Optical and thermodynamic properties of the high-temperature superconductor HgBa 2 CuO 4+δ

In- and out-of-plane optical spectra and specific heat measurements for the single layer cuprate superconductor HgBa{sub 2}CuO{sub 4+{delta}} (Hg-1201) at optimal doping (T{sub c} = 97 K) are presented. Both the in-plane and out-of-plane superfluid density agree well with a recently proposed scaling relation {rho}{sub s} {proportional_to} {sigma}{sub dc} T{sub c}. It is shown that there is a superconductivity induced increase of the in-plane low frequency spectral weight which follows the trend found in underdoped and optimally doped Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} (Bi-2212) and optimally doped Bi{sub 2}Sr{sub 2}Ca{sub 2}Cu{sub 3}O{sub 10+{delta}} (Bi-2223). We observe an increase of optical spectral weight which corresponds to a change in kinetic energy {Delta}W {approx} 0.5 meV/Cu which is more than enough to explain the condensation energy. The specific heat anomaly is 10 times smaller than in YBa{sub 2}Cu{sub 3}O{sub 6+{delta}} (YBCO) and 3 times smaller than in Bi-2212. The shape of the anomaly is similar to the one observed in YBCO showing that the superconducting transition is governed by thermal fluctuations.