This award supports theoretical research and education on spin ordering and transport in correlated electronic and atomic systems. The PI will investigate problems in the collective spin physics of correlated electron materials and Bose-Einstein condensates of atoms with nonzero spin.
The research is divided into three subfields: spin transport phenomena related to the new class of materials called ''topological insulators''; quantum effects on the phase ordering and coherent dynamics of spinor Bose condensates; applications of quantum information ideas to improved characterization and simulation of frustrated magnets. In each of these subfields, the research builds on the PI?s work performed under prior NSF support. The key elements in the first research area are to understand how correlation physics is modified in a topological insulator and to describe three dimensional topological insulators in greater depth. In the second area, the PI studies effects of topological defects and dipolar interactions on the quantum theory of Bose condensates with spin, as these are believed to be essential for the interpretation of experiments. In the third area, the research tests specific proposals for DMRG-like algorithms in dimension greater than one on frustrated magnetic models of current experimental interest.
The work has broader impact beyond the specific research investigations including education and relevance to emerging device technologies. The work on spin transport in solids is currently of great interest in the applied semiconductor community, and devices using the quantum nature of electron spin are in development. The research is relevant to ideas of future use of spinor Bose condensates as ultrasensitive magnetic field detectors with spatial resolution finer than in the best existing devices with applications beyond MRI devices. Scientifically, improved algorithms to find ground states of local Hamiltonians are important in many areas of physics. This award has educational befits, the first being support of graduate students who will use the research as the basis for the Ph.D. Dissertation. The work influences the efforts of the PI in course development and undergraduate student research supervision within the university. With this award, the PI will continue development of on line educational materials with Lawrence Hall of Science as the major component of the outreach program, in conjunction with annual public lectures or panels for high school students.
NONTECHNICAL SUMMARY: This award supports research and education on the recently discovered phenomena of electrical signals that are not associated with moving electrical charges, but rather associated with the seeming intrinsic rotation or spin that electron possess and the way groups of electrons transfer spin spatially. The phenomena are not unrelated to magnetism which also is connected to the intrinsic electron spin. The phenomena have been observed, but the theoretical explanation is less clear and the research seeks to clarify physical mechanisms and thereby add to the ability to control and utilize the phenomenon in device technology. Eventually, this may be the basis of electronic logic devices that are orders of magnitude faster and more efficient that the current transistor technology based on charge movement and charge accumulation.
The work has broader impact beyond the specific research investigations including education and relevance to emerging device technologies. The work on spin transport in solids is currently of great interest in the applied semiconductor community, and devices using the quantum nature of electron spin are in development. The research is relevant to ideas of future use of spinor Bose condensates as ultrasensitive magnetic field detectors with spatial resolution finer than in the best existing devices with applications beyond MRI devices. Scientifically, improved algorithms are important in many areas of physics. This award has educational befits, the first being support of graduate students who will use the research as the basis for the Ph.D. Dissertation. The work influences the efforts of the PI in course development and undergraduate student research supervision within the university. With this award, the PI will continue development of on line educational materials with Lawrence Hall of Science as the major component of the outreach program, in conjunction with annual public lectures or panels for high school students.
This grant supported research on several problems in the basic science of novel materials. The primary use of funding was to support graduate students in conducting this research, which has the secondary benefit of contributing to the development of a highly educated US workforce. One key research result, developed with graduate students, postdoctoral researchers, and Prof. David Vanderbilt (Rutgers), is a theory for how the motion of electrons in a solid contributes to the "magnetoelectric effect": when many solids are placed in an electric field, the solid generates a magnetic moment, and conversely a magnetic field generates an electrical moment. This basic effect in solid state physics has been measured for several decades and has potential applications but was never theoretically understood; our approach gives ideas for how to make materials with faster and more reliable magnetoelectric effects that could be useful in electrical engineering. Another development was an approach to the description in a computer of the very complicated quantum-mechanical states that arise when electrons in a solid are not independent particles but rather are "correlated". Ideas that were originally developed either in the early days of quantum mechanics, such as entanglement, or in the context of trying to build a quantum computer turn out to be very helpful for the simulation of quantum systems with present-day computers. We extended the validity of one class of numerical methods by developing a theory of "finite-entanglement scaling". Entanglement is a measure of how quantum the correlations in a system of particles are, and states with a large amount of entanglement are difficult to represent accurately on a classical computer. Our theory describes quantitatively how the approximate description of physical quantities becomes more accurate as larger and larger amounts of computer memory are used to describe the quantum state. The PI developed, with Prof. Joseph Orenstein, a theory of how light striking a very clean quantum well (a system in which electrons move almost freely in two dimensions but are confined in the third) produces a photocurrent whose direction depends on whether the light is right circularly or left circularly polarized. This circular photogalvanic effect has been seen in experiments for about a decade, but we believe that the mechanism for those observations was not correctly understood, and our theory makes a number of testable predictions that we hope will be confirmed in current experiments. In addition to conducting research on existing materials, including the topological insulators (materials that are insulating in bulk but have atomically thin conducting surfaces) that were the focus of a previous period of the grant, the PI and collaborators proposed several new classes of topological materials, including the Hopf insulator and topological antiferromagnetic insulator. These are examples of ``symmetry-protected topological order,'' in which the symmetries of a particular crystalline solid lead to an unusual phase of the electrons. Topological insulators require only time-reversal symmetry. If one adds additional crystalline symmetries, one can obtain a variety of possible phases that are less protected from disorder than the original topological insulator but should have clear signatures in sufficiently clean samples. An important case is the ``antiferromagnetic topological insulator'', introduced by the PI and students Roger Mong and Andrew Essin: in this phase time-reversal is broken but there is symmetry under the combination of time-reversal symmetry and a lattice translation. This type of symmetry is quite common in antiferromagnetic materials, and in the nontrivial topological case there are unusual surface states that result. Some surfaces are gapless and similar to those of the usual topological insulator, albeit less robust to disorder, while others are gapped but have 1D conducting edge channels at step edges, which should be observable via scanning tunneling microscopy measurements. The alloy GdPtBi was proposed as an example, and there are experiments under way at Iowa State/Ames seeking to observe the surface state. The PI wrote two full-length technical reviews, and an invited mini-review on "The birth of topological insulators" for Nature has become a common reference for people new to the field. The NSF grant enabled the PI to supervise the Ph.D.s of Andrew Essin (now a postdoc at Colorado) and Vasudha Shivamoggi (now postdoc at Illinois). Three undergraduates were supervised in summer projects by the PI: Chayut Thanapirom, Yun Liu, and Yasaman Bahri. As part of the outreach component, the PI wrote a number of commentaries and popular articles. The PI wrote a popular article on topological insulators for IEEE Spectrum and another (with C. Kane) for Physics World. The PI gave an invited general-audience lecture at the 2011 APS March Meeting ``Trends'' session and another at the 2012 IEEE Aerospace conference.
