Collaborative Research: One-Dimensional Correlated and Topological Electronic States in Ultra-Clean Carbon Nanotubes

非技术：通过将金属和半导体集成到电路中，人类已经学会了控制电子流动来处理信息。尽管在这一领域取得了巨大的成功，但仍有未解决的挑战。现有的控制电子流的方法产生不精确的电流水平，并且经常导致能量以热量的形式浪费掉。在这个项目中，该团队探索了一种控制电流的新方法，使用一种新颖的方法来泵送电子。该泵由一根碳纳米管构成，该碳纳米管与控制随时间变化的电场的微观结构相结合。预计该泵能输送电流而不耗散能量。它还被预测为从频率源产生精确电流的计量标准。此外，该系统揭示了关于相互作用电子行为的新知识，这在这种降维系统中是根本不同的。该项目培训学生，包括代表性不足的少数民族，并加强为科学和工程劳动力提供的渠道。面向少数族裔高中生的拓展活动包括一年一度的科学夏令营。技术：一维（1D）电子系统是自然相关的，而费米液体通常在更高的（二维和三维）形成。虽然拓扑顺序已经在二维和三维中得到了深入的研究，但在一维中却很少受到关注，其中拓扑和相关性的结合导致了迷人的可能性。在80年代早期，Thouless预测，当磁场被时变周期势取代时，在一维系统中会出现与量子霍尔效应相同的拓扑不变量。这个系统，被称为绝热电荷泵或索利斯泵，由于单电子充电和样品无序的问题，还没有在凝聚态物质中干净地实现。研究小组的初步结果证明了他们的长、悬浮、超清洁碳纳米管（CNTs）在实现Thouless泵和相关奇异现象方面的适用性。电子在一个长，超清洁碳纳米管形成要么维格纳晶体，卢廷格液体，或相关绝缘体状态。在周期势的作用下，系统可能演变为整数索利斯泵浦、分数索利斯泵浦、人工莫特绝缘体或其他奇异态。这个项目的重点是丰富的物理，可以发现，以及之间，这些奇异的状态。为了获取和控制各种现象，该团队将调整(i)碳纳米管中的电子密度，（ii）外部电位的波长，以及（iii）库仑相互作用强度（碳纳米管带隙的函数）。该项目的具体目标是：1。在没有外部周期势的碳纳米管系统中映射一维相关态的参数空间。2. 通过产生具有表面声波和精确倒装芯片几何形状的外部周期势来引入拓扑秩序。3. 研究一维中相关性和拓扑顺序的相互作用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Non-Technical: By integrating metals and semiconductors into circuits, humans have learned to control the flow of electrons to process information. Despite enormous successes in this field, there are still unsolved challenges. Existing methods to control electron flow produce imprecise levels of electrical current, and often lead to energy wasted as heat. In this project, the team explores a new way of controlling electric current using a novel method for pumping electrons. The pump is built from a single carbon nanotube that is integrated with a microscopic pattern of wires that controls a time-varying electric field. The pump is predicted to carry an electrical current without dissipation of energy. It is also predicted to be useful as a metrological standard for generating a precise current from a frequency source. Additionally, the system unravels new knowledge about the behavior of interacting electrons which is fundamentally different in such reduced-dimensional systems. The project trains students including under-represented minorities and strengthens the pipeline that feeds the science and engineering workforce. Outreach activities for high-school students from under-represented minorities include an annual science summer camp. Technical: One dimensional (1D) electronic systems are naturally correlated, in contrast to the Fermi liquids that usually form in higher (two and three) dimensions. While topological order has been studied intensely in 2D and 3D, it has received relatively little attention in 1D where the combination of topology and correlations leads to fascinating possibilities. In the early 80s, Thouless predicted that the same topological invariant as in the quantum Hall effect arises in 1D systems, when the magnetic field is replaced by a time-varying periodic potential. This system, known as an adiabatic charge pump or Thouless pump, has not been realized cleanly in condensed matter, due to problems of single-electron charging and sample disorder. The research team’s preliminary results demonstrate the suitability of their long, suspended, ultra-clean carbon nanotubes (CNTs) for realizing the Thouless pump, and related exotic phenomena. Electrons in a long, ultra-clean CNT form either a Wigner crystal, Luttinger liquid, or a correlated insulator state. Upon application of the periodic potential, the system may then evolve into an integer Thouless pump, a fractional Thouless pump, an artificial Mott insulator or other exotic states. This project focuses on the rich physics that can be found in, and between, these exotic states. To access and control the various phenomena, the team will tune (i) the electron density in the CNT, (ii) the wavelength of the external potential, and (iii) the Coulomb interaction strength (a function of CNT band gap). The specific aims of the project are: 1. Map the parameter space of 1D correlated states in the CNT system without an external periodic potential. 2. Introduce topological order by generating an external periodic potential with surface acoustic waves and a precision flip-chip geometry. 3. Study the interplay of correlations and topological order in 1D.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.