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arXiv:cond-mat/0506095 · Physical Review B

Rectification in one-dimensional electronic systems

Bernd Braunecker, Dima E. Feldman, John Bradley Marston

Published Sep 8, 2005• 20 citations
arXivHTMLPDF

Abstract

Asymmetric current-voltage $[I(V)]$ curves, known as the diode or rectification effect, in one-dimensional electronic conductors can have their origin from scattering off a single asymmetric impurity in the system. We investigate this effect in the framework of the Tomonaga-Luttinger model for electrons with spin. We show that electron interactions strongly enhance the diode effect and lead to a pronounced current rectification even if the impurity potential is weak. For strongly interacting electrons and not too small voltages, the rectification current ${I}_{r}=[I(V)+I(\ensuremath{-}V)]∕2$, measuring the asymmetry in the current-voltage curve, has a power-law dependence on the voltage with a negative exponent, ${I}_{r}\ensuremath{\sim}{V}^{\ensuremath{-}\ensuremath{\mid}z\ensuremath{\mid}}$, leading to a bump in the current-voltage curve.

DOI
10.1103/physrevb.72.125311

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Asymmetric current-voltage [I(V)][I(V)][I(V)] curves, known as the diode or rectification effect, in one-dimensional electronic conductors can have their origin from scattering off a single asymmetric impurity in the system. We investigate this effect in the framework of the Tomonaga-Luttinger model for electrons with spin. We show that electron interactions strongly enhance the diode effect and lead to a pronounced current rectification even if the impurity potential is weak. For strongly interacting electrons and not too small voltages, the rectification current Ir=[I(V)+I(\ensuremath−V)]∕2{I}_{r}=[I(V)+I(\ensuremath{-}V)]∕2Ir​=[I(V)+I(\ensuremath−V)]∕2, measuring the asymmetry in the current-voltage curve, has a power-law dependence on the voltage with a negative exponent, Ir\ensuremath∼V\ensuremath−\ensuremath∣z\ensuremath∣{I}_{r}\ensuremath{\sim}{V}^{\ensuremath{-}\ensuremath{\mid}z\ensuremath{\mid}}Ir​\ensuremath∼V\ensuremath−\ensuremath∣z\ensuremath∣, leading to a bump in the current-voltage curve.
We investigate rectification of a low-frequency ac bias in Y-junctions of one-channel Luttinger liquid wires with repulsive electron interaction. Rectification emerges due to three scatterers in the wires. We find that it is possible to achieve a higher rectification current in a Y-junction than in a single wire with an asymmetric scatterer at the same interaction strength and voltage bias. The rectification effect is the strongest in the absence of the time-reversal symmetry. In that case, the maximal rectification current can be comparable to the total current  ~ e2V/h{e}^{2}V/he2V/h even for low voltages, weak scatterers, and modest interaction strength. In a certain range of low voltages, the rectification current can grow as the voltage decreases. This leads to a bump in the III-VVV curve.
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.
The electronic transport through a single impurity in a repulsive Luttinger liquid (LL) has been theoretically studied. It has been found that the direct current Ī above the threshold voltage related to the strength of the impurity potential is accompanied by coherent oscillations with frequency f = Ī / e . There is an analogy with the Josephson junctions: the well-known regime of the power-law I − V curves in the LL corresponds to the damping of the Josephson current below the critical one, while the oscillatory regime in the LL can be compared with the Josephson oscillations above the critical current.
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.
The spin transport as the current flows through an impurity in a one-dimensional conductor is analyzed. The interacting electrons are described in terms of the Luttinger liquid theory. Both the Coulomb and short-range interactions are considered; the latter appears when the gate screens the long-range part of the Coulomb potential. The cases of magnetic and nonmagnetic impurities are considered. It has been revealed that, for a magnetic impurity, the electric current flow induces the generation of the spin current, which has direct and alternating components. At low temperatures and voltages, the current can be completely spin-polarized. For a nonmagnetic impurity, the spin current generation is absent. The spin current flowing though the wire affects the current-voltage characteristic for both magnetic and nonmagnetic impurities. The results have been obtained for a rather strong electron-electron interaction.
We study steady-state charge transfer across an interacting resonance-level model connected asymmetrically to two leads. For a linear energy dispersion relation of the leads, we calculate current-voltage characteristics of the model exactly employing the scattering Bethe ansatz of Mehta-Andrei and find symmetric transport showing the absence of diode effect. Next we study a lattice version of this model with a nonlinear dispersion for the leads using the Lippmann-Schwinger scattering theory. We find that the inclusion of nonlinearity in the leads' dispersion causes rectification for asymmetric junctions but does not rectify for asymmetric interactions and perfect junctions. The model in the latter case can be mapped into a model of a single noninteracting electron in higher dimensions.