  We construct cohomogeneity-three, finite temperature stationary black brane
solutions dual to a field theory exhibiting checkerboard order. The
checkerboards form a backreacted part of the bulk solution, and are obtained
numerically from the coupled Einstein-Maxwell-scalar PDE system. They arise
spontaneously and without the inclusion of an explicit lattice. The phase
exhibits both charge and global U(1)-current modulation, which are periodic in
two spatial directions. The current circulates within each checkerboard
plaquette. We explore the competition with striped phases, finding first-order
checkerboard to stripe phase transitions. We also detail spatially modulated
instabilities of asymptotically AdS black brane backgrounds with neutral scalar
profiles, including those with an hyperscaling violating IR geometry at zero
temperature.
