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

非技术摘要：在过去的十年里，利用物质涌现状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种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，两种具有互补性质的材料被放置在彼此非常接近的位置，例如，允许在具有互补性质的材料中引入超导电性。最突出的是，可以通过在一维导线中诱导超导来设计Majorana束缚态，这是可以支持某些形式的量子计算的最简单的态。随着对Majorana束缚态的实验性搜寻的加强，出现了一个问题，即是否可以使用同样的合成方法实现更丰富的基态。这项提议描述了一种在一类新发现的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绝缘体。值得注意的是，这些超材料允许在人工晶格中以单一位置的分辨率设计出必要的完全不同的特性，为量子设备打开了全新的设计原则。技术摘要：在过去的十年里，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种雄心勃勃但合理的可能性。最近的进展在很大程度上要归功于将重点转向“综合”方法。与寻找非阿贝尔任意子作为“天然”电子系统的基本激发不同，所需的不同成分是通过邻近效应组装起来的。例如，Majorana束缚态--最简单的非阿贝尔缺陷态--可以通过在实际上没有自旋的一维费米线中诱导超导来实现。随着对Majorana束缚态的实验性搜寻的加强，出现了一个问题，即是否可以使用相同的合成方法来实现更丰富的副费米子和斐波那契任意子基态。这一建议描述了一条在最近发现的石墨烯异质结构中实现非阿贝尔缺陷的途径，包括准费米子束缚态。分数陈绝缘体是分数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能级电荷激发具有任意子统计特性；然而，晶格自由度赋予了它们新的实验可调性。根据目前的提议，我们将在光刻定义的超晶格中对分数陈氏绝缘体基态进行分类，并使用它们来设计晶格缺陷和亚晶格选择性接触，以仅用于测量编织非阿贝尔缺陷状态。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.