A higher-dimensional electronic superstructure in a misfit chalcogenide (PbSe)_1.16(TiSe₂)₂

Aperiodic crystals, despite lack of translational invariance, are characterized by the primitive vectors as periodic crystals. A characteristic of aperiodic ones is number of the primitive vectors, which is larger than the physical dimension. This represents higher-dimensional nature of aperiodic crystals, resulting in exotic phenomena in atomic quasicrystals, light, and ultracold atom. However, no higher-dimensional phenomena have been found in electronic matters, where inner degrees of freedom and strong correlation are involved to yield rich phenomena. Here we show a higher-dimensional electronic modulation in a misfit chalcogenide (PbSe)_1.16(TiSe₂)₂ with spectroscopic imaging scanning tunneling microscopy. We find that the local density-of-states exhibits an aperiodic superstructure while the periodic charge density wave of 1T-TiSe₂ is completely suppressed. Our finding demonstrates that the interplay between hexagonal and tetragonal sublattices provides the electronic matters with extra degrees of freedom from higher dimensions and higher-dimensional electronic properties can be explored in a wider range of materials including artificial heterostructures.