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Using ab initio calculations we have studied the optical linear response of different configurations of twisted trilayer graphene systems. We have found that when one of the outer layers is rotated the system shows an angle-dependent optical spectrum as its twisted bilayer counterpart; however, in this case there are two absorption peaks located in the visible range of the spectrum and one more in the intermediate infrared range for large relative rotation angles. When two layers are rotated the spectrum exhibits only two absorption peaks in the visible range revealing information about the two relative rotation angles between the layers in the structure. All these absorption peaks in the visible range shift to the intermediate infrared range for small angles.
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