Peierls Distortion in Two-Dimensional Tight-Binding Model

Abstract

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 *

Imperfect nesting and Peierls instability for a two-dimensional tight-binding model

“…This is physically understandable: they have a different wave vector from the nesting one. Very recently, a more complex lattice distortion pattern with incommensurate structure was studied by Ono and Hamano in the case of [14]. However it will not be included here since it is not unique [14].…”

Berry's Phase in the Multimode Peierls States

“…In actual calculations, we first determine the lattice distortion of the ground state of the Hamiltonian (1) self-consistently. 4) We then evaluate Berry's phase by changing the phase of the local bond variable keeping the distortion fixed. In this way, we obtain information on the topological aspect of the ground state wave function of the system (1).…”

“…It has been shown 4,5) that the state is the ground state of the half filled tight-binding model on the 2D square lattice described by the HamiltonianHere the lattice distortion at the site r is denoted by v(r) = (v x (r), v y (r)) and is defined by the difference of the lattice displacements u(r) aswhere e x(y) denotes the unit vector in the x(y) direction. In the present note, the spin degrees of freedom are neglected for simplicity.…”

“…It has been shown 4,5) that the state is the ground state of the half filled tight-binding model on the 2D square lattice described by the Hamiltonian…”

“…4,5) It is called "multimode" since its lattice distortion pattern consists of more than one Fourier components. It has been shown 4,5) that the state is the ground state of the half filled tight-binding model on the 2D square lattice described by the Hamiltonian (1)…”