We study charge and spin transport through an interacting quantum wire, caused by backscattering of electrons off an effective impurity potential with a periodic time dependence. The adiabatic regime of this pump for charge and spin is shown to depend on the presence of interactions in the wire. For the noninteracting case, the transported quantities in a period are calculated and found to be adiabatic (independent of the pumping frequency) for all frequencies $\ensuremath{\Omega}\ensuremath{\ll}{v}_{F}/\mathcal{l},$ where
l is the range of the scattering potential and
vF is the Fermi velocity; this result is along the lines of adiabatic pumping in mesoscopic systems. On the other hand, we show that for a wire with repulsive electron-electron interactions, the adiabatic regime is confined to $\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\ll}{\ensuremath{\omega}}_{\ensuremath{\Gamma}},$ where ${\ensuremath{\omega}}_{\ensuremath{\Gamma}}$ is an energy scale set by the backscattering potential. Using symmetry and scaling properties of the quantum wire Hamiltonian, we relate the charge Q and spin S transported through the wire in a period $2\ensuremath{\pi}/\ensuremath{\Omega}$ to an integral involving quasistatic backscattering conductances. We also show that the pumped charge Q (or the spin
S) is quantized in the adiabatic limit if the conductance of the system is zero at the stable fixed point of the renormalization-group (RG) transformations. The quanta transported are given by the winding number of a complex coupling $\ensuremath{\Gamma}(\ensuremath{\Omega}t)$ as it traverses a closed path
C enclosing the origin $\ensuremath{\Gamma}=0.$ No adiabatic charge or spin is transported when the RG fixed point corresponds to a perfectly conducting wire, or if the path
C does not enclose the point $\ensuremath{\Gamma}=0.$ By contrast, for a RG marginal conductance---which is the case for noninteracting electrons---the charge transported in a cycle is not quantized, rather it is proportional to the area enclosed by the path or circuit
C, in agreement with previous studies of noninteracting mesoscopic systems. Finite size, temperature, and frequency effects on the transported quantities follow from the relation between adiabatic transport coefficients (backscattering conductances) and the quasistatic conductance of the system.
We develop a detailed theory for spin transport in a one-dimensional quantum wire described by Luttinger-liquid theory. A hydrodynamic description of the quantum wire is supplemented by boundary conditions, taking into account the exchange coupling between the magnetization of ferromagnetic reservoirs and the boundary magnetization in the wire. Spin-charge separation is shown to imply drastic and qualitative consequences for spin-dependent transport. In particular, the spin accumulation effect is quenched except for fine-tuned parameter regimes. We propose several feasible setups involving an external magnetic field to detect this phenomenon in transport experiments on single-wall carbon nanotubes. In addition, electron-electron backscattering processes, which do not have an important effect on thermodynamic properties or charge transport, are shown to modify spin-dependent transport through long quantum wires in a crucial way.
We consider strongly interacting one-dimensional electron liquids where elementary excitations carry either spin or charge. At small temperatures a spinon created at the bottom of its band scatters off low-energy spin and charge excitations and follows the diffusive motion of a Brownian particle in momentum space. We calculate the mobility characterizing these processes and show that the resulting diffusion coefficient of the spinon is parametrically enhanced at low temperatures compared to that of a mobile impurity in a spinless Luttinger liquid. We briefly discuss that this hints at the relevance of spin in the process of equilibration of strongly interacting one-dimensional electrons, and comment on implications for transport in clean single-channel quantum wires.
We discuss the violation of spin-charge separation in generic nonlinear Luttinger liquids and investigate its effect on the relaxation and thermal transport of genuine spin-1/2 electron liquids in ballistic quantum wires. We identify basic scattering processes compatible with the symmetry of the problem and conservation laws that lead to the decay of plasmons into the spin modes. We derive a closed set of coupled kinetic equations for the spin-charge excitations and solve the problem of thermal conductance of interacting electrons for an arbitrary relation between the quantum wire length and spin-charge thermalization length.
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=2gc, where
g is the interaction parameter in a spinless Luttinger liquid and
gc 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.
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 is computed for $T\ensuremath{\gg}\ensuremath{\omega}$. In particular, this allows to study the proximity effect, related to the Andreev reflection. In addition, 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 charge-density wave at $T<{L}^{(3/2)(K\ensuremath{-}1)}$ 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, the conductance fluctuations, equal to that of $\mathcal{R}=g\ensuremath{-}{2e}^{2}/h$, are computed. They depend on the interaction parameters, and are different for electrons with or without spin. But the ratio
Var(R)/R2 stays always of the same order: it is equal to ${L}_{T}/L\ensuremath{\ll}1$ in the high-temperature limit, then saturates at
1/2 in the low-temperature limit, indicating that the relative fluctuations of
R are universal.