Holographic Checkerboards

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.Comment: 26 pages, 11 figures. v2: Published versio

Incompatibility of modulated checkerboard patterns with the neutron scattering resonance peak in cuprate superconductors

Checkerboard patterns have been proposed in order to explain STM experiments on the cuprates BSCCO and Na-CCOC. However the presence of these patterns has not been confirmed by a bulk probe such as neutron scattering. In particular, simple checkerboard patterns are inconsistent with neutron scattering data, in that they have low energy incommsensurate (IC) spin peaks rotated 45 degrees from the direction of the charge IC peaks. However, it is unclear whether other checkerboard patterns can solve the problem. In this paper, we have studied more complicated checkerboard patterns ("modulated checkerboards") by using spin wave theory and analyzed noncollinear checkerboards as well. We find that the high energy response of the modulated checkerboards is inconsistent with neutron scattering results, since they fail to exhibit a resonance peak at (pi,pi), which has recently been shown to be a universal feature of cuprate superconductors. We further argue that the newly proposed noncollinear checkerboard also lacks a resonance peak. We thus conclude that to date no checkerboard pattern has been proposed which satisfies both the low energy constraints and the high energy constraints imposed by the current body of experimental data in cuprate superconductors.Comment: 5 pages, 5 figures, Fig.2 update

The effective conductivity of arrays of squares: large random unit cells and extreme contrast ratios

An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends recent work on multi-component checkerboards at medium contrast ratios. General improvement include the simplification of a long-range preconditioner, the use of a banded solver, and a more efficient placement of quadrature points. This, together with a reduction in the number of unknowns, allows for a substantial increase in achievable accuracy as well as in tractable system size. Results, accurate to at least nine digits, are obtained for random checkerboards with over a million squares in the unit cell at contrast ratio 10^6. Furthermore, the scheme is flexible enough to handle complex valued conductivities and, using a homotopy method, purely negative contrast ratios. Examples of the accurate computation of resonant spectra are given.Comment: 28 pages, 11 figures, submitted to J. Comput. Phy

Coexistence of double-Q spin density wave and multi-Q pair density wave in cuprate oxide superconductors

Spatial 4a x 4a modulations, with a the lattice constant of CuO_2 planes, or the so called checkerboards can arise from double-Q spin density wave (SDW) with Q_1 = (pm pi/a, pm 3 pi/4a) and Q_2 = (pm 3 pi/4a, pm pi/a). When multi-Q pair density wave, that is, the condensation of d gamma-wave Cooper pairs with zero total momenta, pm 2Q_1, pm 2Q_2, pm 4Q_1, pm 4Q_2, and so on is induced by the SDW, gaps can have fine structures similar to those of the so called zero-temperature pseudogaps.Comment: 4 pages, 3 figure

Order of acquisition in learning perceptual categories: a laboratory analogue of the age-of-acquisition effect?

In the age-of-acquisition (AoA) effect, an advantage for recognition and production is found for items learned early in life, as compared with items learned later. In this laboratory analogue, participants learned to categorize novel random checkerboard stimuli. Some stimuli were presented from the onset of training; others were introduced later. At test, when early and late stimuli had equal cumulative frequency, early stimuli were classified significantly more quickly. Because stimuli were randomly assigned to be introduced either early or late, we can conclude that early stimuli were categorized more quickly because of their order of acquisition. This finding suggests that age- or order-of-acquisition effects are a general property of any learning system

Attentional load and sensory competition in human vision: Modulation of fMRI responses by load fixation during task-irrelevant stimulation in the peripheral visual field.

Perceptual suppression of distractors may depend on both endogenous and exogenous factors, such as attentional load of the current task and sensory competition among simultaneous stimuli, respectively. We used functional magnetic resonance imaging (fMRI) to compare these two types of attentional effects and examine how they may interact in the human brain. We varied the attentional load of a visual monitoring task performed on a rapid stream at central fixation without altering the central stimuli themselves, while measuring the impact on fMRI responses to task-irrelevant peripheral checkerboards presented either unilaterally or bilaterally. Activations in visual cortex for irrelevant peripheral stimulation decreased with increasing attentional load at fixation. This relative decrease was present even in V1, but became larger for successive visual areas through to V4. Decreases in activation for contralateral peripheral checkerboards due to higher central load were more pronounced within retinotopic cortex corresponding to 'inner' peripheral locations relatively near the central targets than for more eccentric 'outer' locations, demonstrating a predominant suppression of nearby surround rather than strict 'tunnel vision' during higher task load at central fixation. Contralateral activations for peripheral stimulation in one hemifield were reduced by competition with concurrent stimulation in the other hemifield only in inferior parietal cortex, not in retinotopic areas of occipital visual cortex. In addition, central attentional load interacted with competition due to bilateral versus unilateral peripheral stimuli specifically in posterior parietal and fusiform regions. These results reveal that task-dependent attentional load, and interhemifield stimulus-competition, can produce distinct influences on the neural responses to peripheral visual stimuli within the human visual system. These distinct mechanisms in selective visual processing may be integrated within posterior parietal areas, rather than earlier occipital cortex

Checkerboard and stripe inhomogeneities in cuprates

We systematically investigate charge-ordering phases by means of a restricted and unrestricted Gutzwiller approximation to the single-band Hubbard model with nearest ($t$) and next-nearest neighbor hopping ($t'$). When $|t'/t|$ is small, as appropriate for ${\rm La_{2-x}Sr_xCuO_4}$, stripes are found, whereas in compounds with larger $|t'/t|$ (such as ${\rm Ca_{2-x}Na_x CuO_2Cl_2}$ and ${\rm Bi_2Sr_2CaCu_2O_{8+\delta}}$) checkerboard structures are favored. In contrast to the linear doping dependence found for stripes the charge periodicity of checkerboard textures is locked to 4 unit cells over a wide doping range. In addition we find that checkerboard structures are favored at surfaces.Comment: 5 pages, 3 figure