VOLTAGE-DEPENDENT STM IMAGE OF A CHARGE-DENSITY-WAVE

In the present work we write a general expression for the local densit y of states (LDOS) due to a commen-surate charge density wave (CDW). T he main goal is to investigate the voltage dependence of the contrast in the scanning tunneling microscope (STM) images of materials showing CDW's. For layered materials, having nearly two-dimensional electroni c structures, the problem is complicated by the many-band situation ne ar the Fermi level, and by the incomplete band gapping. Nevertheless, a simple perturbation method allows one to relate the amplitude and ph ase of the CDW to features of the band structure. We emphasize the rol e of particular characteristic energies, at which the CDW has a large contribution from special k points of the surface Brillouin zone, lead ing to different modulations in the STM image. In a second part of the paper, we consider the voltage-dependent contrast of NbSe2. For this material, we find that the amplitude and the phase of the CDW change s ignificantly as a function of energy (or voltage), resulting in a numb er of different possible motifs. For example, the direct comparison be tween occupied and empty states reveals that new states on the order o f E-F+/-Delta, giving a dominant contribution to the LDOS, have differ ent phases. As a result, in the corresponding STM images, the maxima o f the corrugation have shifted positions along the diagonal of the con ventional unit cell.