1. Metal-Insulator Transition via Spatially Heterogeneous State Jongsoo Yoon, University of Virginia, DMR 0239450 Differential resistance (dV/dI) of a 5nm think Ta film near the B-induced metal-insulator transition is shown. In the low field metallic phase, isolated insulating puddles exist in the background of the metallic region (top right panel) and d 2 V/dI 2 > 0 at all currents. At B ≳ B c (pink traces) the sign of d 2 V/dI 2 changes with increasing bias current because of narrow insulating gaps in the current flow path (dashed line, middle panel). At B >> B c, where isolated puddles of metallic phase exist in the background of the insulating region (bottom panel), d 2 V/dI 2 < 0 at all currents (red traces). Homogeneously disordered 2D superconductors in the zero temperature limit are known to become insulators under sufficiently high magnetic fields (B). However, the nature of the B-induced transition into the insulating phase, particularly the origin of the accompanying single parameter scaling behavior, has been controversial. While some argue that the scaling is due to a percolation-type transition involving a heterogeneous state, others interpret the scaling arising from the Cooper pair-vortex duality proposed in “dirty boson” model. We found evidence for the heterogeneous state by studying intrinsic nonlinear transport properties near the transition [1]. In the low field conducting phase (blue traces), the transport is characterized by d 2 V/dI 2 > 0 at all bias current, and in the high field insulating phase (red traces) d 2 V/dI 2 0). This is an evidence for a heterogeneous state [2]. At B < B c the system is mostly in the conducting phase with puddles of isolated insulating regions (top panel in the right column). With increasing B to just above B c, the conducting phase regions shrink, and eventually break into domains connected by narrow insulating gaps (yellow circle, middle panel). At low currents the transport is dominated by the insulating gaps because they act as bottlenecks for the transport. With increasing current, the insulating gaps become less resistive and the conducting regions become more resistive because of their contrasting nonlinear transport properties. The conducting regions start to dominate the transport at current (marked by arrows) where the narrow insulating gaps no longer act as bottlenecks. [1] Phys. Rev. Lett. 97, 057005 (2006). [2] Phys. Rev. B 74, 100507(R) (2006).

2. Jongsoo Yoon, University of Virginia, DMR 0239450 This research is lead by a post doc (Carlos Vicente) and a graduate student (Yongguang Qin). Two undergraduate students participated in the research. Carlos Vicente: after completion of the project, he moved to the University of Puerto Rico as an assistant professor. Yongguang Qin: graduated with a Ph.D. degree, and currently looking for a post-doc position in academia. Brian Gross (undergraduate): He is currently at the Havard Law School. Chester Rubbo (undergraduate): Currently in the PhD (physics) program at the University of Colorado. Education Two-dimensional electronic systems are the foundation of current science and technology because most of the modern and future-oriented devices are made in thin film form. Conventional theories for the 2D electronics physics have provided the framework to understand the principles and mechanisms of various phenomena that are unique to the electrons confined in a 2D geometry. The results of our research provide an unambiguous answer to an outstanding issue regarding the framework to understand the behavior of electronics in 2D. The impact of this will reach far beyond physics community, and influence modern and future science, engineering, and industry. Broader Impact Metal-Insulator Transition via Spatially Heterogeneous State