Periodic Reporting for period 1 - ComEPT (Combining Electrons and Phonons in Twisted materials)
Berichtszeitraum: 2021-05-01 bis 2023-04-30
If one places a regularly ruled transparent plastic sheet on top of another identical plastic sheet and then rotates the top sheet while holding the bottom one fixed, a beautiful moiré pattern emerges. Since 2018, experimentalists have been able to create similar moiré patterns with atomically thin two-dimensional (2D) materials, such as graphene or transition-metal dichalcogenides (TMDs), with precisely controlled rotation or twist angles between the layers. These novel moiré materials exhibit many fascinating electronic, vibrational, and optical properties that are all tunable through the twist angle, such as flat electronic bands, moiré phonons, and excitons. This has generated tremendous excitement and given rise to the new field of twistronics. One of the striking features of the moiré materials is the emergence of intriguing phenomena that are not present in individual layers and its tunability with twist angle and doping. Despite significant progress in experiments in this field, the computation of electronic and optical properties based on accurate first-principles calculations remains highly challenging. This has hindered atomistic understanding of how electrons and phonons couple with each other to create exotic electronic and excitonic transport. The major challenge in performing first-principles calculations is that they are computationally much more demanding as the unit cells of the moiré superlattices often contain several thousands of atoms.
In this project, we address the key challenge of developing and employing new and computationally efficient first-principles-derived atomistic methods to facilitate accurate computation and to provide key insights into the exotic electronic, vibrational, and optical properties of moiré materials.
Overall objectives: We set out to achieve three Research Objectives (ROs).
• RO1: Investigate emergent phonons and electron-phonon coupling mediated phenomena in moiré materials using a combination of first principles and forcefields based simulations.
• RO2: Atomistic modelling of moiré excitons
• RO3: Investigate role of atomic relaxations in formation of flat electronic bands in several moiré materials relevant to experimentalists using first-principles methods.
In this project, we address the key challenge of developing and employing new and computationally efficient first-principles-derived atomistic methods to facilitate accurate computation and to provide key insights into the exotic electronic, vibrational, and optical properties of moiré materials.
Overall objectives: We set out to achieve three Research Objectives (ROs).
• RO1: Investigate emergent phonons and electron-phonon coupling mediated phenomena in moiré materials using a combination of first principles and forcefields based simulations.
• RO2: Atomistic modelling of moiré excitons
• RO3: Investigate role of atomic relaxations in formation of flat electronic bands in several moiré materials relevant to experimentalists using first-principles methods.
In the first 12 months, we primarily focused on RO1. Using accurate classical force-field based simulations, we have discovered valley phonons in moiré materials could be chiral. Additionally, we discovered two sets of emergent chiral valley phonon modes that originate from an inversion symmetry breaking at the moiré scale. Moreover, we also discovered the formation of flat phonon bands in these materials. We demonstrated the existence of chiral and flat phonon modes in twisted bilayer WSe2, MoSe2/WSe2 heterobilayer, and a strain engineered moiré pattern created from WSe2 bilayer. These results were published as a Letter in Phys. Rev. B. After the completion of this project, we focused on understanding the temperature-dependent electronic properties of moiré materials as a direct signature of electron-phonon coupling. We have combined extensive large-scale ab-initio electronic structure calculations and molecular dynamics simulations to demonstrate that the moiré potential in a MoSe2/WSe2 heterobilayer is dynamic at finite temperature. The origin of the dynamic moiré potential can be ascribed to two factors: a moiré magnification, where the atomic displacements are magnified at the moiré scale, and the presence of special low-energy phonon modes called phasons which correspond to the relative sliding of the two layers. We show that electrons and holes follow the movements of the dynamic moiré potential and surf the phason waves. These results are under review at ACS Nano Letters.
In the last 12 months, we primarily focused on addressing RO2. A major challenge associated with RO2 was both the development of new algorithms to solve the Bethe-Salpeter-Equation (BSE) and the implementation of those algorithms into a computer package. In particular, we have used a Wannierization procedure to generate an ab-initio tight-binding model of the moiré materials and then exploit the localization of the Wannier functions to efficiently evaluate the electron-hole interaction matrix elements required to solve the BSE. The implementation of the new algorithms for solving the BSE resulted in the new PyMEX package (A Python package for Moiré EXcitons) with both MPI and OpenMP support. Using this package, we were able to compute the interlayer and intralayer excitons in WS2/WSe2 heterobilayers. Our calculations were in excellent agreement with previous experiments. We are finalizing our manuscript for publication. Our work on excitons and phonons has resulted in nice international collaborations with experimentalists at Lawrence Berkeley National Lab with Prof. Archana Raja and Prof. Alex Weber-Bargioni’s group and at Cornell University with Prof. Jared Maxson’s group. In these works, we studied how phonons couple with electrons and excitons in WS2/WSe2 (under review at Nature Materials) and MoSe2/WSe2 heterobilayers (to be submitted to Nature Materials).
Most of these works are available on the arXiv for free. We have presented our works in multiple national and international conferences, such as American Physical Society March meeting 2022 and 2023 (United States), Psi-k 2022 (Switzerland), ETSF-Young-Researchers-Meet-2021 (Italy), Moiré twistronics workshop 2021 (United Kingdom), Materials Chemistry Consortium meeting 2022 (United Kingdom), and multiple in-house seminars at Imperial College London. To ensure a broader public engagement, a summary was also posted on social media platforms, such as Facebook and Twitter at the time of the publication. We plan to publish summaries of the work done during the fellowship through Imperial College’s news and views website as well (upon the acceptance of the rest of the publications).
In the last 12 months, we primarily focused on addressing RO2. A major challenge associated with RO2 was both the development of new algorithms to solve the Bethe-Salpeter-Equation (BSE) and the implementation of those algorithms into a computer package. In particular, we have used a Wannierization procedure to generate an ab-initio tight-binding model of the moiré materials and then exploit the localization of the Wannier functions to efficiently evaluate the electron-hole interaction matrix elements required to solve the BSE. The implementation of the new algorithms for solving the BSE resulted in the new PyMEX package (A Python package for Moiré EXcitons) with both MPI and OpenMP support. Using this package, we were able to compute the interlayer and intralayer excitons in WS2/WSe2 heterobilayers. Our calculations were in excellent agreement with previous experiments. We are finalizing our manuscript for publication. Our work on excitons and phonons has resulted in nice international collaborations with experimentalists at Lawrence Berkeley National Lab with Prof. Archana Raja and Prof. Alex Weber-Bargioni’s group and at Cornell University with Prof. Jared Maxson’s group. In these works, we studied how phonons couple with electrons and excitons in WS2/WSe2 (under review at Nature Materials) and MoSe2/WSe2 heterobilayers (to be submitted to Nature Materials).
Most of these works are available on the arXiv for free. We have presented our works in multiple national and international conferences, such as American Physical Society March meeting 2022 and 2023 (United States), Psi-k 2022 (Switzerland), ETSF-Young-Researchers-Meet-2021 (Italy), Moiré twistronics workshop 2021 (United Kingdom), Materials Chemistry Consortium meeting 2022 (United Kingdom), and multiple in-house seminars at Imperial College London. To ensure a broader public engagement, a summary was also posted on social media platforms, such as Facebook and Twitter at the time of the publication. We plan to publish summaries of the work done during the fellowship through Imperial College’s news and views website as well (upon the acceptance of the rest of the publications).
Existing strategies to model excitons in moiré materials, such as those based on effective mass models, neglect several important factors including atomic relaxations that take place in a moiré material. On the other hand, the state-of-the-art first principles many-body perturbation theory and Bethe-Salpeter Equation (GW-BSE) approach is highly accurate but computationally much more demanding, if not intractable. The computational expense can be significant even for systems containing only a few tens of atoms, but moiré materials often contain thousands of atoms in their unit cell. Therefore, the computation of excitonic spectra based on first-principles calculations for different moiré materials require both world-class high-performance computing resources and efficient approximations to the conventional GW-BSE method. We have solved this problem through RO2 and therefore, made significant contribution to studying optical properties of large systems. This will enable the study of optical properties of defects in two-dimensional (2D) materials, which was not previously possible due to the huge expense associated with conventional GW-BSE approaches. Our work might open up new avenues to faster identification of interesting defects for quantum technologies.