Absence of long-ranged charge order in $\rm Na_{x}Ca_{2-x}CuO_{2}Cl_{2}$ at x=0.08

TL;DR

This study investigates the presence of long-range charge order in NCCOC at x=0.08 using resonant soft x-ray scattering, finding no evidence of the checkerboard pattern observed in STM, thus challenging its relation to stripe order.

Contribution

The paper demonstrates that the checkerboard DOS modulation in NCCOC is not related to stripe order, suggesting alternative electronic behaviors or surface effects.

Findings

No 4a×4a DOS modulation detected with RSXS

Checkerboard pattern not directly related to stripe order

Indications of glassy electronic behavior or surface phase transition

Abstract

A periodic $4a \times 4a$ density of states (DOS) modulation (a "checkerboard pattern") was observed with STM in $\rm Na_{x}Ca_{2-x}CuO_2Cl_2$ (NCCOC) [T. Hanaguri \emph{et al.}, Nature \textbf{430}, 1001 (2004)]. Its periodicity is the same as that of the "stripe" charge order observed with neutron scattering in $\rm La_{1.875}Ba_{0.125}CuO_4$ (LBCO) [J. M. Tranquada \emph{et al.}, Nature \textbf{429}, 534 (2004)] and $\rm La_{1.48}Nd_{0.4}Sr_{0.12}CuO_4$ (LNSCO) [J. M. Tranquada \emph{et al.}, Phys. Rev. B \textbf{54}, 7489 (1996)]. An obvious question is whether the "stripes" are actually "checkers". Unfortunately, because NCCOC samples are small and LBCO samples do not cleave, neutron and STM measurements cannot be carried out on the same system. To determine the relationship between stripes and checkers we used resonant soft x-ray scattering (RSXS), previously applied to LBCO [P. Abbamonte \emph{et al.}, Nature Physics \textbf{1}, 155 (2005)], to study single crystals of NCCOC. No evidence was seen for a $4a \times 4a$ DOS modulation, indicating that the checkerboard effect is not directly related to the stripe modulation in LBCO. Our measurements suggest either glassy electronic behavior or the existence of a surface-nucleated phase transition in NCCOC [S. E. Brown \emph{et al.}, Phys. Rev. B \textbf{71}, 224512 (2005)].