Electrons are fundamental particles that carry a quantum of charge, e, and a quantum of angular momentum, 1/2. The angular momentum is usually called spin because it is intrinsic to the electron rather than being dependent on the external center-of-mass motion of the electron. Electrons are a type of particle called a fermion, meaning that two electrons cannot occupy the same quantum state, according to the Pauli exclusion principle. Electrons have a very small mass compared to protons, which means that it is easier for us to access the quantum-mechanical wave-like nature of electrons. Although even the existence of electrons was unknown for most of human history, we now manipulate them routinely and easily during the course of our everyday lives. The ability to manipulate electrons, particularly electrons in electronic materials such as semiconductors, was essential for the communication and information revolution of the past century.
The goal of my research is to answer two questions about the fundamental behavior of electrons in materials. First, how does quantum decoherence occur? Electrons in atoms and electrons in many nanodevices behave quantum-mechanically; that is, their wave-like nature is apparent. What processes, specifically, causes electrons in materials to lose their wave-like nature at temperatures of more than a few degrees above absolute zero and length scales above many nanometers? Second, what is the correct theoretical description of strongly correlated electron materials? The theory of semiconductors was a great achievement, and we have not yet made a similar breakthrough to describe electrons in so-called strongly correlated materials. In strongly correlated electron systems, the behavior of each electron is greatly influenced by what all the other electrons are doing. The theory of strongly correlated electron systems is particularly intractable when the electrons are acting quantum-mechanically, and so the solution of these problem may ultimately require a detailed understanding of the decoherence processes that are not yet fully understood even in relatively simple model systems.
The experimental strategy of my research program is based on the premise that collective electron effects often create magnetic signatures on mesoscopic length scales, length scales that are small compared to the size of the sample but large compared to a single atom. Under carefully chosen conditions, these magnetic signatures can tell us about the mechanisms of quantum decoherence in electronic materials, and the correct theoretical description of strongly correlated electron systems in reduced dimensions. Using modern nanofabrication techniques on unconventional materials, my students and I are designing and fabricating specialized magnetic probes for experiments to help resolve these two problems. With the specialized probes that we develop, we make sensitive, quantitative, high-resolution images of the local magnetic field in the materials that we study. The local imaging capability is important because the most fundamental effects are those that occur on natural length scales associated with many electrons. These length scales are usually large compared to the size of an atom, but small compared to the size of a typical sample or device. Local measurements are also important for the less glamorous reason that many materials are inhomogeneous, simply because society cannot afford to devote a huge effort to optimizing every interesting material. Making local magnetic measurements is unusual because the signals are so small, but I believe that work during the past few years has begun to demonstrate the usefulness of local probes for basic condensed matter studies.
To study quantum coherence, we have developed a unique very-low-temperature scanning SQUID (Superconducting QUantum Interference Device) microscope to look specifically for magnetic signals created by long-lived currents that result from the wave-like nature of the electrons. Studying quantum coherence through magnetic measurements is an unusual approach. It is more common to make sensitive electrical measurements than to make sensitive magnetic measurements. Most mesoscopic measurements are electrical, so they involve connecting leads to the sample. Magnetic measurements have the advantage that they can be less invasive, or at least perturb the sample differently. They have the disadvantage that the magnetic signals associated with the electronic states are very weak, so the measurements are highly demanding.
To study strongly correlated electron systems, we are making a thorough investigation of individual magnetic flux quanta in high-temperature superconductors. High-temperature superconductivity is arguably the most dramatic and yet poorly understood phenomenon in strong correlated electron systems. One elegant idea for the mechanism of superconductivity is the hypothesis of spin-charge separation, also called fractionalization. Spin-charge separation is the idea that, in strongly correlated electron systems, electrons break up into two types of separate excitations, one of which carries spin and one of which carries charge. The charge-carrying excitations are thereby freed from their fermionic nature, allowing them to superconduct. Much of my effort over the past five years has been devoted to testing this specific hypothesis. So far, unfortunately, we have ruled out two attractive versions of this hypothesis. Nevertheless, the quantization of magnetic flux is one of the most striking features of superconductivity, and I believe that a systematic characterization of the dynamics, structure, and energetics of individual flux quanta will provide clues to the nature of strongly correlated electron systems.
My general goals for the next five years are 1) to create a toolbox of sensitive, quantitative, high-resolution local magnetic sensors, enabling routine and noninvasive characterization of small magnetic fields in novel quantum materials, and to share the designs for these tools with other scientists; 2) to conduct a systematic survey of the energetics and dynamics of individual quanta of magnetic flux in various superconductors, to elucidate the mechanism of superconductivity; 3) to design and execute a set of experiments that will conclusively test the hypothesis of spin-charge separation in strongly correlated electron systems in two dimensions; 4) to conduct a systematic survey of persistent currents in mesoscopic normal metals and superconductors, to understand the mechanisms of quantum decoherence in electronic systems and 5) to educate a set of creative and highly skilled graduate and undergraduate students.
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