DMREF: Theory-Guided Experimental Search of Designed Topological Insulators and Band-Inverted Insulators

****技术摘要****“拓扑绝缘”代表了一种新的功能，即3D块体绝缘体中能带顺序的特定反转需要相应的二维表面是金属的，具有线性分散的交叉表面带。最值得注意的是，随之而来的表面状态是自旋极化的，并且对任何尊重底层对称性的钝化都有弹性。不幸的是，由于缺乏预测性的“设计原则”，事实证明很难指导合成那些具有这种非凡功能的材料。事实上，少数已知的TI材料往往是高原子序数的材料，因此不仅是窄间隙半导体，而且容易产生结构缺陷，产生自由载流子，从而掩盖TI度。我们发现，除了这些“1型TI”所需的能带反演外，还有其他能带反演模式导致不同程度的表面钝化弹性。这种尚未被发现的情况，这里被称为TI-2，以及类型1和2的带反转（BI） （BI-1, BI-2）可能存在于更广泛的材料中，包括宽间隙绝缘体和半导体。我们已经开发了理论上可计算的“设计原则”（TI-ness的度量），我们将通过第一性原理电子结构理论，将其应用于广泛的现有和“设计”材料，筛选导致TI-1， TI-2， BI-1和BI-2行为的特定模式。与合成和ARPES实验的紧密结合将导致下一代宽间隙，轻元素TI和BI，这将极大地拓宽新型拓扑和带反转材料的表面电子结构的范围和理解，为设计由体性能控制的导电表面提供新的范例。***非技术摘要****大多数高科技都是基于独特的功能（电导率，磁性），这些功能“存在”于某些特定材料中，而不是其他材料。识别（从天文数字的可能性中）那些可能具有特定功能的材料是材料研究中一个普遍未解决的问题。这项工作为解决这个问题提供了一个总体策略。它专注于一种新发现的功能——一种具有导电表面但内部绝缘的单一材料，这种特性被称为“拓扑绝缘”（TI）。通过结合可计算的“度量”（基于物质的量子理论）来猜测材料是否可能是TI，与实验室合成和同步加速器测量相结合，我们提供了迄今为止未知的具有这种规定性质的新材料。研究生和博士后研究人员将得到该基金的支持，并将接受材料理论、合成和表征、沟通和领导技能等广泛方面的培训。该奖项由材料研究部（DMR）和数学科学部（DMS）资助。

****Technical Abstract****"Topological Insulation" represents a new functionality whereby a specific inversion in the order of the energy bands in a 3D bulk insulator necessitates that the corresponding 2D surface would be metallic, with linearly dispersed crossing surface bands. Most remarkably, the ensuing surface states are spin-polarized and resilient to any passivation that respects the underlying symmetry. Unfortunately, in the absence of predictive "design principles", it has proven difficult to guide synthesis towards those materials in which this remarkable functionality would live. Indeed, the handful of known TI materials tend to be high-atomic number materials, thus not only being narrow-gap semiconductors, but also prone to structural defects that produce free carriers which obscure the TI-ness. We find that in addition to the band inversion necessitated for these, "Type1 TI's", there are other patterns of band inversion leading to different degrees of resilience to surface passivation. Such yet undiscovered cases, called here TI-2, as well as Band-Inversion (BI) of types 1 and 2 (BI-1, BI-2) could exist in a far wider range of materials, including wide gap insulators and semiconductors. We have developed theoretically calculable "Design Principles" (metrics of TI-ness) which we will apply, via first-principles electronic structure theory, to a wide range of both existing, and "designed" materials, screening for the specific patterns that would lead to TI-1, TI-2, BI-1 and BI-2 behaviors. Close integration with synthesis and ARPES experiments would lead to next-generation wide gap, light element TI's and BI's that would dramatically broaden the scope and understanding of surface electronic structure of new types of topological and band-inverted materials, providing a new paradigm for the design of conductive surfaces controlled by bulk properties. ***Non-Technical Abstract****Most high technologies are based on unique functionalities (conductivity, magnetism) that "live" in certain, specific materials and no others. Identifying, (out of an astronomic number of possibilities) those materials likely to have a specific functionality is a generally unsolved problem in material research. This work offers a general strategy around this problem. It focuses on a newly discovered functionality- a single material having a conducting surface but an insulating interior, a property called "Topological Insulation" (TI). By combining a calculable "metric" (based on quantum theory of matter) that guesses if a material is likely to be a TI or not, with laboratory synthesis and synchrotron measurement, we offer to identify hitherto unknown new materials that have such prescribed properties. Graduate students and post-doctoral researchers will be supported under this grant, and will receive training in broad aspects of materials theory, synthesis, and characterization, as well as communication and leadership skills.This award is funded by the Division of Materials Research (DMR) and the Division of Mathematical Sciences (DMS).