VARIATION OF THE ELECTRON SPECTRUM IN THE VICINITY OF VANHOVE POINTS,LOCALIZATION OF CARRIERS AND STRUCTURAL INSTABILITY DURING THE COUPLING WITH A LONG-WAVE PERTURBATION IN LOW-DIMENSIONAL SYSTEMS

Provided the wave vector k of a periodic perturbation in 1D and 2D cry stals satisfies the condition k << (g/t)1/2 << 1, g and t being the pe rturbation magnitude and bandwidth, the strongly nonequidistant spectr um from the large number of states n = (g/k2t)1/2 >> 1 is shown to ari se in the vicinity of the extreme points of the spectrum in the width 2g. This results in weakening the singularity in the density of states . In 1D systems the square root singularity weakens to logarithmic one and in 2D systems a flat maximum remains from the logarithmic singula rity. The widths of the logarithmic peak in ID case and maximum in 2D case are the magnitudes or the order g << t. The conditions and the ch aracter with respect to the deformation wave formation are clarified. In 1D case the system is unstable for the values of the chemical poten tial mu < mu(c) is similar to t(omega(D)/t)2 <<t. In 2D case the syste m is unstable provided the Fermi energy is exponentially close to the saddle point. In 1D case, the transition into the spontaneous deformat ion state at mu = mu(c) occur's jump-like. The maximum instability occ urs at mu = 0 corresponding to the bottom of the bare band or, as the same, to the half filling of band (-2g, 2g). As a result of transition in 1D case carriers localize completely and do in the single dimensio n for 2D case.