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We study theoretically transport properties of one-dimensional system of interacting electrons pinned by an impurity. Long-range Coulomb interaction in such a system is known to induce a 4 k F electron density modulation characterized by extremely slow, slower than any power law, decay of the density correlations which can be described as a one-dimensional Wigner crystal. We study non-stationary regime of conduction corresponding to sliding of the 1D Wigner crystal depinned by the applied voltage. In this regime the dc current is accompanied by current oscillations with frequency f = I ¯ / e . We calculate I–V curves and ac current generated by sliding. Our approach is based on the ideas of Luttinger liquid. We study also the case of magnetic impurity and show that applied voltage induces not only the electrical current, but also the spin current as well, in other words, the current becomes spin polarized. We find that a spin bias applied to the system contributes to electric current both in case of magnetic and non-magnetic impurity, and this is related to violation of the spin–charge separation at the impurity site.

We study theoretically two effects related to impurity depinning that are common for 1D Luttinger liquid (LL) and linear-chain CDW conductors. First, we consider the electron transport through a single impurity in a 1D conducting channel and study a new regime of conduction related to LL sliding at voltage above a threshold one. The DC current in this regime is accompanied by oscillations with frequency $f =I/e$. This resembles the CDW depinning in linear-chain conductors, the Josephson effect, and the Coulomb blockade. Second, we found that strong pinning of the LL by impurities leads to a magnetic field dependence of the low-temperature specific heat similar to that observed experimentally in CDW compounds. We interpret this in favor of possibility of formation of the LL in linear-chain compounds., 6 pages, paper presented at the ECRYS-2008 conference (Aug. 2008), accepted for publication in Physica B: Physics of Condensed Matter

The electron transport in a 1D conductor with an isolated local defect such as an impurity or a non-adiabatic contact is studied theoretically. New regime of conduction in correlated 1D systems is predicted beyond the well-known regime of tunneling resulting in the power-law I-V-curves. In this regime a quantum wire becomes "opened" at voltage biases above the threshold value $V_T$, giving rise to a rapid increase of the dc current, $\bar I$, accompanied by ac oscillations of frequency $f = \bar I/e$. The effect of ac generation is related to sliding of the Friedel oscillations of electronic density produced by the defect. Manifestations of the effect resemble the Coulomb blockade and the Josephson effect. The spin bias applied to the system is shown to affect the I-V curves due to violation of the spin-charge separation at the defect site. In short quantum wires of length $L < L_0 \sim \hbar v_F/eV_T$ and at high temperatures $T > T_0 \sim eV_T/k_B$ the effect is destroyed by fluctuations. The threshold voltage $V_T$ is determined by $2k_F$-component of impurity potential renormalized by fluctuations. The 1D conductor is described in terms of the Tomonaga-Luttinger Hamiltonian with short range or long-range Coulomb interaction by means of the bosonization technique. We derive boundary conditions that take into account relaxation in the leads and permit to solve non-equilibrium problems. Charge fluctuations are studied by means of Gaussian model which can be justified strictly in the limit of large voltages or strong enough inter-electronic repulsion. Spin fluctuations are taken into account strictly by means of the refermionization technique applicable in case of spin-rotation invariant interaction., 32 pages, 1 figure