Complete details can be found in PNAS, 111, E3026 (2014) & Nat. Phys 12, 150-156 (2016)
Stripes, a specific form of uni-directional charge and spin density wave, were first discovered by neutron scattering measurements in the La-based cuprates. STM was next to detect and visualize low energy electronic state modulations at the same Q-vector in Bi-based and oxchloride cuprates. Recently, NMR and resonant x-ray experiments have extended the observation to YBCO. Even though there is consensus about the presence of a density wave (DW) involving the electronic degrees of freedom new questions arise: 1) is the DW related to the PG state, 2) what is the driving instability of the modulation, 3) is the DW truly disordered in all cuprates, 4) how does it relate to d-symmetry superconductivity, 5) what is the mechanism that drives the magnetic field changes.
A detailed microscopic view of the density wave was achieved by SI-STM from the Davis Lab at Cornell. Spectroscopic energy resolved images near the pseudogap (PG) energy showed beautiful arrangements of a ladder pattern with a bright backbone and an approximate wavelength of 4 unit cells (see image below).
The initial interpretation of this pattern was that they were consistent with stripes, similar to those observed by neutron measurements on La-cuprates. However, during the the last 5 years we have been developing a new set of experimental and analysis tools to perform sub-unit-cell resolved measurements to determine the additional degrees of freedom essential to the structure of the density wave. Having the capability to robustly resolve the local density of states between the copper and two distinct oxygen sites (see CuO figure in last section) within each and every unit cell we demonstrated that the ladder patterns were not stripes but a d-form factor density wave (dFF-DW). The distinction arises exactly at the sub-unit-cell scale: for stripes, the density at the two different oxygen sites within each unit cell modulates in phase whereas in a dFF-DW they are out of phase by π.
A schematic of a dFF-lattice, left panel below, shows the density at every oxygen site along the x-direction (Ox) has the opposite sign as the ones along y, Oy. Modulating this pattern along the x-direction, as shown in the right panel, results in a dFF-DW, where the phase between the sublattice of Ox and Oy are π out of phase.
This form of density wave, never before identified in nature, arranges itself into small unidirectional domains with long range order. The figure below shows our determination of this domain structure using Fourier methods. The orange patches show the density wave running along the x-direction whereas the blue patches show modulations in the y-direction. The white areas in between are regions of coexistence in which the ladder patterns are frustrated.
While X-ray measurements, for example, determine the onset of the density wave at temperatures well below that of the pseudogap state, our energy resolved tracking of the dFF-DW actually reveals that the energies at which the modulations are most intense are those of the pseudogap. In analogy to a classic density wave gap opening in a metal, the energies of maximal modulation typically determine the characteristic gap or energy scale of the ordering.
The origin of density waves, especially in more complex materials, is a difficult problem to tackle. While on the ends of the spectrum either lattice instability or momentum space susceptibility can be primary drivers, in reality both effects must play a role. Our momentum resolved measurements determine that the Q-vector associated with the dFF-DW evolves with doping along the same monotonic trajetory as the vector connecting the tips of Fermi arcs. While this may indicate the the wavelength of the density wave is determined by scattering between k-space hot spots, the highly spatially disordered structure may also indicate that the evolution is a result of domain structure changes.
However, one piece of evidence strongly supporting that Fermiology must play a key role is the observation that the dFF-DW modulation on the filled and empty sides are exactly out of phase as would be expected in a picture where a momentum space instability at hot spots opens a gap across the chemical potential.