## 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 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 Enrico Di Lucente 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.

- Systematic correction of electronic self-interaction with Koopmans functionals
- Combining Koopmans and Hubbard corrections for accurate band structures of materials
- Thermal transport in mixed-valence thermoelectric skutterudites
- Determining protoypes of ferroelectric phases
- 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
- Engineering defect centers for quantum computing
- First-principles quantum simulations of transition-metal compounds
- Jupyter web applications for quantum simulations
- Jupyter web apps for vibrational spectroscopy
- Development of and AiiDA lab application for the calculation of topological invariants
- Towards an improved description of molecular dissociation by using systematic approximations
- Developing an AiiDA workflow for the automated calculation of optical properties
- Workflows for muon spectroscopy: predicting muon stopping sites

##### Systematic correction of electronic self-interaction with Koopmans functionals

**Description**

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

It is possible to augment Koopmans functionals with a Perdew-Zunger correction to address one-electron self-interaction error, ensuring that the functional is exact for one-electron systems [2]. This has already been done to great success, with the so-called KIPZ functional being the best performing on certain benchmarks [3]. However, the KIPZ represents just one of several possible ways to add a Perdew-Zunger correction to Koopmans functionals, and the best method for doing so remains to be seen.

In this project, the student will investigate how best to unite these two approaches. This will involve...

- theoretical work developing on possible strategies for combining Koopmans and Perdew-Zunger corrections
- implementing candidate functionals in Quantum ESPRESSO and the koopmans package
- assessing the performance of candidate functionals on well-established benchmarks

**Requirements**

- coding proficiency is essential, as the project involves implementing novel functionalities in packages written in Fortran and Python
- familiarity with Linux operating systems is helpful
- completion of master's-level courses in computational materials science and atomistic modeling (e.g., EPFL's MSE-423 and MSE-468 or equivalent) is recommended.

**References**

- E. Linscott et al., "koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals", J. Chem. Theory Comput. (2023)
- J. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", Phys. Rev. B 23, 5048 (1981)
- N. Colonna et al., "Koopmans-compliant functionals and potentials and their application to the GW100 test set", J. Chem. Theory Comput. 15, 3, 1905 (2019)

**Contact**

For more information, please contact Edward Linscott

##### Combining Koopmans and Hubbard corrections for accurate band structures of materials

**Description**

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

Meanwhile, Hubbard-corrected DFT (DFT+U) is a well-established correction to DFT [2]. While this correction does not directly target quasiparticle energies, it tends to improve their description while also addressing the self-interaction error inherent to DFT [3].

In this project, the student will unite these two approaches, and test this strategy on systems for which DFT is known to fail. This will involve...

- theoretical work assessing how best to combine Hubbard and Koopmans functionals
- implementing and testing Hubbard functionals in the koopmans package
- performing and analysing calculations on materials of scientific interest

**Requirements**

- proficiency in Python is essential, as the project involves implementing functionality in the koopmans package
- familiarity with Linux operating systems is helpful
- completion of master's-level courses in computational materials science and atomistic modeling (e.g. MSE-423 and MSE-468 or equivalent) is recommended

**References**

- E. Linscott et al. "koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals", JCTC (2023)
- V. Anisimov et al., "Density-functional theory and NiO photoemission spectra", Phys. Rev. B 48, 16929 (1993)
- M. Cococcioni et al., "Linear response approach to the calculation of the effective interaction parameters in the LDA + U method", Phys. Rev. B 71, 035105 (2005)

**Contact**

For more information, please contact Edward Linscott

##### 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).

##### Determining prototypes of ferroelectric phases

Ferroelectricity arises from a polar structure – one lacking an inversion symmetry – which results in a spontaneous electrical polarization switchable under an applied electric field leading to a characteristic hysteresis. In many ferroelectrics, at the nanoscale, the structure can locally host polarizations away from the macroscopic observed one. While such small details can be difficult to resolve experimentally, they can be crucial in developing a full understanding of the system. We have found in previous work that this is the case in barium titanate [1] We deployed a systematic symmetry analysis to construct representative structural models in the form of supercells that satisfy a desired point symmetry but are built from the combination of lower-symmetry primitive cells. Using this method we found structural prototypes that are both energetically and dynamically stable.

In this project, the student will extend this study to other crystal structures, for example, the fluorite crystal structure. The fluorite structure is the high-symmetry phase of hafina - a material currently drawing a great deal of attention due to its high-dielectric constant and ferroelectric properties. Depending on the student’s interests, they can focus more on group theory anaylsis, workflow development, and/or structural analysis.

**Requirements:**
The student should have a solid analytical skills, knowledge of quantum mechanics and condensed matter. Prior experience with first-principles calculations (for example from MSE 468) and basic programming knowledge is a plus.

Contact: Michele Kotiuga

##### 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

##### 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

##### First-principles quantum simulations of transition-metal compounds

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

Description of the project:

Transition-metal compounds (TMCs) have many technological applications, e.g. they are used to fabricate cathodes in Li-ion batteries, thermoelectric devices, photocatalysts, to name a few. 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. DFT+U and DFT+U+V are simple and at the same time powerful tools to model TMCs [1], however, the Hubbard U (on-site) and V (inter-site) parameters are often treated semi-empirically, which is a somewhat unsatisfactory approach. Recently, a new efficient linear-response approach was developed for the first-principles calculation of U and V based on density-functional perturbation theory [2, 3]. In this project, the student will learn how to compute U and V parameters, and how to perform DFT+U and DFT+U+V calculations for TMCs to investigate their structural, electronic, and magnetic [4]. 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 [5, 6]. For more information see this page.

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

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

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

[4] C. Ricca, I. Timrov, M. Cococcioni, N. Marzari, and U. Aschauer, Phys. Rev. Research 2, 023313 (2020).

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

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

This project requires:

- Knowledge of quantum mechanics in condensed matter and solid-state physics
- Basic knowledge of Linux and bash scripting

Contact: Iurii Timrov

##### 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.

**Requirements:** Good knowledge of quantum mechanics and simulations. The candidate should complete course MSE-468 first.

Contact: Giovanni Pizzi

##### Jupyter web applications for quantum simulations

In this project, we plan to develop Jupyter notebooks with educational content for computational materials science and condensed-matter physics classes, addressing a number of existing ones at EPFL focused on quantum-mechanical simulations, as its first goal, but with direct applicability to courses in other universities worldwide.

Importantly, we do not just plan to provide Jupyter notebooks: by preparing these using custom widgets and converting them into fully-interactive web apps, we will make them directly accessible from web platforms (such as our own https://www.materialscloud.org) in full open-access mode. Thanks to this design, students can focus at first on the educational content and challenges, rather than on the underlying technology to create web apps. However, thanks to the possibility to check and modify the app's source code, this approach also encourages active learning and computational thinking.

We will mainly depend on our OSSCAR technologies for this project. Below shows one OSSCAR web application for the numerical solution of the time-dependent Schrödinger equation.

**Requirements:** Good python programming skills and knowledge in quantum mechanics and simulations. The candidate should complete course MSE-468.

Contact: Dou Du and Giovanni Pizzi

##### Jupyter web apps for vibrational spectroscopy

Vibrational spectroscopy is one of the most important techniques for characterization of materials. Interestingly, different vibrational spectroscopy techniques are complementary in some cases - which can be explained by symmetry considerations that make integrals vanish in certain cases. To help students connect the maths with actual materials or molecules we want to build open, interactive web apps that can be used in chemistry and materials science courses at EPFL and other universities.

For instance, to explain selection rules we want to build interactive web apps that couple visualization of vibrational modes in materials/molecules with visualization of the change in the dipole moment/polarizability and simulated spectra.

We will depend on OSSCAR technology, but also try to make the tools interoperable in other platforms, such as the JavaScript-based IR spectrum prediction for molecules.

**Requirements:** Good python programming skills and knowledge in quantum mechanics and simulations. The candidate should complete course MSE-468.

Contact: Giovanni Pizzi (in collaboration with Kevin Jablonka from the LSMO group)

##### Development of and AiiDA lab application for the calculation of topological invariants.

In the past decade, the ability to classify material with a given topological class has been one of the main interests within the field of condensed matter physics[1]. To this end, one or more topological invariants need to be evaluated. They can be used to determine to which topological class a material belongs and can also be shown to be directly tied to the manifestation of interesting properties, such as the Anomalous Quantum Hall Effect (AQHE) and Quantum Spin Hall Effect (QSHE)[2,3]. To this end, several methodologies and corresponding tools have been developed, such as Z2pack[4], which tracks the evolution of the Hybrid Wannier Charge Centers (HWCCs) within a given surface.

In this project, the student will develop a new AiiDA lab application that enables researchers to easily calculate several topological invariants of a material, given only its structure. The idea is to provide a turn-key solution which will remove the barriers that such a problem could present, such as knowledge of DFT calculations and python and bash scripting languages.

[1] Yan, B., & Zhang, S. C. (2012). Topological materials. Reports on Progress in Physics, 75(9), 096501. [2] Kane, C. L., & Mele, E. J. (2005). Z 2 topological order and the quantum spin Hall effect. Physical review letters, 95(14), 146802 [3] Haldane, F. D. M. (1988). Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the" parity anomaly". Physical review letters, 61(18), 2015. [4] Gresch, D., Autes, G., Yazyev, O. V., Troyer, M., Vanderbilt, D., Bernevig, B. A., & Soluyanov, A. A. (2017). Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials. Physical Review B, 95(7), 075146.

The student should have a background in physics oriented towards materials science.

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

Contact: Davide Grassano

##### Towards an improved description of molecular dissociation by using systematic approximations

The proposed project belongs to the field of electronic structure theory, an ever-growing research area, where physics, chemistry and material science meet in a fascinating way. Bond breaking and bond formation are examples of ubiquitous processes in chemistry. Despite this fact, their description from a theoretical point of view is still a very challenging one. At present many theoretical approaches either provide unsatisfactory results, or they are accurate but not widely applicable, mainly due to their high computational cost.

In recent years the framework of the adiabatic connection fluctuation dissipation (ACFD) theorem [1] has become a promising alternative to ground state density-functional theory (DFT). The approach has been applied to tackle the problem of bond breaking and calculation of the correlation energy of atoms, molecules and solids, with very encouraging results [2, 3, 4, 5]. Further progress in this research area has been hindered by the lack of systematic approximations beyond the two simplest ones, that is to say the so-called random phase approximation (RPA) and the RPA plus exact-exchange (RPAx) one.

The aim of the proposed project is to i) build systematic approximations beyond RPA and RPAx, and ii) test their performance on an exactly solvable model system, which is a simplified but still representative version of real ones.

On the long term the project has the potential to also involve implementation of the newly developed approximations in an electronic structure theory code, such as Quantum Espresso, to carry out calculations of the dissociation curve of small molecules.

[1] D. Langreth and J.P. Perdew. Solid State Commun., 17, 1425, (1975).

[2] M. Fuchs and X. Gonze. Phys. Rev. B, 65, 235109, (2002).

[3] M. Hellgren and U. von Barth. Phys. Rev. B, 78, 11510, (2008).

[4] J. Toulouse, I.C Gerber, G. Jansen, A. Savin, and J.G. Ángyán. Phys. Rev. Lett., 102, 096404, (2009).

[5] N. Colonna, M. Hellgren, and S. de Gironcoli. Phys. Rev. B, 93, 195108, (2016).

**Requirements:**
The student taking up this project should have a solid knowledge of quantum mechanics and condensed matter theory. Since the work will involve analytical calculations and the use of technical computing software such as Mathematica a strong mathematical background is highly desirable.

Contact: Giovanna Lani

##### Developing an AiiDA workflow for the automated calculation of optical properties

The optical properties of materials play an important role in many applications, ranging from solar cells to plasmonic nanoparticles. Finding the optimal materials for these applications is challenging, both due to the size of the design space and the costs involved in synthesizing and investigating each material. Here, computer simulations using electronic structure methods can provide an initial screening of large numbers of materials by predicting the relevant properties in an automated fashion.

In this project, the student will develop a workflow for determining the dielectric tensor of a bulk material with AiiDA [1], a powerful materials’ infrastructure for high-throughput calculations. The workflow will subsequently be applied to a class of materials relevant to the application that most piques the student’s interests. Time permitting, these results can then be used to for example derive the Spectroscopic limited maximum efficiency (SLME) [2, 3], a screening metric for single-junction photovoltaic cells, or calculate the extinction spectra of nanoparticles [4] with different morphologies using tools such as DDSCAT [5].

[1] S. P. Huber et al., AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance, Sci. Data 7, 300 (2020). [2] L. Yu and A. Zunger, Identification of Potential Photovoltaic Absorbers Based on First-Principles Spectroscopic Screening of Materials, Phys. Rev. Lett. 108, 068701 (2012). [3] K. Choudhary, M. Bercx et al., Accelerated Discovery of Efficient Solar Cell Materials Using Quantum and Machine-Learning Methods, Chem. Mater. 2019, 31, 15, 5900–5908 (2019). [4] T. Willhammar, et al., Structure and vacancy distribution in copper telluride nanoparticles influence plasmonic activity in the near-infrared, Nat. Commun. 8, 14925 (2017). [5] B. T. Draine and P.J. Flatau Discrete-Dipole Approximation For Scattering Calculations. J. Opt. Soc. Am. A 11, 1491 (1994).

**Requirements**: Moderate experience with the Python programming language and a good understanding of condensed matter theory. Prior experience with electronic structure methods - density functional theory in particular - is a plus.

Contact: Marnik Bercx

##### Workflows for muon spectroscopy: predicting muon stopping sites

Muon spin spectroscopy (μSR) is an extremely powerful technique to analyse the magnetic properties of matter. During the experimental acquisition, the precession of the positive muon spin subject to an external or internal magnetic field is collected [1]. Unlike diffraction-based techniques, μSR can be used to investigate magnetic states without introducing spatial averages since the positive muon, generally at rest in interstitial voids of the atomic lattice, probes the magnetic moments through short ranged interactions. Unfortunately the interstitial position occupied by the muon is not known a priori. Density Functional Theory based simulations have been recently shown to be very effective in the identification of candidate interstitial sites [2-4].

In this project, the student will play a quantum hide-and-seek [5] game with the muon, improving the current strategy for muon site assignment and automating it through the development of an AiiDA workflow [6]. The accuracy of the proposed methodology will be benchmarked by considering different classes of magnetic systems. The work will eventually be part of a new AiiDAlab application that will enable experimental scientist to easily predict muon stopping sites in crystalline materials.

[1] Muon Spectroscopy, An Introduction, Edited by Stephen J. Blundell, Roberto De Renzi, Tom Lancaster, and Francis L. Pratt., Oxford University Press

[2] J. S. Möller, et al. Phys. Rev. B 87, 121108R (2013)

[3] K. J. A. Franke, et al. Phys. Rev. B 98, 054428 (2018)

[4] P. Bonfà, et al., Phys. Rev. Materials 5, 044411 (2021)

[5] J. S. Möller, et al., Phys. Scr. 88 068510 (2013)

[6] S. P. Huber et al., Sci. Data 7, 300 (2020)

The A15 compound V3Si and the two symmetry inequivalent candidate muon sites shown with yellow and green spheres. From arXiv:2202.13742.

**Requirements:** Good python programming skills and knowledge in quantum mechanics and simulations. The candidate should complete course MSE-468.

Contact: Giovanni Pizzi (in collaboration with Pietro Bonfa' from the University of Parma, Italy)