Optical conductivity and kinetic energy of the superconducting state: A cluster dynamical mean field study

We study the evolution of the optical conductivity in the t-J model with temperature and doping using the Cluster Dynamical Mean Field Method. The transition to the superconducting state in the overdoped regime is characterized by an increase in the kinetic energy of the system, in contrast to the underdoped side where kinetic energy of the system decreases upon condensation. In the underdoped and optimally doped regime, the optical conductivity displays anomalous transfers of spectral weight over a broad frequency region. Copyright c © EPLA, 2007 Introduction. – How superconductivity emerges from a strongly correlated normal state is one of the most important problems in the field of strongly correlated electron systems. One of the most powerful bulk probes of carrier dynamics is the optical conductivity. For example, the changes of the integral of the optical conductivity upon superfluid condensation [1,2] can be linked to the kinetic energy change, and therefore gives a direct probe of the origin of the condensation energy. Much effort was recently devoted to measure this kinetic energy difference between normal and superconducting state [3–5] using a sum rule, by integrating careful measurements of the optical conductivity up to large enough cutoff of the order of 1 eV in both normal and superconducting state. It has been shown that in the overdoped regime, the absolute value of the kinetic energy decreases, while in the underdoped regime the system gains kinetic energy. These surprising experimental results have been the subject of lively controversy [4,6,7] but have by now been obtained by at least three experimental groups. It is well known that the approach to a Mott transition causes a dramatic reduction of the low energy spectral optical weight. In this paper we address the more refined issue of how the difference between the optical conductivity in the normal and superconducting state, and the consequent difference in kinetic energy are affected by the proximity to the Mott transition. The optical conductivity of an electronic model governed by a Hamiltonian H consisting of a band with dispersion εk and gauge invariant interaction terms obeys the f -sum rule [8,9] ∫ ∞