2D moiré materials, by twisting 2D bilayers or multilayers, have enormously attracted the attention of researchers in science and engineering due to their fascinating electronic, mechanical, optical, and thermal properties which are not observed in their untwisted 2D counterparts. Recent new discovery by an experimental group [Nature 556, 44 (2018)] has shown that a transition from the semi-metal to an unconventional superconductivity was observed in twisted bilayer graphene at a magic angle (? = 1.05!) with a critical temperature ?". Another new discovery is found in the twisted MoS2/WS2 heterostructures [Sci. Adv. 6, 1-9 (2020)]. The delocalized excitons in the bilayer MoS2/WS2 become localized interlayer moiré excitons by twisting it at a magic angle of 3.480. Such moiré excitons could form ordered quantum dot arrays, paving the way for unprecedented optoelectronic and quantum information applications. These discoveries have laid the footprints to explore intriguing materials properties in other 2D materials such as h-BN, transition metal dichalcogenides, and phosphorene. The prudent assembly of these 2D monolayers into multilayer heterostructures with moiré patterns has opened a new area to engineer multilayer systems with fascinating properties.
In this thesis proposal, we plan to explore the fundamental aspect of moiré patterns of twisted phosphorene bilayers from our first-principles study. Phosphorene, the monolayer of black phosphorus, is an emerging semiconductor material with layer dependent bandgap, anisotropic structure, high carrier mobility, and anisotropic thermal and mechanical properties. Since its discovery in 2014, phosphorene has fetched a great amount of attention of researchers worldwide. By twisting phosphorene bilayers, a moiré potential is generated which introduces very interesting effects between these bilayers. It has recently been identified as a promising 2D moiré material to explore despite its limited air-stability. Moreover, twisted bilayer phosphorene is expected to possess more chances to exist in the real world owing to its multiple alternatives. Recent theoretical and experimental work have reported interesting features of moiré patterns of twisted phosphorene bilayers [ACS Appl. Nano Matter 2, 3138-3145 (2019), J. Phys.: Condens. Matter 32, 234001 (2020), J. Mater. Chem. C 8, 6264-6272 (2020)]. Because of the unique anisotropic structural and physical properties of phosphorene, the effects of stacking and twisting bilayer phosphorene including the commensurability and local strain should be considered concurrently. Our preliminary study has shown that the equilibrium interlayer distance, the cohesive energy, the band structures, and the distribution of top valence band and bottom conduction band strongly depend on the stacking arrangement, the twisted commensurate angles, and the local strains. Based on our preliminary results, we plan to perform a systematic study to seek the whole aspect of the moiré physics of phosphorene bilayers by exploring the intriguing anisotropic properties of phosphorene monolayer coupled with stacking and twisting effects in these bilayer nanostructures.
We plan to consider various commensurate structures with different stacking arrangement and local strain. Accordingly, we plan to (1) systematically study the moiré physics of phosphorene bilayers with different stacking orders, (2) systematically study the effect of twist angle on the different stacking orders, (3) systematically study strain effects on the moiré patterns of phosphorene bilayers, and finally, (4) systematically study the electronic and optical properties of these optimized nanostructures. The outcome of these studies is expected to provide a fundamental understanding of the intriguing details of the novel structural, electronic, optical, thermal and mechanical properties of these systems and guide current and future works in designing nanoelectronics devices at the microscopic level.