Charge density waves as the origin of dip-hump structures in differential tunneling conductance of cuprates: the case of $d$-wave superconductivity

Abstract: Conductance-voltage characteristics (CVCs) for non-symmetric tunnel junctions between $d$-wave superconductors with charge-density waves (CDWs) and normal metals were calculated. It was shown that they have a V-like form at small voltages $V$ and are asymmetric at larger $V$ owing to the presence of CDW peak in one of the $V$-branches. The spatial scatter of the dielectric (CDW) order parameter smears the CDW peak into a hump and induces a peak-dip-hump structure (PDHS) typical of CVCs observed for such junctions. At temperatures larger than the superconducting critical temperature, the PDHS evolves into a pseudogap depression. The results agree well with the scanning tunneling microscopy data for Bi${2}$Sr${2}$CaCu${2}$O${8+\delta}$ and YBa${2}% $Cu${3}$O$_{7-\delta}$.