Modulation of the local density of states within the $d$-density wave   theory in the underdoped cuprates
  The low temperature scanning tunneling microscopy spectra in the underdoped regime is analyzed from the perspective of coexisting $d$-density wave and d-wave superconducting states. The calculations are carried out in the presence of a low concentration of unitary impurities and within the framework of the fully self-consistent Bogoliubov-de Gennes theory, which allows local modulations of the magnitude of the order parameters in response to the impurities. Our theory captures the essential aspects of the experiments in the underdoped BSCCO at very low temperatures. 
Amit Ghosal, Angela Kopp, Sudip Chakravarty