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arXiv:0811.2231 · Physical Review B

Spin-charge separation in strongly interacting finite ladder rings

Julián Rincón, K. Hallberg, Armando A. Aligia

Published Sep 29, 2008• 8 citations
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Abstract

We study the conductance through Aharonov-Bohm finite ladder rings with strongly interacting electrons, modeled by the prototypical $t\text{\ensuremath{-}}J$ model. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux, predicted so far only in chains which are a signature of spin and charge separation. These results open the possibility of observing this peculiar many-body phenomenon in anisotropic ladder systems and in real nanoscopic devices.

DOI
10.1103/physrevb.78.125115

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We study the conductance through Aharonov-Bohm finite ladder rings with strongly interacting electrons, modeled by the prototypical t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux, predicted so far only in chains which are a signature of spin and charge separation. These results open the possibility of observing this peculiar many-body phenomenon in anisotropic ladder systems and in real nanoscopic devices.
We study manifestations of spin-charge separation (SCS) in transport through a tunnel-coupled interacting single-channel quantum ring. We focus on the high-temperature case (temperature TTT larger than the level spacing $\mathrm{\ensuremath{\Delta}}$) and discuss both the classical (flux-independent) and interference contributions to the tunneling conductance of the ring in the presence of magnetic flux. We demonstrate that the SCS effects, which arise solely from the electron-electron interaction, lead to the appearance of a peculiar fine structure of the electron spectrum in the ring. Specifically, each level splits into a series of sublevels, with their spacing governed by the interaction strength. In the high-TTT limit, the envelope of the series contains of the order of $T/\mathrm{\ensuremath{\Delta}}$ sublevels. At the same time, SCS suppresses the tunneling width of the sublevels by a factor of $\mathrm{\ensuremath{\Delta}}/T$. As a consequence, the classical transmission through the ring remains unchanged compared to the noninteracting case: the suppression of tunneling is compensated by the increase of the number of tunneling channels. On the other hand, the flux-dependent contribution to the conductance depends on the interaction-induced dephasing rate which is known to be parametrically increased by SCS in an infinite system. We show, however, that SCS is not effective for dephasing in the limit of weak tunneling. Moreover, generically, in the almost closed ring, the dephasing rate does not depend on the interaction strength and is determined by the tunneling coupling to the leads. In certain special symmetric cases, dephasing is further suppressed. Similarly to the spinless case, the high-TTT conductance shows, as a function of magnetic flux, a sequence of interaction-induced sharp negative peaks on top of the classical contribution.
We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the $t\text{\ensuremath{-}}V$ spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism.
We consider a ring of strongly interacting electrons connected to two external leads by tunnel junctions. By studying the positions of conductance resonances as a function of gate voltage and magnetic flux, the interaction parameter ggg can be determined experimentally. For a finite ring the minimum conductance is strongly influenced by device geometry and electron-electron interactions. In particular, if the tunnel junctions are close to one another, the interaction-related orthogonality catastrophe is suppressed and the valley current is unexpectedly large.
We investigate how the different velocities characterizing the low-energy spectral properties and the low-temperature thermodynamics of one-dimensional correlated electron systems (Luttinger liquids) affect the transport properties of ringlike conductors. The Luttinger liquid ring is coupled to two noninteracting leads and pierced by a magnetic flux. We study the flux dependence of the linear conductance. It shows a dip structure that is governed by the interaction dependent velocities. Our work extends an earlier study that was restricted to rather specific choices of the interaction parameters. We show that for generic repulsive two-particle interactions, the number of dips can be estimated from the ratio of the charge current velocity and the spin velocity. In addition, we clarify the range of validity of the central approximation underlying the earlier study.
We calculate the conductance through rings with few sites LLL described by the $t\text{\ensuremath{-}}J$ model, threaded by a magnetic flux $\ensuremath{\Phi}$ and weakly coupled to conducting leads at two arbitrary sites. The model can describe a circular array of quantum dots with large charging energy UUU in comparison with the nearest-neighbor hopping ttt. We determine analytically the particular values of $\ensuremath{\Phi}$ for which a depression of the transmittance is expected as a consequence of spin-charge separation. We show numerically that the equilibrium conductance at zero temperature is depressed at those particular values of $\ensuremath{\Phi}$ for most systems, in particular at half filling, which might be easier to realize experimentally.