Direct observation of an incommensurate two-dimensional checkerboard charge density wave in the superconductor Ta4Pd3Te16

We report the observation of a highly unusual incommensurate two-dimensional checkerboard charge density wave (CDW) in the superconductor Ta4Pd3Te16, using synchrotron X-ray diffraction. We observe two CDW wavevectors, related by a crystal symmetry, developing below 16 K at ambient pressure. The wavevectors, which remain incommensurate at all observed temperatures, lie neither within the quasi-one-dimensional (Q1D) chains nor the Q2D planes in which the chains reside in this monoclinic crystal structure. The bulk CDW wavevectors are shown to reconcile previous scanning tunneling microscopy and transport studies. We also conducted de Haas-van Alphen (dHvA) quantum oscillation measurements and found no evidence of Fermi surface reconstruction through the CDW transition, suggesting a very subtle gap opening. We determine the temperature-pressure (T-P) phase diagram, and find the superconductivity (SC) dome to be centered at the pressure where the CDW instability vanishes, suggesting that the SC in Ta4Pd3Te16 could have its origin in a CDW quantum critical point, reminiscent of the observations in many unconventional superconductors. With a thorough comparison to other CDW materials, we conclude that Ta4Pd3Te16 is a unique CDW system that features a mixed character of Q1D, Q2D, and 3D.