Numerical investigations of ensembles of Boguliubov-deGennes Hamiltonians

Boguliubov-deGennes 哈密顿量系综的数值研究

• 批准号: 281653456
• 负责人: Professor Dr. Ferdinand Evers
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/281653456?language=en
• 关键词: Numerical; investigations; ensembles; Boguliubov; deGennes

The physics of disordered metals and semiconductors continues to hold surprises and therefore is still one of the important active fields in contemporary condensed matter physics. In recent years, the interplay between disorder and interaction has come into focus again, e.g., in disordered superconductors in connection with the superconductor-insulator junction. Despite intensive efforts, the theoretical understanding of such systems is still limited, among other reasons because analytical calculations in the most interesting parameter regime can hardly be carried out in a systematically controlled manner, i.e. the regime in which disorder, interaction and kinetic energy of similar strength, This is where the project proposed here comes into play.In the first funding period, a code could be developed that allows for an extremely efficient self-consistent numerical treatment of disorder and interaction within the framework of the attractive Hubbard model and Boguliubov-deGennes theory. Large ensembles of self-consistent random matrices can be generated and systematically evaluated with regard to their statistical properties. It was thus possible for the first time to numerically access the important intermediate parameter regime and to confirm the long suspected formation of superconducting islands there. For the second funding period, we propose to exploit this success and study physical observables that are to be determined in current experiments, some of which are still in planning stage. Specifically, a strong interest is in the form of the gap in the local spectral function and in understanding the apparent “gapless superconductivity”, which was recently observed experimentally. The explanatory hypothesis we will test involves free magnetic moments, which inevitably arise due to the disorder and whose existence our calculations are able to demonstrate. Another subject of investigation will be the superconducting stiffness, as well as its dependence on magnetic field and temperature, which recently became accessible also to high precision experiments.Finally, as last stage of the project a phase diagram should be created with axes of magnetic field, temperature and disorder strength. On the one hand, the diagram is about identifying a regime in which the putative "failed superconductors" could reside. On the other hand, an American-Indian team recently proposed a phase diagram, which, however, could did not account sufficiently accurately for the formation of local moments. Specifically, the importance of repulsive interactions has not been recognized. In the follow-up project, these investigations are to be deepened and expanded to include an extended model with attractive and repulsive interaction.

无序金属和半导体物理学继续保持着令人惊讶的发现，因此仍然是当代凝聚态物理学中重要的活跃领域之一。近年来，无序和相互作用之间的相互作用再次成为焦点，例如，在无序超导体中与超导体-绝缘体结有关。尽管作出了大量努力，但对这种系统的理论理解仍然有限，其中一个原因是，在最有趣的参数范围内的分析计算很难以系统控制的方式进行，即在无序，相互作用和类似强度的动能的范围内，这就是这里提出的项目发挥作用的地方。在第一个资助期，可以开发一种代码，该代码允许在有吸引力的Hubbard模型和Boguliubov-deGennes理论的框架内对无序和相互作用进行极其有效的自洽数值处理。可以生成自洽随机矩阵的大集合，并系统地评估其统计特性。因此，这是第一次有可能在数字上访问重要的中间参数制度，并确认长期怀疑那里形成超导岛。对于第二个资助期，我们建议利用这一成功，并研究将在当前实验中确定的物理观测值，其中一些仍处于规划阶段。具体来说，强烈的兴趣是在局部谱函数的差距的形式，并在理解明显的“无间隙超导”，这是最近观察到的实验。我们将要检验的解释性假设涉及自由磁矩，它不可避免地由于无序而产生，我们的计算能够证明它的存在。另一个研究课题将是超导刚度，以及它对磁场和温度的依赖性，最近也可以进行高精度实验。最后，作为项目的最后阶段，应该创建一个相图，其中包含磁场，温度和无序强度的轴。一方面，该图是关于确定假定的“失败的超导体”可能存在的制度。另一方面，一个美国和印度的研究小组最近提出了一个相图，但是，它不能足够准确地解释局部时刻的形成。特别是，排斥相互作用的重要性尚未得到承认。在后续项目中，这些研究将得到深化和扩大，以包括一个具有吸引力和排斥力相互作用的扩展模型。