On the basis of both the inhomogeneity of a superconductor, BSCCO-2212, and the effect of measurement, we reveal that an anomalously large gap anisotropy known as evidence of dx2-y2-wave symmetry [Phys. Rev. Lett. 70 (1993) 1553] is not intrinsic, an
d that the constant Fermi velocity at node as an unsolved problem [Nature 423 (2003) 398] is due to the dx2-y2-wave insulator-metal transition.
Switching voltage of first-order metal-insulator transition (MIT) in VO_2, an inhomogeneous strongly correlated system, is changed by irradiating an infrared light with wavelength, 1.5 micrometer, and applying the electric field (photo-induced switch
ing). This was predicted in the hole-driven MIT theory in which hole doping of a low concentration below 0.01% into conduction band (Fermi surface) induces the abrupt MIT as correlation effect. The switching is explained by the Mott transition not the Peierls transition.
