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Register a new userStructural Determination of Multilayer Graphene via Atomic Moir{e} Interferometry
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Authors
David L. Miller
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Rotational misalignment of two stacked honeycomb lattices produces a moire pattern that is observable in scanning tunneling microscopy as a small modulation of the apparent surface height. This is known from experiments on highly-oriented pyrolytic graphite. Here, we observe the combined effect of three-layer moire patterns in multilayer graphene grown on SiC ($000bar{1}$). Small-angle rotations between the first and third layer are shown to produce a double-moire pattern, resulting from the interference of moire patterns from the first three layers. These patterns are strongly affected by relative lattice strain between the layers. We model the moire patterns as a beat-period of the mismatched reciprocal lattice vectors and show how these patterns can be used to determine the relative strain between lattices, in analogy to strain measurement by optical moire interferometry.
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Encapsulating graphene in hexagonal Boron Nitride has several advantages: the highest mobilities reported to date are achieved in this way, and precise nanostructuring of graphene becomes feasible through the protective hBN layers. Nevertheless, subtle effects may arise due to the differing lattice constants of graphene and hBN, and due to the twist angle between the graphene and hBN lattices. Here, we use a recently developed model which allows us to perform band structure and magnetotransport calculations of such structures, and show that with a proper account of the moire physics an excellent agreement with experiments can be achieved, even for complicated structures such as disordered graphene, or antidot lattices on a monolayer hBN with a relative twist angle. Calculations of this kind are essential to a quantitative modeling of twistronic devices.
Strain-induced lattice mismatch leads to moir{e} patterns in homobilayer transition metal dichalcogenides (TMDs). We investigate the structural and electronic properties of such strained moir{e} patterns in TMD homobilayers. The moir{e} patterns in strained TMDs consist of several stacking domains which are separated by tensile solitons. Relaxation of these systems distributes the strain unevenly in the moir{e} superlattice, with the maximum strain energy concentrating at the highest energy stackings. The order parameter distribution shows the formation of aster topological defects at the same sites. In contrast, twisted TMDs host shear solitons at the domain walls, and the order parameter distribution in these systems shows the formation of vortex defects. The strained moir{e} systems also show the emergence of several well-separated flat bands at both the valence and conduction band edges, and we observe a significant reduction in the band gap. The flat bands in these strained moir{e} superlattices provide platforms for studying the Hubbard model on a triangular lattice as well as the ionic Hubbard model on a honeycomb lattice. Furthermore, we study the localization of the wave functions corresponding to these flat bands. The wave functions localize at different stackings compared to twisted TMDs, and our results are in excellent agreement with recent spectroscopic experiments [1].
Molecular and atomic imaging required the development of electron and scanning probe microscopies to surpass the physical limits dictated by diffraction. Nano-infrared experiments and pico-cavity tip-enhanced Raman spectroscopy imaging later demonstrated that radiation in the visible range can surpass this limit by using scanning probe tips to access the near-field regime. Here we show that ultimate resolution can be obtained by using scanning microwave imaging microscopy to reveal structures with feature sizes down to 1~nm using a radiation of 0.1~m in wavelength. As a test material we use twisted bilayer graphene, which is not only a very important recent topic due to the discovery of correlated electron effects such as superconductivity, but also because it provides a sample where we can systematically tune a superstructure Moire patterns modulation from below one up to tens of nanometers. By analyzing the tip-sample distance dynamics, we demonstrate that this ultimate 10$^8$ probe-to-pattern resolution can be achieved by using liquid immersion microscopy concepts and exquisite force control exerted on nanoscale water menisci.
An important step in understanding the exotic electronic, vibrational, and optical properties of the moir{e} lattices is the inclusion of the effects of structural relaxation of the un-relaxed moir{e} lattices. Here, we propose novel structures for twisted bilayer of transition metal dichalcogenides (TMDs). For $thetagtrsim 58.4^{circ}$, we show a dramatic reconstruction of the moir{e} lattices, leading to a trimerization of the unfavorable stackings. We show that the development of curved domain walls due to the three-fold symmetry of the stacking energy landscape is responsible for such lattice reconstruction. Furthermore, we show that the lattice reconstruction notably changes the electronic band-structure. This includes the occurrence of flat bands near the edges of the conduction as well as valence bands, with the valence band maximum, in particular, corresponding to localized states enclosed by the trimer. We also find possibilities for other complicated, entropy stabilized, lattice reconstructed structures.
The visibility of graphene sheets on different types of substrates has been investigated both theoretically and experimentally. Although single layer graphene is observable on various types of dielectrics under an optical microscope, it is invisible when it is placed directly on most of the semiconductor and metallic substrates. We show that coating of a resist layer with optimum thickness is an effective way to enhance the contrast of graphene on various types of substrates and makes single layer graphene visible on most semiconductor and metallic substrates. Experiments have been performed to verify the results on quartz and NiFe-coated Si substrates. The results obtained will be useful for fabricating graphene-based devices on various types of substrates for electronics, spintronics and optoelectronics applications.
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