A 'checkerboard' electronic crystal state in lightly hole-doped Ca _2-xNa_xCuO₂Cl₂

The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the 'pseudogap' regime. This regime is rich in peculiar electronic phenomena, prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca _2-xNa_xCuO₂Cl₂. Tunnelling spectroscopy (at energies |E| > 100meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for |E| < 100meV, the spectrum exhibits a V-shaped energy gap centred on E = 0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO₂-unit-cell square 'checkerboard', independent of energy. Intricate atomic-scale electronic structure variations also exist within the checker-board. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca_2-xNa_xCuO₂Cl₂.