Direct proof of static charge stripe correlations in La$_{2-x}$Ba$_x$CuO$_4$

The nature of charge stripe order in the cuprates, and in particular whether the stripes are static or dynamic, is a key issue in understanding the relationship between stripes and superconductivity. In La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) a low temperature structural distortion is widely believed to pin stripes into fixed, static domains, but such an assertion has never been directly verified. We performed resonant soft x-ray photon correlation spectroscopy (XPCS) to probe the charge order Bragg peak of 1/8 doped LBCO. At low temperatures, we observe time-independent x-ray speckle patterns persisting for more than three hours, proving the static nature of the stripes and we go on to discuss how stripe order melts with increasing temperature. Our results demonstrate that the combination of XPCS with diffraction limited light sources such as the National Synchrotron Light Source II can probe the dynamics of even subtle order parameters such as stripes in the cuprates.