### Abstract

We calculate the d.c. Josephson current through charge density wave (CDW) region connected to two superconductors (S_{1}, S_{2}) by tunnel junctions. At T = 0 and without impurities, we discover infrared divergence in the d.c. Josephson current caused by the phase mode in the long-junction limit: d/v_{F} ≫ ℏ/Δ_{S}, ℏ/Δ_{CDW} where T is temperature. These limits are expressed by using the energy gap in S region Δ_{S}, the length d, the Fermi velocity v_{F}, and the energy gap Δ_{CDW} in CDW region. The critical current is proportional to (Δ_{CDW}ℏv_{F}/d)^{1/2} ∝ Δ_{CDW}(ξ_{CDW}/d)^{1/2}. At βΔ_{S}(T), βΔ_{CDW}(T) ≫ 1 and βℏv_{F}/d ≪ 1, the T-dependence of the correction caused by the phase mode is T-linear where β = 1/k_{B}T and k_{B} is Boltzmann constant. At finite temperatures and with impurities, the correction caused by the phase mode becomes proportional to ln T. At finite temperatures and without impurities, the critical current is similar to the Ambegaokar-Baratoff formula which is proportional to Δ_{S}(T) in the short-junction limit: d/v_{F} ≪ ℏ/Δ_{S}, ℏ/Δ_{CDW}.

Original language | English |
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Pages (from-to) | 308-322 |

Number of pages | 15 |

Journal | Physica C: Superconductivity and its Applications |

Volume | 351 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 Apr 1 |

### Keywords

- Charge density wave
- Critical current density
- Josephson current

### ASJC Scopus subject areas

- Condensed Matter Physics

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## Cite this

*Physica C: Superconductivity and its Applications*,

*351*(3), 308-322. https://doi.org/10.1016/S0921-4534(00)01626-9