Quantum Criticality in Quasi-One Dimensional Li 0.9 Mo 6 O 17 J.W. Allen, University of Michigan, DMR Award # For many — indeed most — physical systems there are characteristic energy scales set by the various forces that act. For example, the ferromagnetism of iron disappears if the temperature T is greater than 1043K (1418 °F) because thermal energy then exceeds the characteristic energy of the magnetic forces in iron. Quantum critical systems are strikingly different in having no energy scale except temperature itself. Quantum criticality (QC) is predicted in theories of quasi-one dimensional systems. QC may be important in nano-technology. Studies of systems in nature are just beginning. Here we use a technique called photoemission spectroscopy to observe QC in the spectra of the energy distribution of the electrons of a quasi- one dimensional chemical compound. The spectra have the QC scaling property, that their shape depends only the ratio of energy to temperature. E-E F (eV) 0 Before scaling  K 250K 150K 50K 150K Time sequence of spectra at various T shows repeat- ability.  43 50K  K 0 QC spectra all have the same shape when plotted vs the ratio of energy to temperature. (E-E F )/k B T All data scaled

Quantum Criticality in Quasi-One Dimensional Li 0.9 Mo 6 O 17 J.W. Allen, University of Michigan, DMR Award # One focus of current condensed matter research is the quantum phase transition, in which a system at a temperature (T) of zero Kelvins can switch from one phase to another as the relative strengths of competing forces are varied or “tuned,” e.g. with applied pressure or magnetic field. Just at the transition, or for nonzero temperature in the vicinity of the transition, the competition between the two phases produces very unusual properties that are much different from those of an ordinary phase transition at non-zero T, e.g.. the phase transition in which the ferromagnetism of iron disappears above 1043K. One of these properties is quantum criticality (QC), that there is no characteristic energy scale governing the system’s properties, other than that of T itself. In consequence, various energy spectra of the material, such as the energy distribution of electrons measured in photoemission spectroscopy, should have the scaling property that their shapes are all the same when graphed against the ratio of energy to temperature. QC is particularly dramatic in certain one-dimensional systems where it occurs automatically, without any tuning. Thus it may be of great importance for certain low-dimensional fabricated nano-technology devices. Spectroscopic studies of QC in such devices and in a few special systems found in nature are just beginning. Here we describe the first observation of QC in electron spectra of a quasi-one dimensional chemical compound.

Education: This grant provides partial support for two graduate students, Sung-Kwan Mo and Feng Wang. Both have passed their Ph.D. candidacy exams. The grant also supports summer research opportunities for undergraduates like Spencer Dowdall, a UM double major in physics and math. Spencer has joined the experiments at the Wisconsin SRC. Training for Multi-Institutional Research This work is a good example of the multi- institutional and internationally collaborative style of research for which science students must now be trained. The photoemission experiments are performed by UM researchers at the NSF- funded Wisconsin Synchrotron Radiation Laboratory using samples prepared at the Oak Ridge National Laboratory (David Mandrus group), and LEPES-CNRS, Grenoble, France (C. Schlenker,J. Dumas). Theoretical guidance has been provided by S. Moukouri (UM) and José Alvarez, formerly a UM postdoc, now returned to his native Spain, at the University of Madrid. Quantum Criticality in Quasi-One Dimensional Li 0.9 Mo 6 O 17 J.W. Allen, University of Michigan, DMR Award #

Students involved with this research are learning more just than the science that is being studied. They are learning about the doing of science in the modern era, particularly how most scientific research today requires a coming together of the intellects and skills of many persons, and of the capabilities and resources of many institutions. Learning the formal and informal protocols, the simple courtesies, and the fluctuating roles of leading and following in such an enterprise, can be as challenging, but just as important, as learning the science itself.