Periodic Reporting for period 1 - TeraExc (Terahertz excitons in monolithically integrated carbon nanostructures)
Reporting period: 2023-02-01 to 2025-01-31
At present, mobile networks and emerging wireless technologies (internet of things etc.) require broadband channels to exchange rapidly a huge amount of data. The usage of frequencies from 0.1 to 10 THz has potential to increase the state-of-the-art high speeds by 2 orders of magnitude. However, despite the latest advancements in THz technology, we still lack proper materials to realize suitable THz photonic components. This project aimed to understand principles of designing THz devices based on carbon nanostructures integrated into a monolithic flexible and durable substrate. The route to harnessing THz radiation for compact devices is seen in the usage of carbon nanostructures as building blocks for detectors, emitters etc. Such carbon nanostructures, as nanotubes and graphene nanoribbons, exhibit unique electronic and optical properties that make them very promising candidates for THz components. However, carbon nanotube and nanoribbon monolithic on-chip integration is challenging because it may results in significant change of their intrinsic properties after an embedment into a substrate. We investigated with first principles and theoretical methods the successful routes of such integration and calculate electronic and optical properties of the integrated structures. We modeled such systems with 2D graphene superlattices. In these structures, quasi-metallic and dielectric regions are alternated, for instance, either by selective hydrogenation of graphene. The project was focused on (i) the topological edge states at interfaces; (ii) topological singularities in optical matrix element and (iii) excitonic effects. The results of the project may have a significant impact in THz technology and wireless communications. Its results shall be useful for the realization of ultrafast wireless networks for multi-user environment. The potential benefits may include EU leadership in the telecom market.
In order to achieve the project research objectives we used an insight of the semi-empirical tight-binding (TB) methods to guide our density functional theory (DFT) based first principle investigations. The two techniques were used in a sort of the prediction-correction scheme in order to combine the computational speed of semi-empirical models with the precision of the first principle calculations.
THz band gaps. We built structural models of two dimensional graphene superlattices with architectures that are equivalent to those of graphene nanoribbons investigated with ER’s TBpack Mathematica package. Then we performed geometry relaxation to determine their stability and then investigated electronic properties of stable structures using Quantum Espresso open-source quantum chemistry kit. For those two-dimensional graphene superlattices showing promising features similar to corresponding nanoribbons, we performed accurate first principles calculations to prove the reliability of the found features. This includes geometry optimization with variable cell relaxation method and symmetry preserved relaxation at the DFT level as well as verification that features survive even when the structure is place on atomically smooth substrate. This followed by finding the Kohh-Sham wavefunctions and eigenvalues for use in many-body perturbation theory (MBPT) calculations in the GW approximation using in-house updated chisig code.
Excitons. Since first principles calculations were computationally demanding, we started from small size superlattices showing promising electronic properties. We calculated optical spectra taking into account screening and excitonic effects within MBPT by solving the Bethe-Salpeter equation (BSE) of the two particle Green’s function. This data confirmed predictions of TB model about the desired THz performance for a single particle picture, but showed an intriguing new results in the many-body approach. The latter points out on existence of 1D-like excitonic insulators.
THz band gaps. We built structural models of two dimensional graphene superlattices with architectures that are equivalent to those of graphene nanoribbons investigated with ER’s TBpack Mathematica package. Then we performed geometry relaxation to determine their stability and then investigated electronic properties of stable structures using Quantum Espresso open-source quantum chemistry kit. For those two-dimensional graphene superlattices showing promising features similar to corresponding nanoribbons, we performed accurate first principles calculations to prove the reliability of the found features. This includes geometry optimization with variable cell relaxation method and symmetry preserved relaxation at the DFT level as well as verification that features survive even when the structure is place on atomically smooth substrate. This followed by finding the Kohh-Sham wavefunctions and eigenvalues for use in many-body perturbation theory (MBPT) calculations in the GW approximation using in-house updated chisig code.
Excitons. Since first principles calculations were computationally demanding, we started from small size superlattices showing promising electronic properties. We calculated optical spectra taking into account screening and excitonic effects within MBPT by solving the Bethe-Salpeter equation (BSE) of the two particle Green’s function. This data confirmed predictions of TB model about the desired THz performance for a single particle picture, but showed an intriguing new results in the many-body approach. The latter points out on existence of 1D-like excitonic insulators.
In contrast to the 7 meV binding energy of excitons in GaAs, in semiconducting 2D materials the binding energy is 100-1000 meV and excitons can be detected at room temperature (25 meV). In semiconducting carbon nanotubes and graphene nanoribbons the exciton binding energies are of about 400-700 meV. In quasi-metallic structures the reported theoretical values for high energy transitions (i.e. not across the curvature gap) are about 50-100 meV. The excitons across the intrinsic-strain-induced THz band gap are not well studied by the first
principles community and, in fact, very few reports based on k∙p models (that is a continuum approximation to semi-empirical tight-binding (TB) models) can be found. Indeed, there are numerical difficulties in treating such systems. It must be also noted that the specified above binding energies are comparable to the THz energy band gaps produced by the intrinsic strain in quasi-metallic nanotubes and nanoribbons. According to the theoretical predictions, when the energy gap is smaller than the binding energy of excitons, a novel strongly interacting phase of matter called exciton insulator may arise . In this phase, excitons form similar to superconducting Cooper pairs. Studies in carbon nanotubes and graphene nanoribbons with theoretical works but no conclusive experimental evidences have appeared so far. In contrast to the conventional 2D materials, the excitonic effects in quasi-metallic two-dimensional graphene superlattices with a quasi-1D nature have not been yet investigated. TeraExc action has studied two-dimensional superlattices with quasi-1D nature with first principles methods and reveal the basic physics of THz interband optical transitions. It obtained the some evidences of the possibility of excitonic insulators at the borderline between 2D [1] and 1D systems [2]. An independent check of these results is underway. Further work is needed in this direction. After verification with different program implementations and advanced theory levels, an experiment is needed to validate the expected effects. In principle such systems could be attempted to synthesize on (111) planes of CuAu that feature somewhat distorted trigonal arrays of Cu and Au atoms. The distortion coming from the tetragonal P4/mmm L1_0 structure of ordered CuAu, can be used as a template for the hydrogen adsorption that have been proven to be preferable for the curved surfaces by Prof. E. Perez group.
The potential impact may include development of optical devices utilizing novel physical principles in the area of THz emitters. This could facilitate development of the ultra-fast wireless communication in EU and beyond as well as ensure EU leadership in the telecom market.
1. Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nature Physics (2021) doi:10.1038/s41567-021-01422-w.
2. Zhao, Y., Qu, H., Zhao, J., Kang, L. & Zhou, S. One-Dimensional Excitonic Insulator of M6 Te6 (M = Mo, W) Atomic Wires. Nano Lett. acs.nanolett.4c05448 (2025) doi:10.1021/acs.nanolett.4c05448.
principles community and, in fact, very few reports based on k∙p models (that is a continuum approximation to semi-empirical tight-binding (TB) models) can be found. Indeed, there are numerical difficulties in treating such systems. It must be also noted that the specified above binding energies are comparable to the THz energy band gaps produced by the intrinsic strain in quasi-metallic nanotubes and nanoribbons. According to the theoretical predictions, when the energy gap is smaller than the binding energy of excitons, a novel strongly interacting phase of matter called exciton insulator may arise . In this phase, excitons form similar to superconducting Cooper pairs. Studies in carbon nanotubes and graphene nanoribbons with theoretical works but no conclusive experimental evidences have appeared so far. In contrast to the conventional 2D materials, the excitonic effects in quasi-metallic two-dimensional graphene superlattices with a quasi-1D nature have not been yet investigated. TeraExc action has studied two-dimensional superlattices with quasi-1D nature with first principles methods and reveal the basic physics of THz interband optical transitions. It obtained the some evidences of the possibility of excitonic insulators at the borderline between 2D [1] and 1D systems [2]. An independent check of these results is underway. Further work is needed in this direction. After verification with different program implementations and advanced theory levels, an experiment is needed to validate the expected effects. In principle such systems could be attempted to synthesize on (111) planes of CuAu that feature somewhat distorted trigonal arrays of Cu and Au atoms. The distortion coming from the tetragonal P4/mmm L1_0 structure of ordered CuAu, can be used as a template for the hydrogen adsorption that have been proven to be preferable for the curved surfaces by Prof. E. Perez group.
The potential impact may include development of optical devices utilizing novel physical principles in the area of THz emitters. This could facilitate development of the ultra-fast wireless communication in EU and beyond as well as ensure EU leadership in the telecom market.
1. Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nature Physics (2021) doi:10.1038/s41567-021-01422-w.
2. Zhao, Y., Qu, H., Zhao, J., Kang, L. & Zhou, S. One-Dimensional Excitonic Insulator of M6 Te6 (M = Mo, W) Atomic Wires. Nano Lett. acs.nanolett.4c05448 (2025) doi:10.1021/acs.nanolett.4c05448.