Interacting electrons with spin in a one-dimensional wire connected to leads

Original · EN

We investigate a one--dimensional wire of interacting electrons connected to one--dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of an incident electron even in the noninteracting leads. The Fourier transform of nonlocal correlation functions are computed for T≫ ω. In particular, this allows us to study the proximity effect, related to the Andreev reflection. A new type of proximity effect emerges when the wire has normally a tendency towards Wigner crystal formation. The latter is suppressed by the leads below a space--dependent crossover temperature; it gets dominated everywhere by the 2kF CDW at T<L³/² ⁽ᵏ⁻¹⁾ for short range interactions with parameter K<1/3. The lowest--order renormalization equations of a weak backscattering potential are derived explicitly at finite temperature. A perturbative expression for the conductance in the presence of a potential with arbitrary spatial extension is given. It depends on the interactions, but is also affected by the noninteracting leads, especially for very repulsive interactions, K<1/3. This leads to various regimes, depending on temperature and on K. For randomly distributed weak impurities, we compute the conductance fluctuations, equal to that of R=g-2e² /h. While the behavior of Var(R) depends on the interaction parameters, and is different for electrons with or without spin, and for K<1/3 or K>1/3, the ratio Var(R)/R² stays always of the same order: it is equal to Lₜ/L≪ 1 in the high temperature limit, then saturates at 1/2 in the low temperature limit, indicating that the relative fluctuations of R increase as one lowers the temperature.