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Measurements of Stationary Josephson Current between High-$T_{c}$ Oxides as a Tool to Detect Charge Density Waves

Stationary Josephson tunnel current $I_{c}$ between superconductors with $d$-wave order parameter symmetry and charge-density-wave (CDW) partial gapping was analyzed in the two-dimensional model appropriate to high-$T_{c}$ cuprates. It was shown that, in certain experimental setups, due to the peculiar overlap of superconducting and CDW gaps in the momentum space, the dependence of $I_{c}$ on the CDW parameters may be strongly nonmonotonic. Hence, we suggested that $I_{c}$ measurements in the wide range of dopings can serve as an indicator of CDW existence in the pseudogap regions of the cuprate phase diagrams. Besides, the orientation $I_{c}$-dependences were analyzed.