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arXiv:cond-mat/0410025 · Physical Review B

Effects of interaction on an adiabatic quantum electron pump

Sourin Das, Sumathi Rao

Published Apr 29, 2005• 23 citations
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Abstract

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.

DOI
10.1103/physrevb.71.165333

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Comment on ``Quantum Pump for Spin and Charge Transport in a Luttinger Liquid''

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arXiv:cond-mat/0111411•Nov 21, 2001•0 citations
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 Qmax=nb\ensuremath−1{Q}_{\mathrm{max}}={n}_{b}\ensuremath{-}1Qmax​=nb​\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−Qint\ensuremath∝T2\ensuremathα)(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{T}^{2\ensuremath{\alpha}})(Q\ensuremath−Qint​\ensuremath∝T2\ensuremathα), or with the system size (Q\ensuremath−Qint\ensuremath∝LW\ensuremath−2\ensuremathα)(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{L}_{W}^{\ensuremath{-}2\ensuremath{\alpha}})(Q\ensuremath−Qint​\ensuremath∝LW\ensuremath−2\ensuremathα​), where \ensuremathα\ensuremath{\alpha}\ensuremathα is a measure of the interactions, and vanishes at T=0(LW=\ensuremath∞)T=0({L}_{W}=\ensuremath{\infty})T=0(LW​=\ensuremath∞). For a double barrier system, our result agrees with the quantisation of pumped charge seen in Luttinger liquids.
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\mathcal{l}l is the range of the scattering potential and vF{v}_{F}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)S)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\mathcal{C}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\mathcal{C}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,\mathcal{C},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 current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, pointlike impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the dc and ac components of the current have power-law dependences on the bias and pumping frequencies with an exponent $2K\ensuremath{-}1$ for spinless electrons, where KKK is the interaction parameter. For K<1∕2K<1∕2K<1∕2, the current grows large for special values of the bias. For noninteracting electrons with K=1K=1K=1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1∕21∕21∕2 electrons.
Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.
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.
We investigate the effects of the electron-electron interactions on the quantum transport through a charge Kondo circuit. The setup consists of a quantum dot sandwiched between two leads by two nearly transparent single mode quantum point contacts. The size of the interacting area LLL in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot aaa. We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.