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

Stanford University, Stanford CA

Investigators

Abstract

****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.