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

非技术摘要：在过去的十年里，利用物质突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，具有互补性质的两种材料彼此靠近放置，例如允许超导性被引入具有互补性质的材料中。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探索的加剧，问题出现了，是否可以使用相同的合成方法来实现更丰富的基态。这个提议描述了一种在新发现的一类拓扑有序的超材料中实现这种状态的途径，这种超材料被称为分数陈式绝缘体。 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所需的不同属性，为量子器件开辟了全新的设计原理。 技术摘要：在过去的十年中，使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。 最近取得的进展在很大程度上归功于将重点转向“综合”办法。在“自然”电子系统中，非阿贝尔任意子不是作为基本激发，而是通过邻近效应组装所需的不同成分。 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探索的加剧，问题出现了，是否可以使用相同的合成方法来实现更丰富的仿费米子和斐波那契任意子基态。该建议描述了一种实现非阿贝尔缺陷的路线，最近发现的分数陈绝缘体在石墨烯异质结构，包括parafermion束缚态。 分数阶陈氏绝缘体是分数阶量子霍尔态在晶格系统中的推广。 与传统的分数量子霍尔态一样，带隙分数陈氏绝缘体的低位带电激发具有任意子统计;然而，晶格自由度赋予它们新的实验可调性。根据目前的建议，我们将分类分数陈省身绝缘体基态光刻定义的超晶格，并使用它们来工程晶格缺陷和亚晶格选择性接触的测量，只有编织nonabelian缺陷states.This奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.