Condensed Matter Systems with Emergent Gauge Fields

Princeton University, Princeton NJ

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education on condensed matter systems with ordering that is characterized by emergent gauge fields instead of emergent local order parameters. Such systems are said to exhibit topological or fractionalized phases of matter. This study is interesting for three reasons. First, the ordering in these systems takes us beyond the broken symmetry paradigm articulated by Landau. Second, there are at least some laboratory systems that unambiguously exhibit this ordering. Third, some members of this class of phases are potentially useful in the context of quantum computation. This award supports work that will range over all three above motivations: the general theory of topological/fractionalized phases will be developed further, two experimental systems will be the objects of detailed study and the effort in one of these will be directed at a phase germane to the quantum computation effort. The first system studied will be the so-called "spin ice" system which exhibits a macroscopic ground state entropy and excitations which are condensed matter analogs of magnetic monopoles. The challenges here include obtaining an understanding of their low temperature dynamical response, finding ways of directly observing the monopoles and understanding a remarkable recent experiment on a "magnetic Wien effect" which appears to have measured their magnetic charge. The second system to be studied is the venerable but still youthful quantum Hall system. The effort here will focus half on double valley systems with anisotropic mass pockets which are active objects of experimental study. It turns out they can exhibit a combination of a spontaneous breaking of spatial rotational invariance or nematicity and a breaking of an Ising pseudospin rotational invariance associated with the valley degrees of freedom. The implications of this possibility for their phase diagram will be explored in depth. The other half of the effort will involve the paired, non-abelian phase capable of hosting quantum computation which is believed to exist at half filling in the second Landau level. Here it is proposed to explore the idea that there is a proximity effect between this paired phase and the metallic phase also known to exist in a half filled Landau level. Such a proximity effect bids fair to fundamentally modify the response of the Pfaffian state to disorder. In addition to these above systems, the balance of the effort will be directed towards more theoretically motivated questions. These include the formulation of a "line tension" diagnostic for topological order, the prospects for irrationally charged excitations in topological phases and a study of specific Hamiltonians for frustrated magnets which are believed to host topologically ordered spin liquid phases. This award supports the training of a graduate student who will take part in this work and the exposure of undergraduates to ideas in this field as part of their research experience. NONTECHNICAL SUMMARY This award supports theoretical research and education on new electronic states of matter in materials and new kinds of transformations that can take place among them. A fundamental frontier activity in the physics of condensed matter is the identification and analysis of new phases of matter. Most such phases historically were understood as examples of spontaneously broken symmetries, where the microscopic entities arrange themselves in particular static patterns that are less symmetric than the underlying forces between them. More recently, it has become clear that matter can exhibit a different family of phases where the symmetry remains unchanged but instead the constituents arrange themselves into fluctuating arrays of loops or more complex geometrical arrangements. Such phases also exhibit the phenomenon of fractionalization wherein their excitations manage to carry fractions of the quantum numbers, such as electrical charge, of the microscopic entities, such as electrons. The study of such actual and potential phases is interesting for their intellectual challenge, to help make sense of an increasing set of laboratory realizations, and most recently, because a set of them have the potential to serve as a basis for the construction of a quantum computer which operates through the manipulation of quantum mechanical states. Such a computer can in principle be many times faster than the fastest supercomputers for certain algorithms. This award supports fundamental theoretical research to advance the general theory of the so-called "topological phases". Two experimental systems will be the objects of detailed study and the effort in one of these will be directed at a phase germane to the quantum computation effort. The first system studied will be the so-called "spin ice" system which exhibits excitations which are condensed matter analogs of magnetic monopoles, independently moving north and south poles of a magnet. The second system to be studied is the venerable but still youthful quantum Hall system which is a potential candidate for hosting a topological quantum computer. Quantum Hall states emerge in a gas of electrons confined to two dimensions in artificial semiconductor materials and exposed to a magnetic field. This award supports the training of a graduate student who will take part in this work and the exposure of undergraduates to ideas in this field as part of their research experience.