Metal-Insulator Quantum Phase Transitions

Metal or insulator - and why? To answer this simple question has been the goal and the driving force for much of the physical science as we know it today. Going back to Newton’s not-so-successful exercises in Alchemy, the scientist had tried to understand what controls the flow of electricity in metals and what prevents it in insulators. To understand it and to control it - achieving this could prove more useful and lucrative than converting lead into gold.

In almost every instance, these advances are based on materials that find themselves somewhere between metals and insulators. Material properties are easy to tune in this regime, where several possible ground states compete. Here most physical quantities display unusual behavior, and prove difficult to interpret using conventional ideas and approaches. In this regime, the electrons simply do not seem to be able to decide: move fast and conduct electricity or get stuck by impurities or inter-particle repulsion - leading to insulating behavior.

Strange properties of the "no-man's land" between metals and insulators can be understood as the Quantum Critical Regime of the metal-insulator transition. To come to grips with this unfamiliar regime, one has to develop conceptual understanding of the interplay of quantum fluctuations and strong electronic correlations on one hand, and the tendency to form strongly inhomogeneous states of matter and slow glassy dynamics on the other. This very difficult but fundamentally important task is the central goal of our theoretical work.

The fractal background pattern behind this Web page shows the distribution of currents in a Coulomb Glass - a Coulomb system in presence of moderate to strong disorder. Using JAVA simulations, we apply an external electric field and watch the electrons move. Here each electron is assigned a different color, and a "tracer" protocol is implemented, creating a colorful trace for each electron. In presence of disorder we observe very large "white" regions - domains where almost no current flows. Remarkably, the flow then assumes "filamentary" form, where the current paths form "rivers". The fractal shapes of these current flows reflect the critical ("marginally stable") nature of the Coulomb Glass.
             This is a green website. We are committed to conserve energy - we only use Baym-Kadanoff conserving approximations
This research is supported by
    NSF grant DMR-1005751