This award funds theoretical research and education on the electronic properties of low-dimensional condensed matter, where topological structure in the state of the system, or encoded directly in the Hamiltonian, induces novel behavior. The latter case can arise when the low-energy electron physics is controlled by a Dirac equation, of which an important example is that of graphene. The former is realized in systems that may be effectively described as a quantum magnet. The quantum Hall bilayer offers a unique environment to probe this physics because its topological structures carry physical charge, and it allows experimental probes that are not possible in other realizations. This project focuses on these two systems as paradigms for how topological structure and textures can affect electronic properties.
Graphene, a two-dimensional carbon network, is unusual among two-dimensional electron systems. In part this is a consequence of the fact that its electronic properties are controlled by a Dirac equation. An analogy may be drawn with quantum electrodynamics, in which Coulomb interactions compete with the kinetic energy to determine the physical behavior of the system. The ratio of these energy scales suggests that Coulomb interactions are relatively strong in pristine graphene, with important consequences both at short and long length scales. The research will focus on the consequences of this physics when disorder, doping, and fluctuations are included, to understand under what circumstances the effects of Coulomb interactions might be observed. The PI will also examine nanostructured graphene systems, where behaviors with no analog in conventional two dimensional electron systems occur. These include the creation of new Dirac points via an external potential, and "effective time-reversal symmetry breaking" as observed in quantum rings. The remarkable insulating behavior of undoped graphene in the quantum Hall regime will also be examined. The PI aims to better understand the effects of disorder, how they affect the state of the system, their consequences for edge states, and to examine recent analogous behavior seen in bilayer graphene.
Quantum Hall bilayers near filling factor 1 display a counterflow resistance that appears to vanish in the zero temperature limit, and a strong but finite resonance in tunneling conductance. The underlying state that allows such unusual behavior to emerge remains poorly understood, but is likely to involve disorder in an intimate way. The PI will examine what happens when large collections of textured defects, merons, are induced by a periodic potential as a first step in examining how their presence affects the coherence of the system in a realistic disorder potential. The PI will also consider the transition from a coherent bilayer to uncorrelated layers as they are separated, for a clean system. The approach adopts the thin cylinder limit as a starting point, for which fluctuations may be handled in a more complete way than is possible for an infinite two-dimensional system.
Graphene is an important candidate for new device technologies. This research contributes to it understanding and may enable applications. Graduate students will participate in this research project; they will be trained in modern methods for analyzing condensed matter systems, preparing them for careers in science and technology. This research will be performed in collaboration with scientists from the US and abroad, strengthening and enriching our own physics community.
NONTECHNICAL SUMMARY This award supports theoretical research and education into new electronic materials. Electronic materials play a crucial role in modern society, finding applications in computers, optics, telecommunications and more. As the demands for high speed and low power consumption increase over time, the need for new materials to meet these demands becomes ever-more more pressing. This project will explore the electronic physics of a new of class materials, possessing properties and behaviors with no analog in traditional semiconductors. A remarkable feature of some of these materials is that in an important sense their electrons behave as if they were moving at the speed of light leading to interesting phenomena. A paradigm for such systems is graphene, a two dimensional honeycomb network of carbon atoms with properties that make it attractive for device applications. The PI will use theoretical methods to study the basic electronic properties of graphene and to understand the similarities and differences between this system and its more conventional semiconductor cousins. The PI will also study how the electrons may organize themselves when the effects of interactions are taken into account. The possibility of observing new electronic states of matter which may have novel conduction and optical properties will be investigated.
The PI will also focus on effects of magnetic fields. A magnetic field can have many remarkable effects on the electronic properties of electrons confined to a plane, including measurable resistances that are fixed by the rules of quantum mechanics and fundamental constants that are independent of the properties of the material. Another striking effect occurs when two such planes are brought very close together: the electrons appear to organize themselves into a new state of matter that is reminiscent of superconductivity. Superconducting states display no resistance to the flow of electricity. The PI seeks to understand this new state of matter, how it arises, and how it differs from superconductivity.
Intellectual Merit: The research conducted in this project focused on condensed matter systems in which topology and/or texture leads to novel physical phenomena, predominantly in low-dimensional electron systems. Textures can occur, most often, in settings where electron states must be described by multi-component wavefunctions, and involve relative weights of these components varying in different ways depending on which direction one moves in within a space of parameters that label the states. If the wavefunctions support some non-trivial winding as this space is traversed, the state or system supports a non-trivial topology. These behaviors can be supported or induced in a variety of settings, including quantum Hall systems, topological insulators, and systems driven by a temporally periodic potential. We conducted theoretical research on all these systems, searching for signatures and consequences of these types of orderings. Periodically driven systems, known formally as Floquet systems, were studied in a concrete setting: graphene subject to circularly polarized light. It was discovered that transport in this system has clear signatures of non-trivial topology, both through conducting states at the edges and via anomalous transport through the bulk. Moreover the system may be driven through many different topological sectors. We found that these transitions have surprising behaviors – for example, conductivity in some cases may be greatly enhanced by disorder. Static topological systems were also studied. These included a model of iridate compounds, which we showed can be robustly pushed into a topological insulating state by placing them in contact with an insulated ferromagnet. Other related studies focused on theories of topological insulator surfaces, in which we developed a simple approach to modeling surfaces whose conduction properties could then be analyzed. Another set of studies focused on quantum Hall systems, in which electrons on a plane are subjected to a strong magnetic field. In some materials – particularly graphene – these can also support discrete degrees of freedom that lead to textures and topology. A number of projects focused on domain walls of such systems, both in a bilayer setting and at the edge of single layer. We found remarkable connections between the edge textures and topological excitations that are known to exist in the bulk of such systems. A great variety of states with diverse conduction properties emerge in such systems. Related to this was a set of studies of "twisted bilayer graphene," where the two layers are rotated, resulting in an intricate Moire pattern, whose electronic spectrum in a magnetic field should have extreme complexity due to competition between the geometric periodicity of the pattern and the effective length scale associated with the field. The evolution of this complexity with energy was studied in a semiclassical approach, and moreover its signatures in electromagnetic absorption spectra were analyzed. Finally, a variety of phenomena were explored in the electronic properties of graphene, including effects of interactions on the states of the electrons, how lattice vibrations display non-trivial signatures of these interactions, and the effects of shaping the graphene potential with electrostatics to fundamentally modify the electron states supported by the system. Broader Impact: The project involved and supported -- both directly and indirectly -- a number of activities with broader societal impacts. Students and postdocs were trained in the course of the work in modern methods of condensed matter physics, preparing them for careers in science and technology, which are areas of need for our nation. In addition a number of international collaborations deepened the contact between our own science communities and those overseas. Beyond this, the PI chaired a conference on graphene physics, at the Kavli Institute for Theoretical Physics in Santa Barbara, for high school teachers from around the nation. The conference helped them to appreciate some of the modern developments in electron physics, and presented material they could use to excite and motivate their own students. Finally, in collaboration with chemist Liang-shi Li, the PI undertook the creation of a new conference series on graphitic materials, under the umbrella of the Gordon Research Conferences. This highly multi-disciplinary conference brings together chemists, physicists, and engineers to learn from one another ways of thinking about these materials that one does not normally encounter within one’s own discipline, and ultimately provides a venue to develop new collaborations and contacts. The conference ran twice during the period of this project, and so far seems to be quite appreciated by this broad scientific and engineering community.
