Peierls Transition and Phonon Softening in 2D Electron-Lattice System

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The Fermi surface (line) of a 2D electron system with a half-filled band is square-shaped. This fact makes us expect the Peierls transition in the presence of the electron-lattice interaction, similarly as in 1D systems. In order to clarify the ground state of the 2D electron-lattice system, we have studied numerically the lattice distortions minimizing the total energy of the system. It is found that the Fourier components of the lattice distortion in the ground state involve not only the nesting vector of the Fermi line but also many other wave vectors parallel to it. We call this state the multimode Peierls (MMP) state. When the temperature is lowered from the high temperature region, the phonon modes with the nesting vector and with those parallel to it are softened due to the interaction between the electrons and the phonons, all at the same critical temperature. This is consistent with the structure of the ground state at lower temperatures.In real systems, there are many effects … More not included in the ideal electron-lattice model, such as anisotropy and electron-electron interactions. By performing detailed numerical works, we have shown that, even in the presence of anisotropy, the MMP state survives as the lowest energy state at the low temperature limit as long as the anisotropy parameter is around a few per cent or below. Nevertheless, a finite anisotropy changes the phonon softening behavior in the vicinity of the critical temperature; namely, the frequency of the nesting vector mode vanishes first as lowering the temperature, which means that the single-mode Peierls (SMP) state is realized just below the critical temperature. Further lowering the temperature leads to the 1st order phase transition from the SMP state to the MMP state at the second critical temperature. The phase diagram in the presence of the anisotropy becomes very complicated.As for the electron-electron interaction, it has been argued that the MMP state is the lowest energy state as long as the electron interaction parameter lies within the weak coupling region, based on the numerical calculations using the so-called Peierls- Hubbard model. The increase of the Hubbard parameter induces a quantum phase transition from the MMP state to the antiferromagnetic spin-density wave (SDW) state. It is confirmed that the coexistence of the MMP state and the SDW state as a uniform phase does not occur. In the strong correlation limit the model is mapped onto the antiferromagnetic spin-Peierls model. In this model, we have found the 1^<st> order type transition from the SDW state to the multimode spin-Peierls state as the spin- lattice coupling is increased exceeding a certain critical value.We can control the ground state of the 2D electron-lattice system by changing slightly the system parameters, and therefore this system would be useful to study a variety of properties, e.g. in organic conductors. This study will open a way to wide applications. Less