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arXiv:0811.2330 · Physical Review B

Features of spin-charge separation in the equilibrium conductance through finite rings

Julián Rincón, Armando A. Aligia, K. Hallberg

Published Jan 15, 2009• 21 citations
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Abstract

We calculate the conductance through rings with few sites $L$ 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 $U$ in comparison with the nearest-neighbor hopping $t$. 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.

DOI
10.1103/physrevb.79.035112

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We calculate the conductance through rings with few sites LLL described by the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model, threaded by a magnetic flux \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ 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 \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ 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 \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ for most systems, in particular at half filling, which might be easier to realize experimentally.
The persistent current and spin-charge separation are studied in a one-dimensional (1D) Hubbard ring with side sites connected to the even sites of the ring. At half filling, the persistent current is always paramagnetic and has a period of flux quantum. Away from half filling, as the onsite repulsion UUU increases, the sign of the current may oscillate depending on the total number of electrons Ne{N}_{e}Ne​ and the hopping ttt between the ring site and the side site. For small hopping ttt, the number of electrons ${N}_{e}^{\ensuremath{'}}$ in the ring sites plays an important role in determining the sign of the current. In contrast to the 1D Hubbard model, a weak or a moderate UUU can strongly enhance the persistent current while the hopping ttt always suppresses the current. The study on the transmittance of the ring with two connected leads indicates that in the large UUU and small ttt case, the transmittance varies with a period $1∕{N}_{e}^{\ensuremath{'}}$ of a flux quantum, demonstrating a spin-charge separation in this system.
This thesis investigates numerically the out of equilibrium properties of quantum rings with magnetic impurities, using the periodic Anderson model (PAM). The model is a simple template for the discussion of the physics of regular arrays of rare-earth impurities in metallic hosts. The system considered is a quantum ring consisting of up to six sites, each of whom are connected to an Anderson impurity site. The dynamical properties of this system are investigated numerically using exact diagonalization and Lanczos adapted time evolution. Two different schemes are used to perturb the system: a magnetic field piercing the ring and a local Zeeman interaction at one of the conduction sites. Comparisons are made with a ring without impurities, and it is shown that for very strong onsite interaction and/or very weak hybridization between the conduction sites and the impurity sites, the physics of a ring without impurities is recovered. Furthermore, a Doniach-type phase diagram in the presence of persistent currents, is provided where it is shown that the Kondo regime is reached for smaller values of the hybridization parameter when a magnetic field piercing the ring is present. The Doniach phase diagram is discussed in connection with persistent currents and entanglement. Preliminary results for the Zeeman field suggests a non trivial interplay between charge and spin currents, and RKKY and Kondo-like couplings.
We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L),D(T,L),D(T,L), in the strongly correlated limit $U\ensuremath{\gg}t$ for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t, we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the $U=\ensuremath{\infty}$ case, the finite-temperature charge stiffness is finite for electronic densities n smaller than 1. These results are essentially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is ${\ensuremath{\Delta}}_{\mathrm{MH}}=U\ensuremath{-}4t,$ and we find that D(T)D(T)D(T) is finite for n<1,n<1,n<1, but is zero at half filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to ${\ensuremath{\Phi}}^{\mathrm{eff}}=\ensuremath{\varphi}{(N}_{h}\ensuremath{-}{N}_{d}{)/(N}_{d}{+N}_{h}),$ and which is zero at half filling, with Nd{N}_{d}Nd​ and Nh{N}_{h}Nh​ being the number of doubly occupied and empty lattice sites, respectively. Further, for half filling, the current transported by any eigenstate of the system is zero and, therefore, D(T)D(T)D(T) is also zero.
The ground-state persistent current and electron addition spectrum in two-dimensional quantum dot arrays and one-dimensional quantum dot rings, pierced by an external magnetic flux, are investigated using the extended Hubbard model. The collective multidot problem is shown to map exactly into the strong-field noninteracting finite-size Hofstadter butterfly problem at the spin polarization transition. The finite-size Hofstadter problem is discussed, and an analytical solution for limiting values of flux is obtained. In weak fields we predict interesting flux periodic oscillations in the spin component along the quantization axis with a periodicity given by $\ensuremath{\nu}h/e$ $(\ensuremath{\nu}<~1)$. The sensitivity of the calculated persistent current to interaction and disorder is shown to reflect the intricacies of various Mott-Hubbard quantum phase transitions in two-dimensional systems: the persistent current is suppressed in the antiferromagnetic Mott-insulating phase governed by intradot Coulomb interactions; the persistent current is maximized at the spin density wave--charge density wave transition driven by the nearest-neighbor interdot interaction; the Mott-insulating phase persistent current is enhanced by the long-range interdot interactions to its noninteracting value; the strong suppression of the noninteracting current in the presence of random disorder is seen only at large disorder strengths; at half-filling even a relatively weak intradot Coulomb interaction enhances the disordered noninteracting system persistent current; in general, the suppression of the persistent current by disorder is less significant in the presence of the long-range interdot Coulomb interaction.
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.