The strong correlated electronic materials we focused on this thesis are 5d transition metal oxides. The interplay of strong spin-orbit coupling (SOC) and intermediate on-site Coulomb repulsion U can give rise to the novel collective phenomenon. During this Ph.D., I focused on two iridate families with strong SOC: La-doped Sr2-yLayIrO4 and Nd2Ir2O7. We observed a soft collective mode in doped Sr2-yLayIrO4. A strange state of affairs: low entropy conducting state we observed in Nd2Ir2O7. The state of affairs is present in superconductors which are known to be heat insulators while being perfect charge conductors. Another case is presented by the charge density wave where collective transport can be accommodated by sliding the charge density wave. These two scenarios can both explain the discrepancy. However, neither the superconducting nor the CDW scenario is compatible with the observed T^2 dependence of the zero-energy spectral weight.