Coupled commensurate charge density wave and lattice distortion inNa2Ti2Pn2O(Pn=As,Sb)determined by x-ray diffraction and angle-resolved photoemission spectroscopy

Abstract

We report single-crystal x-ray-diffraction measurements on ${\mathrm{Na}}_{2}{\mathrm{Ti}}_{2}P{n}_{2}\mathrm{O}\phantom{\rule{0.28em}{0ex}}(Pn=\mathrm{As},\mathrm{Sb})$ which reveal a charge superstructure that appears below the density wave transitions previously observed in bulk data. From symmetry-constrained structure refinements we establish that the associated distortion mode can be described by two propagation vectors ${\mathbf{q}}_{1}=(1/2,0,l)$ and ${\mathbf{q}}_{2}=(0,1/2,l)$ with $l=0$ (Sb) or $l=1/2$ (As) and primarily involves in-plane displacements of the Ti atoms perpendicular to the Ti-O bonds. We also present angle-resolved photoemission spectroscopy measurements, which show band folding and backbending consistent with a density wave with the same wave-vectors ${\mathbf{q}}_{1}$ and ${\mathbf{q}}_{2}$ associated with Fermi-surface nesting, and muon-spin relaxation data, which show no indication of spin density wave order. The results provide direct evidence for phonon-assisted charge density wave order in ${\mathrm{Na}}_{2}{\mathrm{Ti}}_{2}P{n}_{2}\mathrm{O}$ and fully characterize a proximate ordered phase that could compete with superconductivity in doped ${\mathrm{BaTi}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$.