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By the adoption of a quaternion orientational order parameter to describesolidification, the topological origins of the thermal transport properties ofcrystalline and non-crystalline solid states are considered herein. Globalorientational order, achieved by spontaneous symmetry breaking, is prevented atfinite temperatures for systems that exist in restricted dimensions(Mermin-Wagner theorem). Just as complex ordered systems exist in restricteddimensions in 2D and 1D, owing to the dimensionality of the order parameter,quaternion ordered systems in 4D and 3D exist in restricted dimensions. Justbelow the melting temperature, misorientational fluctuations in the form ofspontaneously generated topological defects prevent the development of thesolid state. Such solidifying systems are well-described using O(4) quantumrotor models, and a defect-driven Berezinskii-Kosterlitz-Thouless (BKT)transition is anticipated to separate an undercooled fluid from a crystallinesolid state. In restricted dimensions, in addition to orientationally-orderedground states, orientationally-disordered ground states may be realized bytuning a non-thermal parameter in the relevant O(n) quantum rotor modelHamiltonian; thus, glassy solid states are anticipated to exist as distinctground states of O(4) quantum rotor models. Within this topological frameworkfor solidification, the finite Kauzmann temperature marks a first-ordertransition between crystalline and glassy solid states at a "self-dual criticalpoint" that belongs to O(4) quantum rotor models. This transition is ahigher-dimensional analogue to the quantum phase transition that belongs toO(2) Josephson junction arrays (JJAs). Thermal transport properties ofcrystalline and glassy solid states, above approximately 50 K, are consideredalongside electrical transport properties of JJAs across thesuperconductor-to-superinsulator transition.

journal of physics. condensed matter

Topological Description of the Solidification of Undercooled Fluids and  the Temperature Dependence of the Thermal Conductivity of Crystalline and  Glassy Solids Above Approximately 50 K