This award supports theoretical research on new states of matter. The objective is to understand condensed-matter systems involving many strongly coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics. The electrons in such strongly correlated systems organize spontaneously in electronic liquid crystal phases and topological phases. This is a frontier area of research in which the understanding of some of the most fundamental problems in physics is achieved by experiments done at the cutting edge of technology. Electronic liquid crystal phases are states of matter in which strongly correlated electrons organize themselves in inhomogeneous and anisotropic patterns. They are closely related to mechanisms of high temperature superconductivity, a fundamental problem in physics which already has had a strong impact in technology. Topological phases are quantum fluid states of matter that do not have an order parameter, and therefore do not break any symmetry, but possess a kind of hidden quantum order in which the ground state degeneracy is determined by the topology of the space in which they live. The quantum states of a topological fluid are strongly entangled, a property that can be used to devise a topological quantum computer, a frontier problem in physics and mathematics having great potential impact on technology. Related topics that will be investigated include the relation between electronic liquid crystal phases and high temperature superconductivity, quantum coherence and interference phenomena in quantum Hall systems, quantum entanglement and topological quantum computing. The nature of the problems the PI studies requires the use of the methods and ideas of quantum field theory. These are the best tools with which to attack problems involving the statistical and quantum physics of strongly interacting systems. Such an approach enables the project to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems, high energy physics, and mathematics.
NON-TECHNICAL SUMMARY: This award supports theoretical research that aims to predict new states of matter and to develop fundamental understanding of their novel properties. The emphasis of the research will be on states of matter that emerge from electrons that interact strongly with each other and are confined to two dimensions.
One focus of the research is on exciting states of matter that are theoretically predicted to exist in a sheet of electrons in a strong magnetic field perpendicular to the sheet. These conditions can be realized in special semiconductor structures. The states of matter, called topological states, have yet to be confirmed experimentally. A challenge of the research is to propose experiments that can unambiguously detect them and to understand their properties. Understanding how these states of matter can be controlled may lead to a new kind of computer that depends on the purposeful manipulation of quantum mechanical states for its operation and would be able to carry out certain calculations much more rapidly than current computers.
Another focus of the research is to further understand new quantum mechanical states of electrons that have been proposed by the PI and collaborators. The electrons in these states organize themselves in a way so that they can flow like a liquid but exhibit patterns of orientation and symmetry that are reminiscent of the way atoms are arranged in a solid. Recent experiments support the existence these states which are proposed to play an important role in understanding the high temperature superconductors.
The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientist. It also opens new possibilities for future technologies.
During the lifetime of this grant we have made significant progress in the theory of high temperature superconductivity and topological phases in condensed matter. The problem of high temperature superconductivity is one of the most challenging open questions in condensed matter physics. It is an important problem both conceptually as well as for its potential applications. Fradkin (the PI) proposed back in 1998 that the key to the understanding of this problem is the inherent tendency of strongly interacting electronic systems to form spatially inhomogeneous and/or anisotropic states of matter which we dubbed `electronic liquid crystal phases'. Experimental work done in the past decade has validated this theoretical prediction by detecting at least two of these phases: the stripe and the nematic phase in several high temperature superconductors (as well as in other strongly correlated materials). An important open question is the connection between these novel states of quantum matter and high temperature superconductivity itself. A hint has been provided by experiments done in the past five years in La2-xBaxCuO4 (in which high temperature superconductivity was discovered in 1986) for the special value of the electronic density at `doping' x~1/8 where it is seen to have charge and spin `stripes': static unidirectional modulation of the charge and spin degrees of freedom. In this regime the superconducting critical temperature is seen to be suppressed down to 4K. However up to temperatures of 30K this material appears to behave as a stack of superconducting layers (made of copper and oxygen) which are decoupled from each other. We conjectured that the layer decoupling effect implies that the superconductivity in the layers is itself striped (or modulated), and that in these strongly correlated systems charge, spin and superconducting ordered are intertwined with each other with all three orders having comparable strength. This pair-density-wave superconducting state is the key to the connection between electronic inhomogeneity and high temperature superconductivity, and that the concept of {em intertwined orders} holds the key to the solution of this class of problems. We have also made significant progress in the microscopic mechanism that gives rise to the pair-density-wave state, and a theory of its thermal melting by the topological excitations of the intertwined orders. Topological phases of matter are states of electrons and spins in which no symmetries appear to be broken. Yet, the properties of these two-dimensional quantum fluids depend on the topology of the surface on which they live. In addition the excitations (or vortices) of these fluids carry a fraction of the charge of the electron and also exhibit a property known as fractional statistics. These exotic states of quantum matter have been proposed as a possible setting for topological quantum computing. A key feature of these topological fluids is the large scale quantum entanglement of the ground state wave function (which means that the individual degrees of freedom have information about the behavior of others very far away). PI Fradkin has worked on the theory of topological phases in condensed matter since 1991. My early work in gauge theory (in the late 1970's) has become a key conceptual framework for the current efforts to understand these intriguing states of quantum matter. During this past funding period we have developed a theory of large scale quantum entanglement. We showed that both in topological phases and at quantum critical points the entanglement entropy has universal properties which characterize the topological state and the quantum critical point. We also developed a theory the connection between local measurements and the growth on entanglement, and of the use of entanglement as a way to characterize disordered quantum systems.
