The Peierls distortions in a two-dimensional electron-lattice system described by a Su-Schrieffer-Heeger type model extended to two-dimensions are numerically studied for a square lattice. The electronic band is just half-filled and the nesting vector is (π/a, π/a) with a the lattice constant. In contrast to the previous understanding on the Peierls transition in two dimensions, the distortions which are determined so as to minimize the total energy of the system involve not only the Fourier component with the nesting wave vector but also many other components with wave vectors parallel to the nesting vector. It is found that such unusual distortions contribute to the formation of gap in the electronic energy spectrum by indirectly (in the sense of second order perturbation) connecting two states having wave vectors differing by the nesting vector from each other. Analyses for different system sizes and for different electron-lattice coupling constants indicate that the existence of such distortions is not a numerical artifact. It is shown that the gap of the electronic energy spectrum is finite everywhere over the Fermi surface.KEYWORDS: Peierls transition, two-dimensional electron-lattice systems, nesting, Peierls gap, Peierls distortion, second order perturbation §1. IntroductionThe Peierls transition is caused by the freezing of a lattice distortion mode which can connect degenerate electronic states at the Fermi level.1) The presence of such a distortion induces an energy gap at the Fermi level of the electronic spectrum. This gap which is called Peierls gap lowers the electronic energy. In some cases, this reduction of energy overcomes the increase of the lattice energy due to the frozen mode. In one-dimensional *
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