Spin transport through a 1D Mott-Hubbard insulator of finite length

We study low-energy spin and charge transport through a 1D Mott-Hubbard insulator of finite length L attached to Fermi liquid reservoirs, which, in the presence of spin accumulation, are characterized by different electrochemical potentials for electrons of opposite spin polarizations. At temperatures less than T-L = v(c)/L (v(c): charge velocity in the wire) and under the assumption that the Hubbard gap 2M is large enough, M > T-L, we calculate the average currents (charge and spin) and their zero-frequency correlators. The average spin (charge) current depends only on the difference (sum) of the spin-dependent voltages 2V(s) (2V(c)) and even a weak electron backscattering of low rate Gamma(s) << T-L leads to the spin current suppression v at vertical bar V-s vertical bar smaller than Gamma = const x root TLM exp{-2M/T-L} + Gamma(s). The spin current recovers its free mode behavior at spin voltage or temperature larger than Gamma. Suppression of the spin-charge correlator suggesting the appearance of spin-charge separation needs both vertical bar V-s, c vertical bar to be larger than G. In the absence of the average charge current at V-c = 0 its shot noise is proportional to the average spin backscattered current defined by V-s and can be used to measure the spin accumulation in the reservoirs. The relation of these results to Kondo dot transport in the Toulouse limit is also clarified. Copyright (C) EPLA, 2014