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

渴望：编织：分数陈绝缘体中的晶格工程非阿贝尔缺陷

• 批准号: 1836776
• 负责人: Andrea Young
• 金额: $ 30万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-15 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1836776&HistoricalAwards=false
• 关键词: EAGER; BRAIDING; Lattice; engineered; nonabelian

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.

非技术摘要：在过去的十年中，利用物质涌现态的不寻常的量子统计作为量子计算的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成分。在这种方法中，两种具有互补特性的材料被放置得彼此非常接近，例如允许将超导性引入到具有互补特性的材料中。最突出的是，马约拉纳束缚态是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不断加强，出现了一个问题：是否可以使用相同的合成方法来实现更丰富的基态。该提案描述了在新发现的一类拓扑有序超材料（称为分数陈绝缘体）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造晶格中以单点分辨率设计所需的不同特性，从而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。 最近的进展很大程度上归功于焦点转向“综合”方法。不是在“自然”电子系统中寻求非阿贝尔任意子作为基本激发，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强，出现了一个问题：是否可以使用相同的合成方法来实现更丰富的平费米子和斐波那契任意子基态。该提案描述了一种在最近发现的石墨烯异质结构中的分数陈绝缘体中实现非阿贝尔缺陷的途径，包括对费米子束缚态。 分数陈绝缘体是分数量子霍尔态到晶格系统的推广。 与传统的分数量子霍尔态一样，带隙分数陈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。根据当前的提案，我们将对光刻定义的超晶格中的分数陈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，以实现仅测量的非阿贝尔缺陷态编织。该奖项反映了 NSF 的法定使命，并被认为是值得的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来提供支持。

项目成果

Fractional Chern insulator edges and layer-resolved lattice contacts

分数陈绝缘体边缘和层分辨晶格接触

• DOI: 10.1103/physrevb.99.081114
• 发表时间: 2019
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Knapp, Christina;Spanton, Eric M.;Young, Andrea F.;Nayak, Chetan;Zaletel, Michael P.
• 通讯作者: Zaletel, Michael P.