高温超导赝能隙态电子低能散射的解析与数值研究

The pseudogap state in cuprate high-Tc superconductors is a state of correlated electrons which appears in the underoped regime at temperatures higher than the superconducting Tc. In pseudogap state, there is a partial energy gap in the single particle excitations of electrons despite the absence of superconductivity. Due to strong correlations, various unusual phenomena arise from pseudogap state. The Comprehending of the underlying mechanism of pseudogap state has been considered as one of the most difficult and important problems in the condensed matter field. Recently, numerical simulations and some indirect experimental evidences suggest that in pseudogap state, the electrons has a quasi-pole like low-energy scattering peak. The existence of such a scattering peak hints that the mechanism of pseudogap state may can be described by a concise low-energy effective theory. The current project will use the combination of analytical methods and numerical techniques to study the electron scatterings in pseudogap state and its dependence on system parameters. The current project will reveal the low-energy physics of pseudogap state linked to the scattering peak and its impact on the high-Tc superconductivity, as well as essential experimental setups which can be used to study the properties of such a quasi-pole like scattering peak in future experiments.

高温超导赝能隙态是指在铜氧化物高温超导体中，当温度高于超导临界温度时，出现在欠掺杂区域的一个关联电子态。在赝能隙态，电子没有超导电性，但是会有一个部分打开的单粒子能隙。赝能隙态中的电子多体效应很强，具有许多反常的物理特性。对赝能隙态本质的认识和理解被认为是当今凝聚态领域中的重点和难点问题之一。近年来，一些数值模拟计算，以及一部分间接实验证据显示，在赝能隙态，电子的低能散射似乎可以形成一个近似极点的强散射峰。准极点型散射峰的出现暗示着赝能隙态的本质也许可以用一个较为简洁的低能理论来描述。本项目将综合运用不同的解析、数值方法来交叉研究赝能隙态里的低能电子散射，探究散射峰的系统参数依赖性，揭示其所关联的赝能隙低能物理，及其对高温超导电性的影响；本项目也将探讨将来怎样在实验上进一步研究此低能电子散射峰的性质。

在高温超导赝能隙态电子低能散射的解析与数值研究这一项目中，我们主要研究了Hubbard模型，以及相关物理模型中关联电子的散射性质。我们发现，在赝能隙态电子的准极点型低能散射对系统参数的依赖可以总结为一个简单的经验公式，这个公式与由SU(2)隶粒子方法得到的解析解得预言一致。同时我们还研究了Hubbard模型中电子散射率在不同掺杂区间对温度得依赖关系。我们发现，在过掺杂区间，电子散射率和电阻率呈现所谓奇异金属的线性温度依赖关系，与高温超导实验发现符合得很好。运用涨落分析方法，我们发现此种温度线性的散射率关系起源于系统残余的短程反铁磁关联。本项目的研究对高温超导赝能隙态以及相关物理态的性质的理解和起源的探索具有重要的启示意义。