We have observed with STM moiré patterns corresponding to the rotation of one graphene layer on HOPG surface. The moiré patterns were characterized by rotation angle and extension in the plane. Additionally, by identifying border domains and defects we can discriminate between moiré patterns due to rotation on the surface or subsurface layer. For a better understanding of moiré patterns formation we have studied by first principles an array of three graphene layers where the top or the middle layer appears rotated around the stacking axis. We compare the experimental and theoretical results and we show the strong influence of rotations both in surface and subsurface layers for moiré patterns formation in corresponding STM images.

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We study the quasinormal modes of fermionic perturbations for an asymptotically Lifshitz black hole in four dimensions with dynamical exponent z = 2 and plane topology for the transverse section, and we find analytically and numerically the quasinormal modes for massless fermionic fields by using the improved asymptotic iteration method and the Horowitz-Hubeny method. The quasinormal frequencies are purely imaginary and negative, which guarantees the stability of these black holes under massless fermionic field perturbations. Remarkably, both numerical methods yield consistent results; i.e., both methods converge to the exact quasinormal frequencies; however, the improved asymptotic iteration method converges in a less number of iterations. Also, we find analytically the quasinormal modes for massive fermionic fields for the mode with lowest angular momentum. In this case, the quasinormal frequencies are purely imaginary and negative, which guarantees the stability of these black holes under fermionic field perturbations. Moreover, we show that the lowest quasinormal frequencies have real and imaginary parts for the mode with higher angular momentum by using the improved asymptotic iteration method.

In this work we performed density functional theory calculations for a twisted bilayer graphene (BLG). Several conmensurable rotation angles were analyzed and for each one a constant height mode STM image was obtained. These STM images, calculated under the Tersoff-Hamman theory, reproduce the main features experimentally observed, paticularly superstructures and giant corrugations. In this way we confirm that STM characterization of twisted BLG can produce superstructures whose tunneling current intensity maxima occur over regions with AA stacking. Additionally we give new evidence in favour of an electronic origin for the superstructures instead another physical grounds.