Zero-bias anomaly in two-dimensional electron layers and multiwall nanotubes

The zero-bias anomaly in the dependence of the tunneling density of states n (e) on the energy e of the tunneling particle for two- and one-dimensional multilayered structures is studied. We show that for a ballistic two-dimensional (2D) system the first-order interaction correction to density of states due to the plasmon excitations studied by Khveshchenko and Reizer is partly compensated by the contribution of electron-hole pairs, which is twice as small and has the opposite sign. For multilayered systems the total correction to the density of states near the Fermi energy has the form δv / 0 =max(|ε|,ε *)/4ε F, where ε * is the plasmon energy gap of the multilayered 2D system. For a 2D system with finite-range interaction the particle-hole contribution precisely cancels with the contribution of the zero-sound mode, in agreement with the Fermi liquid theory. In the case of one-dimensional conductors we study multiwall nanotubes with the elastic mean free path exceeding the radius of the nanotube. The dependence of the tunneling density-of-states energy, temperature and on the number of shells is found.