Peierls Transition and Nonlinear Localized Excitations in Two-dimensional Electron-Lattice System

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The purpose of the present project was initially to study the structure and the dynamics of nonlinear localized excitations in 2D electron-lattice systems like solitons or polarons seen in 1D systems as polyacetylene. We had to start with investigating the ground state structure which would give the background for such excitations. To our surprise, the so far known ground state in 2D square lattice electron-lattice system with a half-filled electronic band was not a real ground state. In earlier studies a single mode Peierls state involving only the distortion modes with the nesting vector was considered. In our present study, it has been shown that the true ground state involves not only the nesting vector modes but also many other modes having wave vectors parallel to the nesting vector. It was argued that this multimode Peierls state is realized by second order nesting processes which use electronic states not lying on the Fermi surface as intermediate states. Furthermore we have fo … More und that there are many non-equivalent distortion patterns which give the same ground state energy and that the energy gap in the electronic dispersion does not vanish at any point on the Fermi surface in contrast to the single mode Peierls phase. These features are maintained even at finite temperatures and all the distortion modes vanish at the same transition, temperature when the temperature is increased from the absolute zero. The transition temperature depends on the electron-lattice coupling constant but not on the distortion pattern. This transition is also found to be accompanied by softening of phonon modes. The softening occurs at the transition temperature and the relevant modes are the longitudinal and transverse modes with the nesting vector and the transverse modes with wave vectors parallel to the nesting vector. In the low temperature region where the multimode Peierls distortions are present, the phonon dispersion seems dependent on the distortion pattern.As for the nonlinear excitations we have analyzed only the acoustic polaron in 2D square lattice. The acoustic polaron is stabilized only when the electron-lattice coupling constant exceeds a critical value. If we accelerate the polaron by an external electric field, the extent of the polaron shrinks similarly as in 1D case. Furthermore there is a maximum value of the velocity of a stable polaron, which is about 10% of the sound velocity. The effective mass as well as the maximum velocity shows anisotropy reflecting the square structure of the background lattice. Less