The goal of this NSF program is to study the local electromagnetic properties of strongly interacting electron systems using scanning microwave impedance microscopy. These materials have inherent tendency towards inhomogentiy, making local study highly informative and necessary. Near-field microwave impedance microscopy (MIM) is a novel technique to address this problem. The local dielectric response to electromagnetic waves represents the collective behavior of the electronic system and measures the two-particle correlation functions, complementary to the information obtained by tools sensitive to single particle behavior such as STM. A novel cryogenic variable-temperature (2-300K) MIM equipped with a 9T magnet has been developed and will be used for this study. The combined strength of high resolution microwave imaging (currently at 100 nm, with a plan to further improve) and low-T/high-B environment will enable the visualization of many interesting physical processes, such as metal-insulator transition, phase changing process, regional superconductivity, and multiferroics. Because of the relative ease of operation, the experience of nanoscale electrical imaging is also of pedagogical importance to the undergraduate, graduate students and postdoc in the project.
The goal of this NSF program is to study the local electromagnetic properties of strongly interacting electron systems using scanning microwave impedance microscopy. These materials have great technological potential but are not well understood largely due to inherent tendency towards inhomogentiy, making local study highly informative and necessary. A novel cryogenic variable-temperature (2-300K) near-field microwave impedance microscope equipped with a 9Tesla magnet has been developed and will be used for this study. The combined strength of high resolution microwave imaging and low-T/high-B environment will enable insights not possible to obtain by other means. This tool will be very useful for other fields and for education. Because of the relative ease of operation, the experience of nanoscale electrical imaging is also of pedagogical importance to the undergraduate, graduate students and postdoc in the project.
This NSF program is intended to investigate the nanoscale electromagnetic properties of complex materials using a novel scanning microwave impedance microscope (MIM). Complex quantum materials are important models systems with intellectual implications far beyond these materials themselves. At the same time, these materials have the potential for a wide range of applications for our technological society today. Electromagnetic properties of these materials are among the most important and fundamental physical properties to be understood. During this program support period, important progress in understanding local electromagnetic properties has been achieved. As highlighted in the examples below, we can quantitatively analyze the colossal agnetoresistance effect in manganite thin films, and spatially resolve the quantum Hall edge channels. Magnetoresistance in Nd1/2Sr1/2MnO3 thin films1 Many unusual behaviors in complex oxides are deeply associated with the spontaneous emergence of microscopic phase separation. Depending on the underlying mechanism, the competing phases can form ordered or random patterns at vastly different length scales. When the long-range Coulomb interaction prevails, the competing phases cannot form micrometer-scale orders because of the large electrostatic energy penalty. Quenched disorders, on the other hand, introduce short-range potential fluctuations that result in large clusters with random shapes. In between these two scenarios, weak long-range interactions, such as the elastic strain in epitaxial thin films, may become the dominant factors for self-organized patterns with mesoscopic length scales. Visualization of these non-uniform states, including both the length scale and the ordering, will result in profound understanding on the complex material research. Simultaneous transport and microwave imaging data on two Nd1/2Sr1/2MnO3 (NSMO) thin films, one coherently grown on (110) SrTiO3 (STO) substrates (therefore strained) and the other relaxed, are shown in Fig. 1. The microscopic origin of colossal magnetoresistive (CMR) effect is clearly revealed. Compared with the global resistivity measurement, the impedance maps show much richer information of how the metallic domains emerge from the insulating background on these two samples. For the strained film, the conducting filaments align preferentially along certain crystal axes of the substrate, also shown by the auto-correlation analysis. The large period of the percolating network ~100nm and the orientational order suggest that the anisotropic elastic strain is the key interaction in this system. In contrast, the salient liquid-crystal-like metallic network is missing in the degraded film, again highlighting the importance of elastic strain. We emphasize that although phase coexistence and percolation transition have been confirmed by other experiments, our work shows the first unambiguous evidence of the orientation ordering and the mesoscopic length scale in the CMR effect. Local conductivity mapping of GaAs/AlGaAs quantum well in quantum Hall regime2 Two-dimensional electron gas (2DEG) is the host of many exotic phenomena including quantum Hall effect (QHE) and quantum spin Hall effect (QSHE). When a 2DEG sample is put in a magnetic field perpendicular to the 2DEG plane, the originally continuous electron bands are replaced by discrete Landau levels (LLs). When integral LLs are filled, electrons in the bulk are localized whereas the LLs bend near the edge and intersect with the Fermi energy, forming dissipationless edge channels which cause the Hall resistance to become exactly quantized and the longitudinal resistance to vanish. This phenomenon is known as QHE. In real experiments however, the distribution of conductivity in QHE regime can be very different from that predicted by the above simple physics picture due to electrostatic interactions. Such difference is hard to perceive by transport measurement and thus requires real space imaging. Using the microwave impedance microscope (MIM) we obtain a local conductivity map of GaAs/AlGaAs 2DEG in the QHE regime. In Fig. 2, we provide a global view of the real-space conductivity mapping of the edge and bulk states on a GaAs/AlGaAs 2DEG sample patterned into isolated dots. The sizes, positions, and field dependence of the metallic and insulating strips around the sample perimeter disagree qualitatively with the semi-classical picture, but agree quantitatively the self-consistent electrostatic picture. The local conductivity information yields a complete microscopic description of the evolution through the n = 2 quantum Hall state. Our results pave the way to study the microscopic details of other exotic physics in 2DEG, such as the fractional QHE and the stripe and bubble phases. References: [1] K. Lai, M. Nakamura, W. Kundhikanjana, M. Kawasaki, Y. Tokura, M. A. Kelly, and Z.-X. Shen, "Mesoscopic percolating resistance network in a strained manganite thin film", Science 329, 190 (2010). [2] K. Lai, W. Kundhikanjana, M.A. Kelly, Z.X. Shen, J. Shabani, and M. Shayegan, "Imaging of the Coulomb driven quantum Hall edge states", Phys. Rev. Lett. 107, 176809 (2011).
