There is an interesting PRB Conductivity of hard core bosons: a paradigm of a bad metal by Netanel Lindner and Assa Auerbach.

They calculate the frequency and temperature dependence of a model for hard core bosons on a square lattice at half filling. There is only a single energy scale J, the intersite boson hopping energy, in the Hamiltonian.

At low temperatures (below the Kosterlitz-Thouless transition temperature ~ J) the system is a superfluid. At T > 2J the model is in a metallic phase with a resistivity which increases approximately linearly with temperature and has values larger than the Mott-Ioffe-Regel limit (~ the quantum of resistance). There is a broad "Drude peak" with a width which is much larger than J and a spectral weight which decreases with increasing temperature.

The model also approximately obeys Homes scaling law which relates the superfluid density, the superfluid transition temperature Tc, and the conductivity at Tc, for cuprate superconductors. The authors also speculate that a peak in the optical conductivity associated with order parameter magnitude fluctuations [the Higgs mass] might be associated with the mid-infra-red peak seen in the cuprates. This does have alternative explanations in terms of fermionic excitations [see for example this PRB].

This is a nice paper because it gives very concrete results for a "simple" model Hamiltonian. How relevant it is to the cuprates remains to be seen. A definite connection would mean that the Cooper pairs persist to very high temperatures. It would be nice to see a calculation of the temperature dependence of the thermoelectric power.

## Monday, March 19, 2012

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In a recent experimental paper by Keren's group,

ReplyDeleteAsban et. al., Phys. Rev. B 88, 060502, (2013),

the zero temperature superfluid density was plotted against the normal state resistivity slope for several different optimally doped cuprate compounds.

This paper reports an inverse relation between the two quantities, (which are not simply related in weak coupling BCS or Fermi liquid theories). Moreover, the factor of proportionality is quite close to the numerical value predicted by the resistivity of the hard core bosons model.

While this empirical relation does not rule out the validity of other models, it is quite suggestive that the bosonic model can be a basis for an effective theory descibing BOTH superconductivity and normal state transport.