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Strongly Correlated Electron Systems Near Criticality: From Nodal Semimetals to High-Temperature Superconductors

  • Author(s): Dumitrescu, Philipp
  • Advisor(s): Vishwanath, Ashvin
  • et al.
Abstract

In this thesis, we will study aspects of two phases close to criticality arising in solid state systems with strong interactions between electrons. In the first part, we study finite temperature transport in a non-Fermi-liquid phase arising from a nodal semimetal with long-range interactions – the so-called Luttinger-Abrikosov-Beneslavskii phase. We are particularly interested in calculating the finite temperature shear viscosity of the phase and find that it is consistent with a bound proposed in the context of gauge-gravity duality. In the second part of the thesis, we study a minimal model of nematic fluctuations in the high-temperature superconductor iron selenide. Nematic fluctuations arising from a quantum critical point have been proposed to explain the phenomenology of several high-temperature superconductors. In a numerical simulation using determinant quantum Monte Carlo methods, we find no direct evidence of a nematic critical point. However, we still observe a wide region of superconductivity correlated with nematic fluctuations as well as an unusual antiferro-quadrupole order.

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