van der Waals heterostructures assembled from atomically thin crystalline layers of diverse two-dimensional solids are emerging as a new paradigm in the physics of materials. We use infrared (IR) nano-imaging to study the properties of surface phonon polaritons in a representative van der Waals crystal, hexagonal boron nitride (hBN). We launched, detected and imaged the polaritonic waves in real space and altered their wavelength by varying the number of crystal layers in our specimens. The measured dispersion of polaritonic waves was shown to be governed by the crystal thickness according to a scaling law that persists down to a few atomic layers. Our results are likely to hold true in other polar van der Waals crystals and may lead to their new functionalities.Main Text: Layered van der Waals (vdW) crystals consist of individual atomic planes weakly coupled by vdW interaction, similar to graphene monolayers in bulk graphite (1-3). These materials can harbor superconductivity (2) and ferromagnetism (4) with high transition temperatures, emit light (5-6) and exhibit topologically protected surface states (7), among many other effects (8). An ambitious practical goal (9) is to exploit atomic planes of van der Waals
We present a systematic Raman study of unconventionally-stacked double-layer graphene, and find that the spectrum strongly depends on the relative rotation angle between layers. Rotation-dependent trends in the position, width and intensity of graphene 2D and G peaks are experimentally established and accounted for theoretically. Our theoretical analysis reveals that changes in electronic band structure due to the interlayer interaction, such as rotational-angle dependent Van Hove singularities, are responsible for the observed spectral features. Our combined experimental and theoretical study provides a deeper understanding of the electronic band structure of rotated double-layer graphene, and leads to a practical way to identify and analyze rotation angles of misoriented double-layer graphene.Recently there has been growing interest in double-layer graphene in which the two graphene layers are not conventionally stacked but relatively rotated by an arbitrary angle [1][2][3][4][5][6][7][8][9][10][11][12].Such graphene double layers are expected to display characteristics distinct from both monolayer 2 graphene as well as the extensively studied AB-stacked bilayer graphene [13][14][15][16]. Previous theoretical investigations suggest that electronic and optical properties of double layer graphene will strongly depend on this rotational angle [1][2][3][4][5]. Because the entire range of rotational angles is in principle experimentally accessible via artificial stacking, the properties of rotated double-layer graphene might be tuned to suit the application at hand, making this material a useful component in future nano-electronic devices. Limited low-energy electrical transport measurements have suggested that rotated graphene layers maintain the linear dispersion relation as in single-layer graphene [6,7].Furthermore, angle-resolved photoemission spectroscopy measurement has shown that rotated layers in multilayer epitaxial graphene exhibit weak interlayer interactions [8]. On the other hand, scanning tunnelling microscopy studies in the low rotation angle regime have demonstrated strong interlayer interactions such as carrier velocity renormalization and the occurrence of Van Hove singularities away from the Dirac point energy [9,10]. Despite these suggestive findings and the applications potential, there have unfortunately been no comprehensive experimental studies of the influence of rotation angle on the electronic properties of double-layer graphene.In this Letter we present a systematic experimental and theoretical study of rotated doublelayer graphene. We employ Raman spectroscopy, a powerful tool for investigating the electronic and vibrational properties of carbon-based materials [17][18][19][20], together with theoretical calculations of the electronic-structure-dependent Raman response. We experimentally sample a range of misorientation angles from 0 to 30 degrees in steps of ~1 degree, and we focus on the intensity, peak position, and peak width of the 2D and G Raman modes. Previous limited Raman stud...
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