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Abrikosov proposed in 1974 that a 3D electronic system with its fermi level at the point of quadratic band crossing, as in the (spin-orbit coupled) gray tin or mercury telluride, should represent the simplest non-fermi liquids, due to the common long-range Coulomb interaction between the particles. I will review this idea and discuss how a non-fermi liquid ground state may be unstable to ordering via the mechanism of "fixed-point collision". This mechanism, with its concomitant hierarchy of scales, may also be identified as the culprit behind the notorious dynamical chiral symmetry breaking in the three dimensional electrodynamics, known as the effective theory of several strongly interacting condensed matter systems and as a favorite toy model of particle theorists. Some further applications of the nematic order parameters, possibly relevant  to gray tin or iridates, in the current search for  higher-dimensional interacting field theories will also be mentioned. 

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Igor Herbut, Simon Fraser University, Canada
Seminar room 0.03, ETP
Contact: Michael Scherer