Current Projects:
Quantum Few-Body Systems in 2D Materials
With the emergence of two-dimensional semiconductor materials, it became evident that they host highly stable few-body bound states, characterized by their strong interaction with light. This has led to a wide range of innovative technological applications that leverage the unique properties of these quasiparticles. One of the key applications is found in excitons, which are the bound states of an electron and a hole. Excitons have been instrumental in advancing technologies such as photodetectors, solar cells, LEDs, quantum emitters, nonlinear optics, and chirality logic gates. However, our project aims to go beyond the realm of excitons to explore more complex few-body states. These include trions (charged excitons or the bound state of three electrons and holes), biexcitons (the bound state of two electrons and two holes), and quintons (charged biexcitons or the bound state of five electrons and holes). Trions, in particular, have shown immense potential in optical experiments involving doped samples. These samples can be created through electrostatic gating, subtract charge transfer processes, or chemical methods. An increase in doping levels leads to a notable shift in the exciton's oscillator strength towards the trion, leading to a trion-Fermi polaron transition. Biexcitons, representing four-body neutral bound states in semiconductors, are crucial for understanding the nonlinear optical properties of these materials. Moreover, biexcitons are key players in quantum technologies, especially as mediators for parametric-down conversion in nonlinear anisotropic crystals. Our focus on these confined few-body complexes is driven by their high quantum yield, positioning them as invaluable single-photon sources for various quantum technologies like quantum communication, quantum sensing, and quantum computation.
This collaborative initiative involves researchers from Central State University and Brazilian collaborators from Aeronautics Institute of Technology and the Federal University of Ceará. This collaboration aims to advance our understanding of the complex and promising world of few-body states in two-dimensional semiconductors.
- Trion Structure and Binding Energy Using Faddeev Method: This project aims to develop a comprehensive theoretical framework and computational tools to study trions in semiconductor layered materials. The approach employs the Faddeev equations in momentum space, addressing the bound state of three distinct particles interacting with three different pair interactions in two dimensions. We utilize two different screening schemes for the repulsive electron-electron or hole-hole potential to solve the three coupled Faddeev integral equations for the Rytova-Keldysh interaction. One of these schemes screens the interaction in the infrared region, while the other screens it in the ultraviolet region. Our results demonstrate that both methods provide consistent outcomes for the MoS2 layer, extrapolating the trion energy to the situation without screening. Specifically, we have found a trion binding energy of approximately -50 meV for an exciton energy of approximately −753 meV. Read more at arXiv.2212.09600.
- Exciton Properties in Double-Layered TMDs: This project introduces a novel method for analyzing exciton properties in double-layered transition metal dichalcogenides (TMDs). Utilizing the Chebyshev polynomial expansion, we accurately solve the Wannier equation, integrating critical corrections for the quasiparticle bandgap. This approach allows for a systematic investigation of hetero double-layer TMD systems across a range of chemical compositions. The study primarily focuses on revealing how the spacer width and dielectric constant impact the binding energies of inter- and intralayer excitons. Read more at arXiv:2305.03576.
- Four-Body Universality in 2D: The project aims to examine the universality of four-boson bound states in two dimensions. To achieve this, two different one-term separable potentials, featuring Gaussian and Yamaguchi form factors, are employed to calculate the ground and excited state energies of trimers and tetramers through the solution of Faddeev-Yakubovsky equations in momentum space. A key focus of the study is the exploration of the universality in the binding energies of tetramers and trimers and momentum distribution functions. This will be investigated across a broad spectrum of dimer binding energies and utilizing different form factor powers.
Solution of Faddeev-Yakubovsky equations in momentum space without 2B t-matrices
In this project, we present a solution to the Faddeev-Yakubovsky (FY) equations for three- and four-body bound states in momentum space, using direct two-body interactions. This bypasses the need for 2B t-matrices. This approach simplifies the FY equations, leading to a significant reduction in computational complexity and time by avoiding the coding associated with calculating 2B t-matrices. We initially focused on nonrelativistic 3B and 4B bound states, adopting a three-dimensional approach without partial wave decomposition and utilizing the spin-independent Malfliet-Tjon and Yamaguchi 2B interactions. Our findings indicate that the t-matrix-free version of the FY equations yields exact 3B and 4B binding energies as those obtained from the conventional FY equations using 2B t-matrices. Read more at
arXiv:2312.05132 &
arXiv:2311.08713.
The rovibrational spectrum of rare gas dimers, trimers, and tetramers in momentum space
This project focuses on investigating the structure and rovibrational energy levels of rare gas dimers, trimers, and tetramers through the solution of the Schrödinger equation. To accomplish this goal, we utilize a 3D approach and direct integration over angle variables between Jacobi momentum vectors to solve the Lippmann-Schwinger and Faddeev-Yakubovsky integral equations in momentum space. Our study provides a detailed examination of the properties of rare gas dimers, trimers, tetramer ground and excited state wave functions. By exploring the rovibrational spectrum of these structures, we aim to contribute to a deeper understanding of their physical properties and behaviors.