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The inhomogeneous Tomonaga Luttinger liquid model describing an interactingquantum wire adiabatically coupled to non-interacting leads is analyzed in thepresence of a weak impurity within the wire. Due to strong electroniccorrelations in the wire, the effects of impurity backscattering, finite bias,finite temperature, and finite length lead to characteristic non-monotonicparameter dependencies of the average current. We discuss oscillations of thenon-linear current voltage characteristics that arise due to reflections ofplasmon modes at the impurity and quasi Andreev reflections at the contacts,and show how these oscillations are washed out by decoherence at finitetemperature. Furthermore, the finite frequency current noise is investigated indetail. We find that the effective charge extracted in the shot noise regime inthe weak backscattering limit decisively depends on the noise frequency$\omega$ relative to $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ theTomonaga Luttinger interaction parameter, and $L$ the length of the wire. Theinterplay of finite bias, finite temperature, and finite length yields richstructure in the noise spectrum which crucially depends on theelectron-electron interaction. In particular, the excess noise, defined as thechange of the noise due to the applied voltage, can become negative and isnon-vanishing even for noise frequencies larger than the applied voltage, whichare signatures of correlation effects.Comment: 28 pages, 19 figures, published version with minor change

Transport properties of single-channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise