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

带半填充的二维电子系统的费米面（线）呈方形。这一事实使我们期望在电子-晶格相互作用存在下的佩尔斯跃迁，类似于在一维系统中。为了阐明二维电子晶格系统的基态，我们用数值方法研究了使系统总能量最小的晶格畸变。发现基态晶格畸变的傅里叶分量不仅涉及费米线的嵌套矢量，而且涉及与之平行的许多其他波矢量。我们称这种状态为多模佩尔斯（MMP）状态。当温度从高温区域降低时，由于电子和声子之间的相互作用，具有嵌套矢量和平行于嵌套矢量的声子模式在相同的临界温度下被软化。这与较低温度下基态的结构一致。在实际系统中，存在许多理想的电子-晶格模型中没有包括的效应，如各向异性和电子-电子相互作用。通过进行详细的数值计算，我们已经表明，即使在各向异性存在的情况下，只要各向异性参数在几个百分点左右或更低，MMP状态在低温极限下仍然是最低的能量状态。然而，有限的各向异性改变了声子在临界温度附近的软化行为；即随着温度的降低，嵌套矢量模的频率首先消失，即在低于临界温度时实现单模佩尔斯（SMP）状态。进一步降低温度会导致在第二临界温度下从SMP状态到MMP状态的一级相变。各向异性存在时，相图变得非常复杂。对于电子-电子相互作用，根据所谓的Peierls- Hubbard模型的数值计算，认为只要电子相互作用参数处于弱耦合区内，MMP态就是最低的能态。哈伯德参量的增加引起了从MMP态到反铁磁自旋密度波态的量子相变。证实了MMP态和SDW态不会作为一个均匀相共存。在强相关极限下，该模型被映射到反铁磁自旋佩尔斯模型上。在该模型中，我们发现当自旋-晶格耦合增加超过某个临界值时，从SDW态到多模自旋-佩尔斯态的1^<st>阶型跃迁。我们可以通过稍微改变系统参数来控制二维电子晶格系统的基态，因此该系统将有助于研究各种性质，例如有机导体。这项研究将为广泛应用开辟一条道路。少

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