Moiré pattern in scanning tunneling microscopy of monolayer graphite

Moir\'e patterns observed in scanning tunneling microscopy (STM) of monolayer graphite on transition-metal surfaces are investigated theoretically. STM images of the monolayer graphite on the TiC(111) surface are calculated using the tight-binding method. The calculated STM images show the moir\'e patterns which reproduce well the experimental STM images. The moir\'e patterns cannot be explained in terms of a simple superposition of the atomic structures of the substrate and the overlayer. The calculated moir\'e patterns strongly depend on the bias voltage. At a bias voltage, peaks of the STM image are located at the atomic sites of the substrate, which can be regarded as an example of the trans- parency effect observed in STM. It is found that three factors are important for the appearance of the moir\'e patterns: (1) the strength of the interaction between overlayers and substrates, (2) the height of the tip in scanning over sample surfaces, and (3) the bias voltage that reflects the energy region where bands of the overlayer and the substrate are strongly mixed.