On the checkerboard pattern and the autocorrelation of photoemission data in high temperature superconductors

In the pseudogap state the spectrum of the autocorrelation of angle resolved photoemission (AC-ARPES) data of Bi2212 presents non-dispersive peaks in momentum space which compare well with those responsible of the checkerboard pattern found in the density of states by Scanning Tunneling Microscopy. This similarity suggests that the checkerboard pattern originates from peaks in the joint density of states, as the dispersive peaks found in the superconducting state do. Here we show that the experimental AC-ARPES spectrum can be reproduced within a model for the pseudogap with no charge-ordering or symmetry breaking. We predict that, because of the competition of superconductivity and pseudogap, in the superconducting state, the AC-ARPES data of underdoped cuprates will present both dispersive and non-dispersive peaks and they will be better observed in cuprates with low critical temperature. We finally argue that the AC-ARPES data is a complementary and convenient way to measure the arc length.