  Phase separation in the nanometer- to micrometer-scale is characteristic for
correlated materials, for example, high temperature superconductors, colossal
magnetoresistance manganites, Mott insulators, etc. Resolving the electronic
structure with spatially-resolved information is critical for revealing the
fundamental physics of such inhomogeneous systems yet this is challenging
experimentally. Here by using nanometer- and micrometer-spot angle-resolved
photoemission spectroscopies (NanoARPES and MicroARPES), we reveal the
spatially-resolved electronic structure in the stripe phase of IrTe$_2$. Each
separated domain shows two-fold symmetric electronic structure with the mirror
axis aligned along 3 equivalent directions, and 6$\times$1 replicas are clearly
identified. Moreover, such electronic structure inhomogeneity disappears across
the stripe phase transition, suggesting that electronic phase with broken
symmetry induced by the 6$\times$1 modulation is directly related to the stripe
phase transition of IrTe$_2$. Our work demonstrates the capability of NanoARPES
and MicroARPES in elucidating the fundamental physics of phase-separated
materials.
