Publicação
Exciton generation by inelastic tunneling in heterostructures with two-dimensional semiconductors
| Resumo: | In this thesis, we study the emission of excitons via inelastic tunneling in mesoscopic devices with two electrodes separated by a non-conductive material, subjected to a biased electrostatic potential. We study this problem applying both a simplified toy model and a detailed model for a graphene/hexagonal boron nitride/graphene (gr-hBN-gr) van der Waals (vdW) heterostructure. Specifically, we focus on the corrections to the current arising from the interaction between the tunneling electrons and the two-dimensional excitons hosted by a transition metal dichalcogenide (TMD) layer placed a few nanometers apart. To this end, we start by applying the non-equilibrium Green’s function (NEGF) technique to a generalized transport problem for a two-contact mesoscopic system with general electron-boson interactions, thus obtaining analytic expressions for the non-interacting elastic current - the Landauer formula - written as the energy integral of the contact’s occupied levels and the transmission function, which is related to the probability of an electron with a given energy to tunnel through the device. Treating the electron-boson interaction as a perturbation, we also obtain the second order corrections that these interactions introduce, separating the cases of elastic and inelastic processes. In order to gain insight about the general features that arise in the electron tunneling problem, we apply these generic results to a one-dimensional toy-model at zero temperature and calculate both the transmission functions and the I-V curves for this idealized system. Although simple in its nature, it is sufficient to capture the phenomena of inelastic tunneling assisted by the emission of a bosonic excitation. As such, it captures some of the essential features of the more complex vdW device. We are able to show that, when accounting for interactions up to the second order, there is an increase in the total current for bias voltages in resonance with the model sample, while for voltages exceeding this threshold there is a suppression in the total current dominated by the elastic correction, even though its inelastic counterpart contributes with a small increase. Additionally, we also show that these interactions open new tunneling channels that depend on boson’s energy. Finally, we tackle the problem of finding the exciton-assisted inelastic tunneling current flowing in the vdW heterostructure, electromagnetically coupled to the excitonic layer (TMD). To do so, we calculate the matrix element for the electron-exciton interaction, mediated by the emission and absorption of virtual photons, in a second order perturbation theory and use it to obtain the transition rate from Fermi’s golden rule, from which we are able to find the inelastic current flowing through the system and the corresponding rate of generation of excitons in the TMD layer. |
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| Autores principais: | Barreiro, Marcelo Silva |
| Assunto: | Non-equilibrium Green’s functions Inelastic tunneling Excitons Van der Waals heterostructures Electroluminescence Funções de Green fora do equilíbrio Tunelamento inelástico Excitões Heteroestruturas de van der Waals Eletroluminescência Ciências Naturais::Ciências Físicas |
| Ano: | 2024 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | In this thesis, we study the emission of excitons via inelastic tunneling in mesoscopic devices with two electrodes separated by a non-conductive material, subjected to a biased electrostatic potential. We study this problem applying both a simplified toy model and a detailed model for a graphene/hexagonal boron nitride/graphene (gr-hBN-gr) van der Waals (vdW) heterostructure. Specifically, we focus on the corrections to the current arising from the interaction between the tunneling electrons and the two-dimensional excitons hosted by a transition metal dichalcogenide (TMD) layer placed a few nanometers apart. To this end, we start by applying the non-equilibrium Green’s function (NEGF) technique to a generalized transport problem for a two-contact mesoscopic system with general electron-boson interactions, thus obtaining analytic expressions for the non-interacting elastic current - the Landauer formula - written as the energy integral of the contact’s occupied levels and the transmission function, which is related to the probability of an electron with a given energy to tunnel through the device. Treating the electron-boson interaction as a perturbation, we also obtain the second order corrections that these interactions introduce, separating the cases of elastic and inelastic processes. In order to gain insight about the general features that arise in the electron tunneling problem, we apply these generic results to a one-dimensional toy-model at zero temperature and calculate both the transmission functions and the I-V curves for this idealized system. Although simple in its nature, it is sufficient to capture the phenomena of inelastic tunneling assisted by the emission of a bosonic excitation. As such, it captures some of the essential features of the more complex vdW device. We are able to show that, when accounting for interactions up to the second order, there is an increase in the total current for bias voltages in resonance with the model sample, while for voltages exceeding this threshold there is a suppression in the total current dominated by the elastic correction, even though its inelastic counterpart contributes with a small increase. Additionally, we also show that these interactions open new tunneling channels that depend on boson’s energy. Finally, we tackle the problem of finding the exciton-assisted inelastic tunneling current flowing in the vdW heterostructure, electromagnetically coupled to the excitonic layer (TMD). To do so, we calculate the matrix element for the electron-exciton interaction, mediated by the emission and absorption of virtual photons, in a second order perturbation theory and use it to obtain the transition rate from Fermi’s golden rule, from which we are able to find the inelastic current flowing through the system and the corresponding rate of generation of excitons in the TMD layer. |
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