We study two different parametric pumps--one for pumping spin currents, the other for charge currents--in interacting quantum wires. We find that, as a function of pumping frequency, the spin or charge pumped per cycle has a nonuniversal crossover--depending on pumping details--between two universal fixed point values of 0 and twice the electronic spin or charge quantum number. The direction of flow between these two fixed points depends on whether the interactions are repulsive or attractive, while the quantization itself is a signature of interactions.
In a series of papers we combined the Bethe ansatz with a kinetic (Boltzmann) equation in order to compute exactly transport properties in a Luttinger liquid with an impurity. In a recent comment [cond-mat/9708163], Skorik claimed that while our results were correct in linear response, there was a ``serious flaw'' in our calculation at finite voltage. We explain here why Skorik's arguments are inappropriate, and that there is no flaw in our work [cond-mat/9408068; cond-mat/9505031; cond-mat/9503172].
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 study the effects of interelectron interactions on the charge pumped through an adiabatic quantum electron pump. The pumping is through a system of barriers, whose heights are deformed adiabatically. (Weak) interaction effects are introduced through a renormalisation group flow of the scattering matrices and the pumped charge is shown to always approach a quantized value at low temperatures or long length scales. The maximum value of the pumped charge is set by the number of barriers and is given by ${Q}_{\mathrm{max}}={n}_{b}\ensuremath{-}1$. The correlation between the transmission and the charge pumped is studied by seeing how much of the transmission is enclosed by the pumping contour. The (integer) value of the pumped charge at low temperatures is determined by the number of transmission maxima enclosed by the pumping contour. The extra dissipation at finite temperatures leading to the nonquantized values of the pumped charge scales as a power law with the temperature $(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{T}^{2\ensuremath{\alpha}})$, or with the system size $(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{L}_{W}^{\ensuremath{-}2\ensuremath{\alpha}})$, where $\ensuremath{\alpha}$ is a measure of the interactions, and vanishes at $T=0({L}_{W}=\ensuremath{\infty})$. For a double barrier system, our result agrees with the quantisation of pumped charge seen in Luttinger liquids.