Interacting States of Low Dimensional Electrons

About This Grant

NONTECHNICAL SUMMARY Quantum physics plays a determining role in the behavior of electrons in materials. Beyond the impact of the crystal lattice of atoms within which electrons move, the interactions among them help pick out particular collective electron states that determine a materials conduction, magnetic, and thermal properties. In principle, these states and their associated properties may be modified, manipulated, or probed by the coupling of the electrons to other degrees of freedom, such as a magnetic field. This project focuses on the properties of materials in which coupling to electromagnetic fields is important. This is particularly relevant due to the recent development of material structures that host electromagnetic modes –-essentially confined light/photons-- that can strongly couple to the electrons in a material. Both the photons and electrons have intrinsically quantum natures. Moreover, the mathematical descriptions of such systems involve geometric and topological properties of the quantum states themselves, which have profound implications for how the electronic states may evolve with time. This project will uncover novel physics that emerges when quantum cavity modes, electron-electron interactions, and quantum geometry and topology come together. The materials of focus are low-dimensional electron systems, which can be found in materials that can be thinned to single layers such as graphene, or may be created within semiconductor structures. The work will identify how strongly coupled photon fields modify the states and properties of the electrons, and, conversely, how the electrons impact the states and properties of the photons. Novel probes of the electron system via detection of the photons to which they are coupled will also be developed, with potential relevance for quantum information processing. In addition to elucidation of this novel physics, this project will have broader significance, by providing valuable training for young physicists in methods for analyzing quantum materials, helping them to participate in our nation's ever-evolving STEM economy. The PI will also mentor students in the IU Physics Department Bridge Program. Through the IU SynergySci program, K-12 outreach will be undertaken by partnering with high-school teachers, to develop lesson plans and activities that expose students to important themes in modern physics. TECHNICAL SUMMARY The specific systems to be investigated in this research will involve both van der Waals and semiconductor materials hosting two-dimensional electron gases, with and without magnetic fields. Part of the work will focus on semiconductor excitations known as excitons, in particular a quantum geometric dipole (QGD). The accompanying electric dipole moment changes with time when excitons are dynamical; the studies will focus on the implications of this for exciton modes with a band structure. Exciton transport models will be developed and used to understand how they may radiate into free space or couple to cavity modes. Situations where the excitons follow classical statistics or Bose-condense will be considered. Studies of transport properties, cavity photon statistics, and their correlations will be undertaken to learn what information they reveal about the internal structure and quantum geometry of low-lying excitations. An important focus of these studies will involve identifying situations where the QGD dynamics produces high harmonics of a fundamental frequency that can be detected in free radiation, or harvested when coupled to a cavity. A second set of studies will focus on quantum Hall systems coupled to a cavity, for which recent studies suggest the Hall conductivity may have its usual topological quantization weakened or even breached. The PI will consider edge state physics in such systems, using this to model coupling between electron reservoirs exterior to the cavity and current carrying states within the cavity, to develop a Buttiker-Landauer formulation for transport in these types of systems. Another thrust of the project will focus on collective modes when the system is in a waveguide or a cavity, to understand its thermal properties as well as transport activation gaps, which have shown surprising behaviors in experiment. The project will also consider the impact of a cavity on quantum Hall plateau transitions, and how cavities may modify coherent states such as those of a quantum Hall bilayer at or near integer filling factors. In addition to elucidation of this novel physics, this project will have broader significance, by providing valuable training for young physicists in methods for analyzing quantum materials, helping them to participate in our nation's ever-evolving STEM economy. The PI will also mentor students in the IU Physics Department Bridge Program. Through the IU SynergySci program, K-12 outreach will be undertaken by partnering with high-school teachers, to develop lesson plans and activities that expose students to important themes in modern physics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.