Visualizing quantum Hall ferromagnets, their 1D topological edge modes and their interplay with superconductivity

拓扑相的研究既与量子场论中的概念有关，也与容错量子计算机的提出方法有关。凝聚态物质系统中的低能浮现准粒子可以提供一个实验室来测试场论概念，这一想法遵循了在能量和长度尺度上推广物理学概念的悠久传统。对于拓扑材料的研究同样重要的是，拓扑相和相关的浮现准粒子很可能为电子学提供基本的新方法。例如，固体中电子波函数的谷自由度，这是这里研究的一种特性，已被提出用于创建新型电子设备。在这个项目上接受培训的研究生和本科生正在学习最先进的扫描探针显微镜、低温和材料物理实验技术，这些技术是工业界和学术界都非常感兴趣的。随着普林斯顿大学一年级学生研讨会课程的发展，实验室研究正被转移到课堂上，向学生介绍量子力学和量子计算的一些基础知识，并让他们接触到量子凝聚态物理的桌面发现，如超导、超流、激光冷却和玻色凝聚。该课程旨在向那些只接受过最少培训的人介绍量子现象，只有高中的科学和数学课程。这种方法将允许来自不同学术背景和兴趣的学生在职业生涯早期接触到凝聚态物理和量子现象的兴奋。技术摘要本项目专注于电子相的研究，其中电子之间的相互作用和波函数的拓扑必须在平等的基础上处理。这些都是量子霍尔铁磁相，其中电子的谷自由度使得拓扑量子霍尔态在电子之间的交换作用的驱动下也表现出破缺的对称性。为了实现其目标，该程序利用扫描隧道显微镜(STM)的高能量和空间分辨率光谱映射的能力，不仅可以在真实空间中可视化山谷量子霍尔铁磁体，还可以探测它们的拓扑边界模式，并通过改变它们的载流子密度或使用应变以及与超导和磁体的接近来调整它们的性质。在本程序中，我们研究了在不同量子霍尔谷相之间的拓扑边界上形成的一种新的一维相互作用的Luttinger液体。此外，该程序还探索了低载流子浓度下的相互作用物理，以驱动STM可访问的电子系统(铋和其他表面态)中的条形、气泡或分数量子霍尔相，并首次可视化了这些相。还研究了特殊杂化结构中量子霍尔谷极化相与超导电性的相互作用。这些工作将探索当传统超导体的涡旋晶格与具有强自旋轨道耦合的二维(2D)电子气在量子化朗道能级(LL)存在下耦合时，Majoranas的“晶格”和拓扑超导可能出现的方式。我们将探索一些不同的材料，以将我们可视化朗道波函数的能力扩展到其他2D系统。该计划将汇集广泛的实验、新颖的材料创造和薄膜结构，以实现拓扑电子相和相关的新现象，这些现象可以使用扫描隧道显微镜直接以高空间和能量分辨率进行研究。这项研究是通过由首席研究员和他的研究团队设计和建造的高分辨率STM仪器实现的。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。

Non-technical AbstractResearch on topological phases has connection to both concepts in quantum field theory and proposed approaches for creation of fault tolerant quantum computers. The idea that low energy, emergent quasiparticles in condensed matter systems can provide a laboratory to test field theory concepts follows the long tradition of generalizing concepts in physics across energy and length scales. Equally important to the study of topological materials, topological phases and associated emergent quasiparticles may well provide fundamental new approaches to electronics. For example, valley degree of freedom for electronic wavefunction in solids, a property examined here, is a feature that has been proposed to create new types of electronic devices. The graduate and undergraduate students trained on this project are learning state-of-the-art scanning probe microscopy, cryogenics, and materials physics experimental techniques that are of strong interest to both industry and academia. Lab research is being moved into the classroom with the development of a Princeton freshman seminar course introducing students to some basics of quantum mechanics, quantum computing, and exposing them to 'tabletop' discoveries in quantum condensed matter physics such as superconductivity, superfluidity, laser cooling and Bose condensation. The course is designed to introduce quantum phenomena to those with minimal training, with only high school courses in science and math. This approach will allow students from various academic backgrounds and interests to be exposed to the excitement of condensed matter physics and quantum phenomena early in their career.Technical AbstractThis project is focused on the study of electronic phases in which interaction between electrons and topology of their wavefunctions must be treated on equal footing. These are quantum Hall ferromagnetic phases in which electrons' valley degree of freedom makes the topological quantum Hall states also display broken symmetry driven by the exchange interaction between electrons. To accomplish its goals, the program brings the power of high energy and spatial resolution spectroscopic mapping with a scanning tunneling microscope (STM) to not only visualize valley quantum Hall ferromagnets in real space, but also to probe their topological boundary modes and to tune their properties by changing their carrier density, or using strain, and proximity with superconductors and magnets. A new class of interacting 1D Luttinger liquids that form at the topological boundary between different quantum Hall valley phases is examined during this program. In addition, the program explores the physics of interactions at low carrier concentrations to drive stripe, bubble, or fractional quantum Hall phases in an electronic system (Bi and other surface states) accessible to STM, and visualize these phases for the first time. The interplay between quantum Hall valley-polarized phases with superconductivity in special hybrid structures are also studied. These efforts will explore ways in which Majoranas' "lattices" and topological superconductivity may emerge when a vortex lattice from a conventional superconductor is coupled with a two-dimensional (2D) electron gas with strong spin-orbit coupling in the presence of a quantized Landau level (LL). A number of different materials will be explored to extend our ability to visualize Landau wavefunction to other 2D systems. The program will bring together a wide range of experiments, novel creation of materials and thin film structures to realize topological electronic phases and associated novel phenomena that can be directly studied with high spatial and energy resolution using the STM. The research is made possible by high-resolution STM instrumentation that have been designed and constructed by the principal investigator and his research team.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.