Moiré image patterns on double-walled carbon nanotubes observed by scanning tunneling microscopy

Long-range quasiperiodic patterns are found in scanning tunneling microscopy (STM) images of double-walled carbon nanotubes (DWNTs) on top of the atomic images of six-membered carbon rings of the outer tubes. By comparing the results of first-principles calculations on model DWNTs, we conclude that they are moir\'e patterns showing local modulations of electronic states due to the interlayer interactions between the outer and inner tubes. We also demonstrate that these moir\'e patterns can be used to assign the chiral vector of the inner tube of a DWNT which is usually inaccessible by STM.