Researchers have devised a way to use atoms in optical lattices to model high-temperature superconductors, whose behavior is not yet fully understood.By Ryan Wilkinson C ertain materials become superconducting when their electrons pair up.This phenomenon is well understood in conventional superconductors, which operate only at extremely low temperatures.But it remains obscure in some unconventional superconductors, which can function at surprisingly high temperatures.Now Henning Schlömer at the University of Munich and his colleagues have proposed a method to investigate electron behavior in these high-temperature superconductors using a quantum simulator based on atoms arranged in lattices of laser light [1].
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.