Stacked CMB lensing and ISW signals around superstructures in the DESI
  Legacy Survey
  The imprints of large-scale structures on the Cosmic Microwave Background can
be studied via the CMB lensing and Integrated Sachs-Wolfe (ISW) signals. In
particular, the stacked ISW signal around supervoids has been claimed in
several works to be anomalously high. In this study, we find cluster and void
superstructures using four tomographic redshift bins with $0<z<0.8$ from the
DESI Legacy Survey, and measure the stacked CMB lensing and ISW signals around
them. To compare our measurements with $\Lambda$CDM model predictions, we
construct a mock catalogue with matched galaxy number density and bias, and
apply the same photo-$z$ uncertainty as the data. The consistency between the
mock and data is verified via the stacked galaxy density profiles around the
superstructures and their quantity. The corresponding lensing convergence and
ISW maps are then constructed and compared. The stacked lensing signal agrees
with data well except at the highest redshift bin in density peaks, where the
mock prediction is significantly higher, by approximately a factor 1.3. The
stacked ISW signal is generally consistent with the mock prediction. We do not
obtain a significant signal from voids, $A_{\rm ISW}=-0.10\pm0.69$, and the
signal from clusters, $A_{\rm ISW}=1.52\pm0.72$, is at best weakly detected.
However, these results are strongly inconsistent with previous claims of ISW
signals at many times the level of the $\Lambda$CDM prediction. We discuss the
comparison of our results with past work in this area, and investigate possible
explanations for this discrepancy.
