EAGER: BRAIDING: Lattice engineered nonabelian defects in fractional Chern insulators

摘要：在过去的十年中，利用物质涌现态的不寻常量子统计作为量子计算基础的可能性已经从一个遥远的梦想变成了一个雄心勃勃但合理的可能性。最近的进展是基于通过邻近效应组装所需的成分。在这种方法中，两种具有互补特性的材料被放置在彼此靠近的地方，例如允许超导性引入具有互补特性的材料中。最突出的是，马约拉纳束缚态——可以支持某些形式的量子计算的最简单的状态——可以通过在一维导线中诱导超导性来设计。随着对马约拉纳束缚态的实验搜索的加强，问题出现了，即是否可以使用相同的合成方法实现更丰富的基态。本提案描述了在新发现的一类拓扑有序的超材料（称为分数陈氏绝缘体）中实现这种状态的途径。值得注意的是，这类超材料允许在人工晶格中以单点分辨率设计必要的不同特性，为量子器件开辟了全新的设计原则。技术摘要：在过去的十年中，利用基态拓扑简并作为量子计算基础的可能性已经从一个遥远的梦想变成了一个雄心勃勃但合理的可能性。最近的进展在很大程度上归功于将重点转向“综合”方法。与其在“自然”电子系统中寻找非阿贝尔任意子作为基本激发，不如通过邻近效应将所需的不同成分组合起来。例如，马约拉纳束缚态——最简单的非阿贝尔缺陷态——可以通过在有效无自旋的一维费米子线中诱导超导性来设计。随着对马约拉纳束缚态的实验搜索的加强，问题出现了，即是否可以使用相同的合成方法实现更丰富的对偶子和斐波那契任意基态。本提案描述了在石墨烯异质结构中最近发现的分数chen绝缘体中实现非abel缺陷的途径，包括对介子束缚态。分数阶陈氏绝缘子是将分数阶量子霍尔态推广到晶格系统。与传统分数阶量子霍尔态一样，间隙分数阶陈氏绝缘子的低位带电激发具有任意统计量；然而，晶格自由度赋予了它们新的实验可调性。根据目前的建议，我们将在光刻定义的超晶格中对分数chen绝缘子基态进行分类，并使用它们来设计晶格缺陷和亚晶格选择接触，以进行非abel缺陷态的仅测量编织。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Nontechnical Abstract: in the last decade, the possibility of utilizing unusual quantum statistics of emergent states of matter as a basis for quantum computation has gone from being a distant dream to an ambitious but reasonable possibility. Recent advances are based on assembly of required ingredients through proximity effects. In this approach, two materials with complementary properties are placed in close proximity to each other, for example allowing superconductivity to be introduced into materials which have complementary properties. Most prominently, Majorana bound states, the simplest states that can support certain forms of quantum computation, can be engineered by inducing superconductivity in a one-dimensional wire. As the experimental hunt for Majorana bound states intensifies, the question arises as to whether even richer ground states can be realized using the same synthetic approach. This proposal describes a route towards realizing such states in a newly discovered class of topologically ordered metamaterials known as fractional Chern insulators. Remarkably, these class of metamaterials allow the requisite disparate properties to be engineered with single-site resolution in an artificial lattice, opening completely new design principles for quantum devices. Technical Abstract: in the last decade, the possibility of using ground state topological degeneracy as a basis for quantum computation has gone from being a distant dream to an ambitious but reasonable possibility. Recent advances owe much to a shift in focus to a `synthetic' approach. Rather than seeking nonabelian anyons as elementary excitations in 'natural' electronic systems, the disparate ingredients required are assembled through proximity effects. For example, Majorana bound state - the simplest nonabelian defect state - can be engineered by inducing superconductivity in an effectively spinless, one dimensional fermionic wire. As the experimental hunt for Majorana bound states intensifies, the question arises as to whether richer parafermion and Fibonacci anyon ground states can be realized using the same synthetic approach. This proposal describes a route towards realizing nonabelian defects in the recently discovered fractional Chern insulators in graphene heterostructures, including parafermion bound states. Fractional Chern insulators are generalizations of fractional quantum Hall states to lattice systems. Like conventional fractional quantum Hall states, the low-lying charged excitations of gapped fractional Chern insulators have anyonic statistics; however, the lattice degree of freedom endows them with new experimental tunability. Under the current proposal, we will classify fractional Chern insulator ground states in lithographically defined superlattices and use them to Engineer lattice defects and sublattice selective contacts for measurement-only braiding of nonabelian defect states.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.