in particular python; knowledge of Julia programming is a bonus, but can also be acquired as we go along; interest in learning about the numerical and mathematical underpinnings of first-principle based materials simulations.

Contact: Michael Herbst or Austin Zadoks

[1] E. Cancès, G. Dusson, G. Kemlin and A. Levitt. *SIAM J. Sci. Comp.* **44** (2022). ArXiv 2111.01470v1

[2] M. Herbst, A. Levitt and E. Cancès *Proc. JuliaCon Conf.* **3**, 69 (2021). https://dftk.org

[3] S. Huber, et al. *Scientific Data.* **7**, 300 (2020). https://www.aiida.net/

##### Topology in 1D and Majorana fermions: the case of exfoliable one-dimensional Ag_{2}Se_{2}

One-dimensional materials are extremely attractive due to their unique electronic properties and potentialities in next-generation applications. Their low-dimensional nature leads to exotic and intriguing phenomena, such as charge-density waves, Luttinger liquid behaviour and Majorana fermions.

Our group has developed an extended database of novel 1D/quasi-1D materials that can be obtained experimentally from exfoliation of three-dimensional Van der Waals crystals (have a look to [1] for more details). Therefore, we now have a playground of completely novel one-dimensional materials, with new physics waiting to be discovered just behind the corner!

In this particular project we want to investigate the possibility of one-dimensional topology [2], which reveals itself trough Majorana fermions, i.e., zero-energy states at the border of a nanowire.

One-dimensional topology has been proposed as very promising for applications in quantum computing. At the same time, materials where the formation of Majorana edge states occurs intrinsically are very rare, and nowadays they are obtained experimentally using superconductor wires on semiconductor substrate. In this regards, finding a one-dimensional Van der Waals exfoliable wire showing topological properties would be therefore of enormous interest.

In our previous work, we select a possible promising candidate to show 1D topology: Ag2Se2. In this work the student will careful analyse the material in question and investigate its topological properties, computing the 1D topological invariant.

The student will therefore have the opportunity to study ground-breaking low-dimensional materials and learn high-level physics; and, most important, give a little contribute to the future nanotechnologies!

The project will be carry on with the QuantumESPRESSO package (QuantumEspresso). Moreover, the student will learn the basics of Wannier functions [4] and the use of Wannier90 (Wannier90), as well as WannierTools (WannierTool) to compute topological properties.

**Requirements**: The student should have a knowledge of quantum mechanics and condensed matter physics (MSE 423 or equivalent is suggested), as well as experience with first-principles calculations (MSE 468 or equivalent is strongly recommended). Basic knowledge of Bash and Python preferred.

Contact: Chiara Cignarella

[1] N. Mounet et al., "Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds", Nature nanotechnology, 13, 2018;

[2] M. Leijnse and K.Flensberg, "Introduction to topological superconductivity and Majorana fermions", Semicond. Science and Tecnh., 27, 2012;

[3] N. Marzari, I. Souza and D. Vanderbilt, "An Introduction to Maximally-Localized Wannier Functions", WannierFunctions

##### Mechanical properties of novel exfoliable one-dimensional materials

One-dimensional materials are extremely attractive due to their unique electronic properties and potentialities in next-generation applications. Finding novel materials with one-dimensional structure can open up new perspectives in the future downscaled technologies, such as local interconnects and field-effect transistor (FET) channels [1].

Our group has developed an extended database of novel 1D/quasi-1D materials that can be obtained experimentally from exfoliation of three-dimensional Van der Waals crystals (have a look to [2] for more details). Therefore, we now have a playground of completely novel one-dimensional materials, with new physics waiting to be discovered just behind the corner!

In this particular project we want to investigate the mechanical properties of quasi-one-dimensional materials. One interesting physical quantity to look at is the Young modulus, also relevant for many applications, i.e., the response of the material to an unaxial stress ε applied: Y=σ(ε)/ε.

Carbon-based one-dimensional materials, like single wallet carbon nanotubes (SWCNTs) or linear C chains like carbyne, have proved to possess excellent mechanical properties and extremely high Young modulus [3]. Is it a particular feature of the carbon-based nature of these systems? Is it otherwise due to the one-dimensional peculiar structure? To answer these questions, we aim to calculate Y for the 1D systems in our database, in order to find a potential trend and an understanding of their behaviour.

As an additional goal we can investigate in depth materials that stand out for good mechanical qualities in order to find new candidates for downscaled applications. For example we can explore electronic and/or vibrational properties, as well as electronic transport and stability.

In this project, the student is going to use the Quantum ESPRESSO package and in addition, since Y involves the calculation of the quantum volume [4], learn the Quantum Environ package. If the student wishes, the project can be perform employing AiiDA to automatise the calculations (also look here) and learn how to handle many calculations in once.

Most important, the student has the opportunity to study ground-breaking low-dimensional materials and give a little contribute to the future nanotechnologies!

**Requirements**: The student should have a knowledge of quantum mechanics and condensed matter physics (MSE 423 or equivalent is suggested), as well as experience with first-principles calculations (MSE 468 or equivalent is strongly recommended). Basic knowledge of Bash and Python required.

Contact: Chiara Cignarella

[1] M. A. Stolyarov et al., "Breakdown current density in h-BN-capped quasi-1D TaSe 3 metallic nanowires: prospects of interconnect applications", Nanoscale, 8, 2016;

[2] N. Mounet et al., "Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds", Nature nanotechnology, 13, 2018;

[3] Y. Zhang et al.,"A one-dimensional extremely covalent material: monoatomic carbon linear chain", Nanoscale Research Letters, 6, 2011;

[4] M. Cococcioni et al., "Electronic-enthalpy functional for finite systems under pressure", Physical review letters, 94, 2005.

##### Developing an analytical model to describe the rattling motion in thermoelectric cage-like structured compounds

Thermoelectric (TE) materials can realize direct conversion between heat and electricity, which is environment friendly and improves the usage efficiency of solar energy [1]. The conversion efficiency of thermoelectric materials can be evaluated by the dimensionless figure of merit, ZT = (S^{2}σT)/(κ_{e} + κ_{l}), where S is the Seebeck coefficient, σ is the electric conductivity, T is the absolute temperature, and κ_{e} and κ_{l} are the electrical and lattice thermal conductivity, respectively. For most semiconductors, the κ_{l} usually dominates thermal conductivity.
To obtain high ZT materials, it is necessary to enhance the electrical conductivity (σ) and reduce thermal conductivity simultaneously. The free move of electrons or holes in the regular crystal lattice increases the power factor, while atoms vibrating with larger atomic displacement and different frequency in comparison to the neighboring ones lead to more phonon–phonon scattering lowering the lattice thermal conductivity [2].

Cage-like thermoelectric (TE) materials have a rigid sub-lattice responsible for the electrical conductivity and large empty cages. When the cages are filled with heavy atoms, these atoms, weakly bound to the cage, can vibrate inside (“rattling”) with a strong amplitude of vibration. These vibrations are optical phonons (coherent vibrations) mainly without dispersion (localized character) and with a weak energy which strongly interfere with acoustic phonons to decrease the thermal conductivity. There are two remarkable signals in the rattling model: (1) avoided crossing between the acoustic and optical modes in the phonon spectra; (2) large atomic displacement parameter (ADP).
The rattling model has been demonstrated in skutterudites, clathrates, penta-hexa-tellurides, Chevrel's phases with Mo clusters, InTe, TlInTe_{2} and some other peculiar systems [2,3].
These materials exhibit intrinsic low κ_{l} values of below 2.0 W m^{–1} K^{–1} at 300 K, which can be regarded as the criteria of ultralow κ_{l} in general.

This project focuses on the development of an analytical formalism that allows to describe the nature of rattling motion starting from the definition of characteristic phonon frequencies and lifetimes for each atom that build up the material [4]. The student will be required to develop the analytical model and validate it through the first principles solution of the phonon Wigner transport equation [5-6].

**Requirements**: From a theoretical point of view, the student should have a solid knowledge of quantum mechanics and condensed matter physics (completion of MSE 423 or equivalent). From a computational proint of view, basic knowledge of Python/Bash scripting are required.

Contact: Enrico Di Lucente

[1] Tritt T. M. "Holey and unholey semiconductors." Science 283.5403 (1999): 804-805.

[2] Li Jielan et al. "High-Throughput Screening of Rattling-Induced Ultralow Lattice Thermal Conductivity in Semiconductors." Journal of the American Chemical Society 144.10 (2022): 4448-4456.

[3] Godart, C., et al. "Role of structures on thermal conductivity in thermoelectric materials." Properties and Applications of Thermoelectric Materials. Springer, Dordrecht, 2009. 19-49.

[4] E. Di Lucente, M. Simoncelli and N. Marzari. Manuscript in Preparation (2022).

[5] Simoncelli, Michele, Nicola Marzari, and Francesco Mauri. "Unified theory of thermal transport in crystals and glasses." Nature Physics 15.8 (2019): 809-813.

[6] Simoncelli, Michele, Nicola Marzari, and Francesco Mauri. "Wigner formulation of thermal transport in solids." arXiv preprint arXiv:2112.06897 (2021).

##### Phonon-mediated heat transport in graphene and hexagonal boron nitride

Two-dimensional materials have received growing interests owing to their unique physical properties, which are the promising candidates for next-generation efficient and reliable energy harvesting. In particular, graphene and hexagonal boron nitride (h-BN) which are excellent heat conductors with superior thermal properties have been demonstrated to provide high-performance thermal management of electronic devices and power batteries [1,2]. Because of the reduced dimensionality, the emergence of quadratic flexural vibrational modes in low dimensions dominates heat transport and play a vital role in exhibiting a non-Fourier conduction regime such as hydrodynamic phonon flow [3].

In this project, we will utilize the state-of-the-art classical molecular dynamics with our recently implemented internal-coordinate potential (ICP) [4] in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to investigate the heat transport in graphene and h-BN. This interatomic potential allows to simulate the large physical system at the micro-/meso-scale with ab initio accuracy. The student will learn how to perform equilibrium molecular dynamics via the Green-Kubo linear response theory and nonequilibrium molecular dynamics via the Fourier’s law to calculate thermal conductivity, and carry out normal mode analysis to extract mode-dependent phonon properties such as lifetime [5]. Besides, transient laser heating can be further performed with molecular dynamics to probe the time evolution of temperature field which signatures the wave-like heat propagation (second sound).

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

Contact: Changpeng Lin

[1] Balandin, A. A. Thermal properties of graphene and nanostructured carbon materials. Nature materials, 2011, 10(8): 569.

[2] Song, H. et al. Two-dimensional materials for thermal management applications. Joule, 2018, 2(3): 442.

[3] Cepellotti, A. et al. Phonon hydrodynamics in two-dimensional materials. Nature communications, 2015, 6(1): 1.

[4] Libbi, F., Bonini, N. and Marzari, N. Thermomechanical properties of honeycomb lattices from internal-coordinates potentials: the case of graphene and hexagonal boron nitride. 2D Materials, 2020, 8(1): 015026.

[5] Lin, C., Chen, X. and Zou, X. Phonon–grain-boundary-interaction-mediated thermal transport in two-dimensional polycrystalline MoS_{2}. ACS Applied Materials & Interfaces, 2019, 11(28): 25547.

##### High-throughput screening of high thermal conductivity materials for efficient thermal management

Engineering materials with superior thermal properties is fundamental to electronic industry for realizing high-performance devices and reliable thermal management. The traditional procedure to discover new materials which relies on in-lab synthesis, characterization and measurements is slow, impeding the rapid economic and societal developments. Thanks to the advances in computational power nowadays, instead the high-throughput calculations can be performed to accelerate the discovery of novel materials, providing an initial screening of promising candidates for subsequent experiment verification.

The goal of this project is to identify high thermal conductivity materials from the recently built database for two-dimensional materials (MC2D) [1], for efficient heat dissipation. The first assessment of more than 1000 candidates based on elastic properties (e.g. elastic moduli, sound velocity and Debye temperature) has been carried out to select materials with potentially high thermal conductivity [2]. The student will play with the Boltzmann transport equation to calculate thermal conductivity from first principles [3] and develop the AiiDA [4] workflow for the automated calculations of thermal transport properties.

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

Contact: Changpeng Lin

[1] Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nature nanotechnology, 2018, 13(3): 246.

[2] Lin, C., Poncé, S. and Marzari, N., in preparation, 2022.

[3] Shindé, S. L. and Srivastava, G. P. Length-scale dependent phonon interactions, Springer, 2014.

[4] Huber, S. P. et al. AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance. Scientific data, 2020, 7(1): 1.

##### Theoretical and computational study of cathode materials for eco-friendly rechargeable batteries

**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.L. Campo Jr. and M. Cococcioni, J. Phys.: Condens. Matter 22, 055602 (2010).

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

[6] I. Timrov, N. Marzari and M. Cococcioni, Phys. Rev. B 103, 045141 (2021).

[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

##### 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: Kristjan Eimre, Giovanni Pizzi