Linear in Temperature Resistivity and Associated Mysteries

Abstract

Recent experimental results: (i) the measurement of the $T\ln T$ specific heat in cuprates and the earlier such results in some heavy fermion compounds, (ii) the measurement of the single-particle scattering rates, (iii) the density fluctuation spectrum in cuprates and (iv) the long standing results on the linear temperature dependence of the resistivity, show that a theory of the quantum-criticality in these compounds based on the solution of the dissipative 2D - XY model gives the temperature and frequency dependence of each of them, and the magnitudes of all four with one dimensionless coupling parameter. These low frequency or temperature dependences persist to an upper cut-off which is measured to be about the same from the singularity in the specific heat or the saturation of the single-particle self-energy. The same two parameters are deduced in the analysis of results of photoemission experiments to give d-wave superconductivity and its transition temperature. The coupling parameter and the cut-off had been estimated in the microscopic theory to within a factor of 2. The simplicity of the results depends on the discovery that orthogonal topological excitations in space and in time determine the fluctuations near criticality such that the space and time metrics are free of each other. The interacting fermions then form a marginal Fermi-liquid.

arXiv commentA section summarizing that the parameters determining d-wave superconductivity and the transition temperature are the same as determining the normal state marginal fermi-liquid is added. A few other improvements including discussion of the "Planckina" coefficient determining the linear in T resistivity have been made. To be published as Review of Modern Physics-colloque

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• When low- and high-energy electronic responses meet in cuprate superconductors
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• Universality of the single-particle spectra of cuprate superconductors
• Quantum Criticality in Quasi-Two Dimensional Itinerant Antiferromagnets
• Quantum criticality in the two-dimensional dissipative quantum XY model-II
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• Dichotomy in the $T$-linear resistivity in hole-doped cuprates
• Specific Heat and Sound Velocity Distinguish the Relevant Competing Phase in the Pseudogap Region of High Temperature Superconductors
• Dynamic structure function of some singular Fermi-liquids
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• CDMFT+HFD : an extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model
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• Mapping the phase diagram of a YBa${}_2$Cu${}_3$O${}_{7-\delta }$ nanowire through electromigration
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• Low-temperature T-linear resistivity in the strange metal phase of overdoped cuprate superconductors due to umklapp scattering from a spin excitation
• Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid
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