Doping a semiconductor to create an unconventional metal

Landau Fermi liquid theory, with its pivotal assertion that electrons in metals can be simply understood as independent particles with effective masses replacing the free electron mass, has been astonishingly successful. This is true despite the Coulomb interactions an electron experiences from the host crystal lattice, its defects, and the other ~1022/cm3 electrons. An important extension to the theory accounts for the behaviour of doped semiconductors1,2. Because little in the vast literature on materials contradicts Fermi liquid theory and its extensions, exceptions have attracted great attention, and they include the high temperature superconductors3, silicon-based field effect transistors which host two-dimensional metals4, and certain rare earth compounds at the threshold of magnetism5-8. The origin of the non-Fermi liquid behaviour in all of these systems remains controversial. Here we report that an entirely different and exceedingly simple class of materials - doped small gap semiconductors near a metal-insulator transition - can also display a non-Fermi liquid state. Remarkably, a modest magnetic field functions as a switch which restores the ordinary disordered Fermi liquid. Our data suggest that we have finally found a physical realization of the only mathematically rigourous route to a non-Fermi liquid, namely the 'undercompensated Kondo effect', where there are too few mobile electrons to compensate for the spins of unpaired electrons localized on impurity atoms9-12.Comment: 17 pages 4 figures supplemental information included with 2 figure

A new approach to the treatment of separatrix chaos and its applications

"Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935 - 2008)" covers the recent developments and advances in the theory and application of Hamiltonian chaos in nonlinear Hamiltonian systems. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. Each chapter in this book was written by well-established scientists in the field of nonlinear Hamiltonian systems. The development presented in this book goes beyond the KAM theory, and the onset and disappearance of chaos in the stochastic and resonant layers of nonlinear Hamiltonian systems are predicted analytically, instead of qualitatively. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico