Absence of long-ranged charge order in NaxCa2-xCuO2Cl2 (x=0.08)

Recent scanning-tunneling spectroscopy (STS) studies of the cupric oxychloride NaxCa2-xCuO2Cl2 (NCCOC) have uncovered a periodic 4ax4a density of states (DOS) modulation, termed a checkerboard [T. Hanaguri , Nature (London) 430, 1001 (2004)]. The periodicity of this phase is the same as that of the stripe charge order observed with neutron scattering in the very similar systems La1.48Nd0.4Sr0.12CuO4 (LNSCO) [J. M. Tranquada , Nature (London) 375, 561 (1995)] and La1.875Ba0.125CuO4 (LBCO) [M. Fujita , Phys. Rev. Lett. 88, 167008 (2002)]. This raises the question of whether the stripes are, in fact, actually checkerboards. Unfortunately, NCCOC samples are very small and LBCO and LNSCO samples do not cleave, so neutron and STS measurements cannot be carried out on the same system. To determine the relationship between stripes and checkers, we used resonant soft-x-ray scattering, previously applied to LBCO [P. Abbamonte , Nat. Phys. 1, 155 (2005)], to study single crystals of NCCOC. No evidence was seen for a 4ax4a DOS modulation, indicating that the checkerboard effect is not directly related to the stripe modulation in LBCO. We place an upper bound on the product of the charge amplitude and the square of the in-plane correlation length of 2.3x10(3) hole A(2). Our measurements suggest that the checkers in NCCOC are either glassy or are nucleated by the surface, as suggested by Brown et al.