Hexatic glass order of topological defects in the nearly-commensurate charge density phase of 1T-TaS₂

Tantalum-disulphide (1T-TaS₂) exhibits a nearly commensurate charge density wave (NCCDW) phase where competition between commensuration energy and strain causes long-range periodic phase shifts and amplitude modulations of the order parameter. This gives rise to a network of domain walls formed by line defects, fundamental topological excitations of the charge density wave whose intersections can be described as vortices akin to Abrikosov vortices in type II superconductors. According to KTHNY theory, melting of a 2D lattice proceeds via an intermediate hexatic phase characterized by quasi-long range orientational order. We developed software to analyze STM scans of the NCCDW in a 1T-TaS₂ sample, allowing us to reveal the nature of the longitudinal and translational correlation functions. We find that the orientational and translational order of the NCCDW vortex lattice is characterized by power law decays with exponents η=0.03(1) and η=0.77(1) respectively. These results suggest that the observed NCCDW vortex lattice forms a rare hexatic glass phase stabilized by interactions with the underlying lattice.