Transport in a spin-incoherent Luttinger liquid

We theoretically investigate transport in a spin-incoherent one-dimensional electron system, which may be realized in quantum wires at low-electron density and finite temperature. Both the pure and disordered cases are considered, both in finite wires and in the thermodynamic limit. The effect of Fermi-liquid leads attached to the finite-length system is also addressed. In the infinite system, we find a phase diagram identical to that obtained for a spinless Luttinger liquid, provided we make the identification $g=2g_c$, where $g$ is the interaction parameter in a spinless Luttinger liquid and $g_c$ is the interaction parameter of the charge sector of a Luttinger-liquid theory for electrons with spin. For a finite-length wire attached to Fermi-liquid leads, the transport depends on the details of the disorder in the wire. A simple picture for the crossover from the spin-incoherent regime to the spin-coherent regime as the temperature is varied is also discussed, as well as some physical implications.

Figure 1

Phase diagram (in the limit $J\to 0$, then $T\to 0$) for a spin-incoherent Luttinger liquid with a double barrier structure. Here $V$ denotes the strength of the backscattering for weak impurities, and $t_0$ the strength of the tunneling for strong impurities. The conductance off resonance is denoted by $G$ and the conductance on resonance is denoted by $G^{*}$. The dashed line at $g_c=\frac{1}{2}$ is the fixed line for transmission off resonance separating the regions where electrons will $(g_c>\frac{1}{2})$ or will not $(g_c<\frac{1}{2})$ propagate through the double barrier structure. The dashed line at $g_c=\frac{1}{8}$ separates the regions of zero $(g_c<\frac{1}{8})$ and nonzero $(g_c>\frac{1}{8})$ conductance on resonance at vanishing energies. The solid line between $g_c=\frac{1}{8}$ and $\frac{1}{4}$ is a line of Kosterlitz-Thouless separatrices. Compare with Fig. 3 of Ref. 8.