Near-commensuration from Intertwined Charge Density Waves in Single-Layer TiSe₂

When the period of an incommensurate charge density wave (ICDW) approaches a multiple of a lattice vector, the energy gain from locking the period can drive a transition into an intermediate near-commensurate (NC) state made of locally commensurate regions separated by phase slips of a complex CDW. In TiSe₂, a paradigmatic CDW system, incommensuration is believed to be induced by carrier doping, yet its putative NC state has never been imaged. Here we observe a striking NC state in ultraclean, doped monolayers of TiSe₂, displaying an intricate network of unidirectional domain walls. Detailed analysis reveals that these are not phase slips of a complex CDW, but rather sign-changing Ising-type domain walls of two coupled real CDWs of different symmetry. In addition, these CDWs are coupled to an unexpected nematic modulation at the lattice Bragg peaks. TiSe₂ is thus a rare example of a NC-CDW of two intertwined real modulations with nematicity.