This award made on a collaborative proposal supports theoretical research and education to investigate the electronic properties of condensed matter systems at very low temperatures, with particular emphasis on universal properties that do not depend on the details of the materials in question. In particular, the PI will further explore analogies between "soft" condensed matter and "hard" condensed matter that have proven to be productive in the PIs' recent work on helimagnets and promise to provide additional insight into other materials of current interest. Problems to be studied include quantum analogs of liquid crystal states that are relevant for quantum hall systems and high-temperature superconductors, quantum phase transitions away from equilibrium, and spiral phases in ferromagnetic superconductors.
The PIs will also pursue two more additional problems: one involves the meaning of certain singularities in the screening of effective electron-electron interactions that are mediated by an exchange of bosons; the other, involves technical problems controlling the perturbative renormalization-group treatment of certain classes of quantum phase transitions.
This project will contribute to advancing our understanding of the basic electronic properties of solids, creating knowledge that is crucial as a basis for future technological innovation. It will train students and postdoctoral associates in an important and very broad research area, and thus contribute to the generation of human resources that are essential for our technologically oriented society.
NON-TECHNICAL SUMMARY This award supports collaborative theoretical research and education to uncover universal electronic properties of materials that appear at low temperatures. Universal properties transcend many of the details of specific materials, such as strength of interactions between electrons or electronic energy relations, and can connect seemingly different materials at a deeper level. The discovery of universal properties may signal the existence of a fundamental principle that provides a unifying understanding of seemingly different materials.
This project will contribute to advancing our understanding of the basic electronic properties of solids, creating knowledge that is crucial as a basis for future technological innovation. It will train students and postdoctoral associates in an important and very broad research area, and thus contribute to the generation of human resources that are essential for our technologically oriented society.
Basic research into the electronic properties of solids is important since it provides a basis for the future development of devices, some of which we cannot even imagine at this point. Examples from the past are the discovery of superconductivity, and the invention of the transistor. The former resulted from an investigation of the electric properties of materials at very low temperatures, and the latter from experimental and theoretical studies of the then-new semiconductors. Our research project continues on this path. It has investigated the properties of electrons in metals at low temperatures, with emphasis on collective behavior that results in magnetism or superconductivity. Helical magnets are a special class of materials in which the magnetization follows a spiral pattern, rather than a uniform pattern as in ordinary ferromagnets such as iron. A typical metallic helical magnet is magnesium silicide (MnSi). This material is of great interest from both a fundamental and an applied point of view. At low temperatures it displays a large number of different phases, and transitions between the phases. Some of these phases have extremely unusual properties that defy established theories of electrons in metals. For instance, in one of these phases, the electrical resistivity of MnSi shows a very unusual temperature dependence. This observation has defied understanding for many years. We have developed a theory that explains it in terms of the scattering of electrons off of the spiral excitations, or waves, in the magnetic texture of the material. The project has also led to a general understanding of the various phases, and their properties, in helical magnets and other low-temperature magnetic materials. Another aspect of the project has focused on unexpected similarities between liquid-crystal phases, which are the basis of the widely used LCD displays, and certain phases of electrons in metals. It turns out, surprisingly, that theoretical concepts developed in the well-understood field of liquid crystals are equally useful for certain problems involving electrons that are poorly understood. For instance, we have investigated a theoretical relation between liquid crystals and so-called stripe phases in high-temperature superconductors, where the electron density spontaneously arranges itself in a linear, or stripe, pattern. By making use of existing information about the undulations of stripes in liquid crystals, we have been able to calculate some of the properties of electronic stripe phases. These results help understand the very complex behavior of superconducting materials. A third aspect of the project involves concepts that are commonly used in research on magnets to gain a better understanding of metals without magnetic or superconducting order. We have found an analogy between nonmagnetic metals and models of magnets that have allowed us to establish exact theoretical results concerning the temperature dependence of the magnetic susceptibility and other important properties of metals. We have made predictions for properties of thin metallic films that can be measured by sophisticated experimental techniques, for instance, scanning-tunneling microscopy. In summary, the project has yielded new insights into the electronic properties of solids that contribute to a knowledge base that will be useful for future research and development, both fundamental and applied.
