Garry Goldstein

(University of Cambridge)

Quantum Dimers

 In this talk we review the slave boson meanfield formulation of the fermion+boson quantum dimer model for the pseudogap phase of the high temperature superconductors. We show that in the presence of weak slowly varying external magnetic and electric fields the fermionic dimers undergo semiclassical motion in the external field. As a result in the presence of magnetic fields strong enough to destroy superconductivity the dimers undergo quantum oscillations. Indeed they satisfy Onsager quantization for their orbits and Lifshtiz-Kosevich formula for the amplitude of oscillations. We also compute the effective charges of the dimers in the presence of external magnetic fields as a function of temperature. We show that the effective magnetic charge changes sign from negative −e at low temperature to positive +e at high temperature. This leads to a change of the sign of the Hall coefficient as a function of temperature. We also compute the magnetoresistance as a function of the external field and temperature within a linearized Boltzmann equation approximation for the fermionic dimers. Furthermore we further show that the dimers undergo a Lifshitz transition as a function of doping with a van Hove singularity appearing at the Fermi surface near optimal doping ∼ 20%. Indeed the van Hove singularity leads to a divergence of the density of states and as such an optimum Tc. We study the interplay of nematic fluctuations and the van Hove singularity both of which occur near optimal doping. We show that the van Hove singularity modifies the critical properties of the QCP (quantum critical point) for nematic fluctuations and that the QCP may be described by Hertz Millis like theory with z = 4. This allows us to calculate the critical exponents of the nematic fluctuations and to show that the fermionic dimers have non-Fermi liquid behavior near the QCP with the self energy diverging ∼  ω3/4  near the QCP.