We investigate theoretically the ac conductivity of a clean two-channel spinless quantum wire in the presence of both short-ranged intra- and inter-channel electron–electron interactions. In the Luttinger-liquid regime, we formulize the action functional of the system with an external time-varying electric field. The obtained expression of ac conductivity for the system within linear response theory is generally an oscillation function of the interaction strength, the driving frequency as well as the measured position in the wire. The numerical examples demonstrate that the amplitude of ac conductivity is renormalized by the both interactions, and the dc conductivity of the system with inter-channel interaction is smaller than that without inter-channel interaction.
We study theoretically the transport properties of an interacting quantum wire in the presence of a time-dependent point impurity. Using the Keldysh formalism within the framework of Luttinger liquid model, we calculate and analyze the dc contribution of the backscattered current and the shot noise of the system with arbitrary Luttinger interaction strength and impurity position. From some numerical examples, we find that the time-dependent point impurity in the wire can enhance the total current in the strongly interaction regime, and the total current enhancement is dependent on both the impurity potential frequency and the equivalent frequency in relation to the drain-source voltage
V. The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength. Furthermore, the oscillation of the dc contribution of the backscattered current is not a finite-length effect, which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with
V. However, the final current-noise relation is similar to that in the case of a static point impurity.
The low-temperature AC conductance of a one-dimensional electron system with a strong interaction of finite range is calculated by using linear response theory. The conductance factorizes into parts which depend on the internal properties of the system, and the external probe. For short-range interaction, the result resembles that for non-interacting electrons, but with the zero-frequency limit and the Fermi velocity renormalized by the interaction strength. For strong and long-range interaction, the conductance shows a peak that is related to charge-wave excitations. In this limit, the AC conductance can be simulated by a quantum capacitance and a quantum inductance .
The low-temperature AC conductance of a one-dimensional electron system with a strong interaction of finite range is calculated by using linear response theory. The conductance factorizes into parts which depend on the internal properties of the system, and the external probe. For short-range interaction, the result resembles that for non-interacting electrons, but with the zero-frequency limit and the Fermi velocity renormalized by the interaction strength. For strong and long-range interaction, the conductance shows a peak that is related to charge-wave excitations. In this limit, the AC conductance can be simulated by a quantum capacitance and a quantum inductance.
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 theoretically electronic transport through an isolated local defect in a 1D conductor described in terms of the Luttinger liquid, and show that the well-known tunneling regime of electronic transport leading to power-law I-V curves takes place only in the limit of small voltage. At voltages exceeding a threshold value a new dynamic regime of transport starts in which the DC current induces AC oscillations of frequency f = /e. In gated quantum wires where interaction between electrons is short-ranged, generation linewidth is small provided the inter-electronic repulsion is strong enough, otherwise a wide-band noise is generated. In case of long-range Coulomb interaction generation is coherent at any interaction strength. The effect is related to interaction of the current with Friedel oscillations of the electronic density around the impurity. Manifestations of the effect resemble the Coulomb blockade and the Josephson effect. Oscillations of the electric current are accompanied by spin current oscillations. The results are related to semiconducting quantum wires, metallic atomic chains, carbon nanotubes, graphene nanoribbons and others.