For a long time, the symmetry of excitons has been discussed (if at all) in the Wannier picture of hydrogen like (s, p, ...) excitonic states. While this classification is valid in the limit of dilute (weakly bound) excitons, it ceases to be valid in the limit of tightly bound excitons in 2D materials, where the space group symmetry of the underlying crystal structure becomes important. We present a comprehensive and rigorous analysis of exciton symmetries using standard group-theoretical methods. We demonstrate the use of exciton symmetries for by applying it to a broad range of systems, including both two-dimensional and three-dimensional materials. We introduce a new concept, the crystal angular momentum, which naturally gives rise to the notion of chirality, an area of great current interest. We apply our methodology to three prototypical systems to understand the role of symmetries in different contexts:
(I) For LiF, we present the symmetry analysis of the entire excitonic dispersion and examine the selection rules for optical absorption.
(II) In the calculation of resonant Raman spectra of monolayer transition-metal dichalcogenides, we demonstrate how the conservation of total crystal angular momentum governs exciton– phonon interactions, leading to the observed resonant enhancement of the A peak, but not of theE peak. We also elucidate the role of symmetries in the quantum-scattering pathways of second order Raman spectra.
(III) In bulk hBN, we analyze the role of symmetries for the coupling of finite-momentum excitons to finite-momentum phonons and their manifestation in the phonon-assisted luminescence spectra.
Prof. Dr. Ludger Wirtz is head of the Physics and Materials Science Research Unit, University of Luxembourg. Ludger does research in theoretical and computational solid-state physics with a particular focus on 2D materials. One of the current project is 'Carrier dynamics in 2D materials.
For a long time, the symmetry of excitons has been discussed (if at all) in the Wannier picture of hydrogen like (s, p, ...) excitonic states. While this classification is valid in the limit of dilute (weakly bound) excitons, it ceases to be valid in the limit of tightly bound excitons in 2D materials, where the space group symmetry of the underlying crystal structure becomes important. We present a comprehensive and rigorous analysis of exciton symmetries using standard group-theoretical methods. We demonstrate the use of exciton symmetries for by applying it to a broad range of systems, including both two-dimensional and three-dimensional materials. We introduce a new concept, the crystal angular momentum, which naturally gives rise to the notion of chirality, an area of great current interest. We apply our methodology to three prototypical systems to understand the role of symmetries in different contexts:
(I) For LiF, we present the symmetry analysis of the entire excitonic dispersion and examine the selection rules for optical absorption.
(II) In the calculation of resonant Raman spectra of monolayer transition-metal dichalcogenides, we demonstrate how the conservation of total crystal angular momentum governs exciton– phonon interactions, leading to the observed resonant enhancement of the A peak, but not of theE peak. We also elucidate the role of symmetries in the quantum-scattering pathways of second order Raman spectra.
(III) In bulk hBN, we analyze the role of symmetries for the coupling of finite-momentum excitons to finite-momentum phonons and their manifestation in the phonon-assisted luminescence spectra.
Prof. Dr. Ludger Wirtz is head of the Physics and Materials Science Research Unit, University of Luxembourg. Ludger does research in theoretical and computational solid-state physics with a particular focus on 2D materials. One of the current project is 'Carrier dynamics in 2D materials.
