Quantum Dots as an Experimental Basis for Studying Well-defined Many-Body Hamiltonians and Quantum Phase Transitions

****非技术摘要****现代技术依赖于理解材料电子特性的能力。为了达到这个目的，物理学家们发展了一些理论，在这些理论中，单个的组件，比如电子被束缚的位置，彼此相互作用。完全测试一个理论的预测可能是困难的，因为材料参数不是单独可调的。该奖项支持遵循替代方法的项目。众所周知的半导体材料和先进的图像化技术用于构建纳米级位点或？量子点吗?它能捕获电子。这种方法的最大优点是，理论参数，如被困在点中的电子与材料中的电子库相互作用的能力，可以通过电子方式控制。该项目利用这种控制来驱动电子的剧烈变化。的行为。通常，人们认为电子是独立运动的，就像它们在铜线中流动一样。相比之下，量子点结构可以调整，使电子表现为一个集体实体。这种变化类似于水到冰的转变，只不过它不是由温度而是由量子涨落引起的。量子涨落的影响比它们的经典对应物温度涨落要少得多。该项目的目标是观察这种量子相变，并定量测试试图解释这些现象的现有理论。该项目将培养学生和博士后在先进的物理理论、半导体加工技能和精密测量技术方面的能力，为他们在学术界或工业界的前沿职业生涯做好准备。****技术摘要****相关电子物理领域的一个关键挑战是找到一个与相互作用的多体哈密顿量相对应的实验系统，并允许对哈密顿量的参数进行精细控制。该奖项支持一个项目，该项目将通过使用充分理解的AlGaAs/GaAs异质结构和先进的图图化技术来制造门控纳米结构，从而迎接挑战。在这些结构中，被称为量子点的小电子液滴与剩余的电子储存库隔离开来。我们感兴趣的两个汉密尔顿尔顿是双通道近藤尔顿和双杂质近藤汉密尔顿尔顿。在双通道近藤系统中，两个独立的离域电子库相互竞争，以筛选束缚在局域位置（量子点）的电子自旋。在双杂质近藤哈密顿量中，一个电子库和一个定域点上的自旋相互竞争，以屏蔽第二个定域点上的另一个自旋。使用门控量子点的优点是可以精确测量点间相互作用和点-库隧穿速率等参数并进行静电调谐。这个项目将利用这种控制来驱动费米液体和非费米液体状态之间的量子相变。目标是调整到非常敏感的量子临界点，并定量测试高度相关的非费米液态如何在相关扰动（如磁场和交换耦合）的影响下演变成更传统的费米液态的理论预测。该项目将为学生和博士后在先进的多体理论、半导体加工技能和精密测量技术方面提供宝贵的培训，为他们在学术界或工业界的前沿职业生涯做好准备。

****NON-TECHNICAL ABSTRACT****Modern technology relies on the ability to understand the electronic properties of materials. Toward this end, physicists develop theories in which individual components, such as a site where electrons are bound, interact with each other. Fully testing the predictions of a theory can be difficult, because material parameters are not individually tunable. This award supports a project that follows an alternative approach. Well-understood semiconductor materials and advanced patterning techniques are used to build nanoscale sites or ?quantum dots? that trap electrons. The great advantage to this approach is that parameters of the theory, such as the ability for the trapped electron in the dot to interact with the reservoir of electrons in the material, can be controlled electronically. The project uses this control to drive a drastic change in the electrons? behavior. Usually, one thinks of electrons acting independently, as they do when flowing through a copper wire. In contrast, the quantum dot structure can be tuned so that the electrons behave as a collective entity. This change is analogous to the transition from water to ice, except that it is not caused by temperature but by quantum fluctuations. The effect of quantum fluctuations is much less understood than their classical counterpart, temperature fluctuations. The goal of this project is to observe this quantum phase transition and quantitatively test current theories that seek to explain these phenomena. This project will train students and post-docs in advanced physical theories, semiconductor processing skills, and precision measurement techniques that will prepare them for cutting-edge careers in academia or industry.****TECHNICAL ABSTRACT****A crucial challenge in the field of correlated electron physics is to find an experimental system that corresponds to an interacting many-body Hamiltonian and allows fine control over the parameters of the Hamiltonian. This award supports a project that will meet the challenge by using well-understood AlGaAs/GaAs heterostructures and advanced patterning techniques to fabricate gated nano-structures. In these structures, small droplets of electrons called quantum dots are isolated from the remaining electron reservoirs. The two Hamiltonians of interest are the two-channel Kondo and the two-impurity Kondo Hamiltonians. In the two-channel Kondo system two independent reservoirs of delocalized electrons compete to screen an electron spin bound to the localized site (a quantum dot). In the two-impurity Kondo Hamiltonian an electron reservoir and a spin on a localized site compete to screen another spin on a second localized site. The advantage of using gated quantum dots is that parameters such as inter-dot interactions and dot-reservoir tunneling rates can be precisely measured and electrostatically tuned. This project will utilize this control to drive a quantum phase transition between a Fermi liquid and a non-Fermi liquid state. The goal is to tune to the very sensitive quantum critical point and quantitatively test theoretical predictions of how the highly-correlated non-Fermi liquid state evolves into the more conventional Fermi liquid state under the influence of relevant perturbations such as magnetic field and exchange coupling. This project will provide valuable training to students and post-docs in advanced many-body theories, semiconductor processing skills, and precision measurement techniques that will prepare them for cutting-edge careers in academia or industry.