Reorganization of Edge Modes: Quantum Phase Transitions and Textures

尽管我们早先试图描述量子霍尔系统边缘的量子相变，但我们提出的项目开辟了新的视野。该提议代表了两个主要推动力：1.一方面，在边缘上自然发生(或诱导)的新型量子相变(QPT)(例如，自旋转换跃迁；自发时间反转对称性破缺)。为什么这很重要？除了发现和分析拓扑系统中新的相变类型的基本物理重要性之外，后者还涉及到通过这样的设置进行电荷和自旋输运。此外，时间反转对称性的自发破坏可能发生在其他时间反转不变的系统中，这可能意味着应该重新关注量子计算所必需的“拓扑保护”(例如，在三重拓扑绝缘体中)。2.另一方面，人工设计的手性和螺旋边缘的物理学。Heiblum小组最近的实验(第一批实验刚刚发表，参见Y.Ronen等人，arxiv：1709.03976(2017年))，预示着一个新纪元：人们可以随意设计整数和分数区域的复合边缘(由多个手征模式组成)。为什么这很重要？这样就可以控制边缘手征模之间的相互作用和隧穿，以及每个模的自旋含量，极大地丰富了相关一维问题的研究范围。人们可能会想到控制干涉仪的想法，从而克服任意子干涉术的回避物理学。此外，通向按需的各种(整数和分数)拓扑绝缘子的道路现在似乎是开放的。解决这些问题所需的工具包括场论方法、对称破缺模式分析、非平衡量子系统理论。这两位PI由于他们之前在量子霍尔和拓扑绝缘体物理领域的经验而非常熟悉这些工具，取得了有影响力的成就，包括：非平衡玻色化的发展和应用；拓扑绝缘体中自发的时间反转对称破缺的预测；通过Mach-Zender干涉测量首次预测分数统计；第一次分析由任意子物理引起的分数Aharonov-Bohm振荡，包括分析Fabry-Perot干涉仪中的相互作用效应。这两个私人投资机构有着长期的合作历史，产生了几种共同的出版物。他们的合作包括多次相互访问，并交流他们团队的年轻成员。

Notwithstanding earlier attempts at describing quantum phase transitions on the edge of quantum Hall systems, our proposed project opens new horizons. The proposal represents two main thrusts: 1. On the one hand, novel classes of naturally occurring (or induced) quantum phase transitions (QPTs) on the edge (e.g., spin switching transitions; spontaneous time reversal symmetry breaking). Why is this important? Beyond the basic physics importance of discovering and analyzing new classes of phase transitions in topological systems, the latter have implications on charge and spin transport through such setups. Moreover, the fact that spontaneous breakdown of time reversal symmetry may take place in otherwise time reversal invariant systems, may imply that renewed attention should be given to “topological protection” (e.g., in TRI topological insulators), necessary for quantum computation. 2. On the other hand, the physics of artificially engineered chiral and helical edges. Very recent experiments by the Heiblum group (the first batch of which has just been posted, see Y. Ronen et al., arXiv:1709.03976 (2017)), herald a new era: one can design a composite edge (made up of multiple chiral modes) both in the integer and the fractional regimes at will. Why is this important? One may then control the interaction and tunneling between edge chiral modes, and the spin content of each mode, tremendously enriching the scope of relevant one-dimensional problems to be studied. One can possibly entertain the idea of controlled interferometers, overcoming the evading physics of anyonic interferometry. Furthermore, the road to an on-demand large variety of (integer and fractional) topological insulators now seems to be open. The tools needed to attack these problems include field theoretical methods, analysis of symmetry breaking patterns, the theory of non-equilibrium quantum systems. The two PIs are well acquainted with these tools due to their previous experience in the fields of quantum Hall and topological insulator physics, with impactful achievements that include: the development and applications of non-equilibrium bosonization; the prediction of spontaneous time-reversal symmetry breaking in topological insulators, the first predictions of fractional statistics through Mach-Zender interferometry; the first analysis of fractional Aharonov-Bohm oscillations due to anyonic physics, including the analysis of interaction effects in Fabry-Perot interferometers. The two PIs have a long history of collaboration that results in several common publications. Their collaboration has included numerous mutual visits, and exchange of young members of their teams.