Abstract
It has been common practice for physicists to assume electronic homogeneity when dealing with condensed matter properties. Recent experimental development, which have revealed fascinating properties of complex materials, demonstrate that such extraordinary macroscopic properties are often associated with microscopic-scale electronic/magnetic inhomogeneity, which limits the Hamitonian-type theoretical approach. Herein, we discuss the microscopic coexistence of metallic and insulating phases in novel materials having an intricate interplay among charge/spin/lattice degrees of freedom. Examples include the coexistence of superconducting-metallic and insulating phases in La
2CuO
4+
δ
as well as Mg
1−
x
B
2. The insulating nature in La
2CuO
4+
δ
originates from electron–electron correlation, but disorder plays a dominant role in producing the insulating behavior in Mg-deficient Mg
1−
x
B
2. We also examine the microscopic coexistence of ferromagnetic-metallic and charge-ordered-insulating phases in mixed-valent manganites, exhibiting colossal magnetoresistance. Possible origins of this electronic phase separation are discussed.