多能带电子模型中新的电子相和量子相变

在实验上发现石墨烯促进了拓扑材料和2维材料科学的爆炸性发展。这些量子材料的关键因素之一是多能带效应、电子关联、淬火无序之间的相互影响。本项目研究具有有限体积费米表面的多能带电子模型，并探索新的(novel)多能带效应、电子关联和无序之间新的相互影响。申请人将主要研究具有有限体积费米面的一对电子型和空穴型的双能带模型。通过这项研究，申请人将（1）阐明和这个模型的激子不稳定性相关的量子临界现象，（2） 阐明在电子-空穴双层（EHDL）系统中的非传统的激子相。这个项目还有另外两个补充的主题。申请人将（3）阐明在3维金属的量子极限下，电子关联与猝火无序的相互影响和几何效应，通过这个揭示稳定奇异电子相（如3维魏格纳晶体相）的新微观机制，（4）阐明无序驱动的从3维拓扑绝缘体到辛类扩散金属的量子相变所属的普适类。预期的结果将为拓扑材料科学领域贡献一部分不可或缺的知识。

Experimental discovery of graphene promotes an explosive development on topological material science as well as two-dimensional (2D) material science. A key ingredient in these quantum materials is an interplay effect among multiple-band effect, electron correlation, and quenched disorder. This project studies multiple-band electron models with finite volume of Fermi surfaces and discovers novel interplay effects among these three. The applicant will primarily study a two-band model with a pair of electron and hole bands with finite Fermi surfaces. Through the study, the applicant will (1) clarify natures of novel superconductivity and quantum phase transition associated with an exitonic instability of the model, and (2) clarify unconventional excitonic phases in an electron-hole double-layer (EHDL) system. .The project has another two complementary topics. The applicant will (3) clarify an interplay effect between electron correlation and the quenched disorder as well as a geometric effect in 3D metals in the quantum limit. By doing so, the applicant will reveal a novel microscopic mechanism that stabilizes exotic electronic phases such as 3D Wigner crystal phase. As a study on an interplay between multiple-band effect and disorder, the applicant will also (4) clarify the universality class of the disorder-driven quantum phase transition from 3D topological insulator to diffusive metals in the symplectic class. The expected result will provide an indispensable piece of knowledge in the field of topological material science.