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arXiv:cond-mat/0407170 · Physical Review B

Spin effects in transport through non-Fermi-liquid quantum dots

Fabio Cavaliere, Alessandro Braggio, Maura Sassetti, Bernhard Krämer

Published Sep 29, 2004• 16 citations
arXivHTMLPDF

Abstract

The current-voltage characteristic of a one-dimensional quantum dot connected via tunnel barriers to interacting leads is calculated in the region of sequential tunneling. The spin of the electrons is taken into account. Non-Fermi liquid correlations implying spin-charge separation are assumed to be present in the dot and in the leads. It is found that the energetic distance of the peaks in the linear conductance shows a spin-induced parity effect at zero temperature $T$. The temperature dependence of the positions of the peaks depends on the non-Fermi liquid nature of the system. For nonsymmetric tunnel barriers negative differential conductances are predicted, which are related to the participation in the transport of collective states in the quantum dot with larger spins. Without spin-charge separation the negative differential conductances do not occur. Taking into account spin relaxation destroys the spin-induced conductance features. The possibility of observing in experiment the predicted effects are briefly discussed.

DOI
10.1103/physrevb.70.125323

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The current-voltage characteristic of a one-dimensional quantum dot connected via tunnel barriers to interacting leads is calculated in the region of sequential tunneling. The spin of the electrons is taken into account. Non-Fermi liquid correlations implying spin-charge separation are assumed to be present in the dot and in the leads. It is found that the energetic distance of the peaks in the linear conductance shows a spin-induced parity effect at zero temperature TTT. The temperature dependence of the positions of the peaks depends on the non-Fermi liquid nature of the system. For nonsymmetric tunnel barriers negative differential conductances are predicted, which are related to the participation in the transport of collective states in the quantum dot with larger spins. Without spin-charge separation the negative differential conductances do not occur. Taking into account spin relaxation destroys the spin-induced conductance features. The possibility of observing in experiment the predicted effects are briefly discussed.
Interactions in one-dimensional (1D) electron systems are expected to cause a dynamical separation of electronic spin and charge degrees of freedom. A promising system for experimental observation of this non-Fermi-liquid effect consists of two quantum wires coupled via tunneling through an extended uniform barrier. Here we consider the minimal model of an interacting 1D electron system exhibiting spin-charge separation, and calculate the differential tunneling conductance as well as the density-density response function. Both quantities exhibit distinct strong features arising from spin-charge separation. Our analysis of these features within the minimal model neglects interactions between electrons of opposite chirality, and therefore applies directly to chiral 1D electron systems realized, e.g., at the edge of integer quantum Hall systems. Physical insight gained from our results is useful for interpreting current experiment in quantum wires, as our main conclusions still apply with nonchiral interactions present. In particular, we discuss the effect of charging due to applied voltages, and the possibility to observe spin-charge separation in a time-resolved experiment.
We study low energy spin and charge transport through a 1D Mott-Hubbard insulator of finite length LLL attached to Fermi liquid reservoirs characterized by different chemical potentials for electrons of opposite spin polarizations as it happens in quantum spin Hall insulators. We calculate the average currents (charge and spin) and their correlators and demonstrate how a transition induced by the reservoirs to the low energy Fermi liquid regime results in breakdown of the spin-charge separation, which is visible in the presence of the spin dependent voltages and a weak one electron scattering in the system. These calculations are carried out under assumption that the Hubbard gap 2M is large enough: M>TL≡vc/LM > T_L \equiv v_c/LM>TL​≡vc​/L (vcv_cvc​: charge velocity in the wire) and the scattering rate Γs≪TLΓ_s \ll T_LΓs​≪TL​. Relation of these results to Kondo dot transport in the Toulouse limit is also clarified.
We study low-energy spin and charge transport through a 1D Mott-Hubbard insulator of finite length L attached to Fermi liquid reservoirs, which, in the presence of spin accumulation, are characterized by different electrochemical potentials for electrons of opposite spin polarizations. At temperatures less than ( v c : charge velocity in the wire) and under the assumption that the Hubbard gap 2 M is large enough, M > T L , we calculate the average currents (charge and spin) and their zero-frequency correlators. The average spin (charge) current depends only on the difference (sum) of the spin-dependent voltages and even a weak electron backscattering of low rate leads to the spin current suppression at smaller than . The spin current recovers its free mode behavior at spin voltage or temperature larger than Γ. Suppression of the spin-charge correlator suggesting the appearance of spin-charge separation needs both to be larger than Γ. In the absence of the average charge current at its shot noise is proportional to the average spin backscattered current defined by V s and can be used to measure the spin accumulation in the reservoirs. The relation of these results to Kondo dot transport in the Toulouse limit is also clarified.
We study correlated two-level quantum dots, coupled in effective one-channel fashion to metallic leads, with electron interactions including on-level and interlevel Coulomb repulsions, as well as the interorbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics, and electronic transport properties are considered, and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterized by a normal Fermi liquid fixed point (FP) and the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of nonintegral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first-order level-crossing transitions at high symmetry points. A ``Friedel-Luttinger sum rule'' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T=0T=0T=0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase, the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.