Topological Landscape of Competing Charge Density Waves in 2H-NbSe_{2}

Despite decades of studies of the charge density wave (CDW) of 2H-NbSe_{2}, the origin of its incommensurate CDW ground state has not been understood. We discover that the CDW of 2H-NbSe_{2} is composed of two different, energetically competing, structures. The lateral heterostructures of two CDWs are entangled as topological excitations, which give rise to a CDW phase shift and the incommensuration without a conventional domain wall. A partially melted network of topological excitations and their vertices explain an unusual landscape of domains. The unconventional topological role of competing phases disclosed here can be widely applied to various incommensuration or phase coexistence phenomena in materials.