We investigate theoretically the energy levels of the coupled double triangular graphene quantum dots (GQDs) based on the tight-binding Hamiltonian model. The double GQDs including the ZZ-type, ZA-type, and AA-type GQDs with the two GQDs having the zigzag or armchair boundaries can be coupled together via different interdot connections, such as the direct coupling, the chains of benzene rings, and those of carbon atoms. It is shown that the energy spectrum of the coupled double GQDs is the amalgamation of those spectra of the corresponding two isolated GQDs with the modification triggered by the interdot connections. The interdot connection is inclined to lift up the degeneracies of the energy levels in different degree, and as the connection changes from the direct coupling to the long chains, the removal of energy degeneracies is suppressed in ZZ-type and AA-type double GQDs, which indicates that the two coupled GQDs are inclined to become decoupled. Then we consider the influences on the spectra of the coupled double GQDs induced by the electric fields applied on the GQDs or the connection, which manifests as the global spectrum redistribution or the local energy level shift. Finally, we study the symmetrical and asymmetrical energy spectra of the double GQDs caused by the substrates supporting the two GQDs, clearly demonstrating how the substrates affect the double GQDs' spectrum. This research elucidates the energy spectra of the coupled double GQDs, as well as the mechanics of manipulating them by the electric field and the substrates, which would be a significant reference for designing GQD-based devices.

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Using the tight-binding Hamiltonian approach, we theoretically study the electronic and optical properties of a triangular phosphorene quantum dot (PQD) including one normal zigzag edge and two skewed armchair edges (ZAA-PQD). It is shown that the energy spectrum can be classified into the filled band (FB), the zero-energy band (ZB), and the unfilled band (UB). Numerical calculations of the FB, ZB, and UB probability distributions show that the FB and the UB correspond to the bulk states, while the ZB corresponds to the edge states, which appear on all of the three edges of the ZAA-PQD sharply different from the other PQDs. We also find that the strains and the electric fields can affect the energy levels inhomogeneously. Then the optical properties of the ZAA-PQD are investigated. There appear some strong low-energy optical absorption peaks indicating its sensitive low-energy optical response that is absent in other PQDs. Moreover, the strains and the electric fields can make inhomogeneous influences on the optical spectrum of the ZAA-PQD. This work may provide a useful reference for designing the electrical, mechanical, and optical PQD devices.

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