Spin orbit interaction in nanotubes

In recent years, silicene, germanene, and stanene have received considerable attention due to their possibilities to show a spin Hall effect. Nanoribbons made of these materials are expected to have topologically protected states. In this work, we study the electronic properties of nanotubes made of Si, Ge, Sn, and functionalized Sn. The main difference between these materials and graphene is the relevance of spin-orbit interaction. The lack of edge states in a seamless tube eliminates the possibility to find a topological edge state. The spin-orbit interaction breaks the degeneracy of Dirac's cones and eliminates the chances of finding a metal nanotube. As a consequence, this transforms all nanotubes with spin-orbit interaction in trivial band insulators. We focus our attention on two features. First, we study the energy band gap as a function of the diameter of the nanotubes. Then, we concentrate on controlling the band gap of a nanotube by applying an external radial electric field.Comment: 8 pages with 8 figure

New Numerical Results Indicate a Half-Filling SU(4) Kondo State in Carbon Nanotubes

Numerical calculations simulate transport experiments in carbon nanotube quantum dots (P. Jarillo-Herrero et al., Nature 434, 484 (2005)), where a strongly enhanced Kondo temperature T_K ~ 8K was associated with the SU(4) symmetry of the Hamiltonian at quarter-filling for an orbitally double-degenerate single-occupied electronic shell. Our results clearly suggest that the Kondo conductance measured for an adjacent shell with T_K ~ 16K, interpreted as a singlet-triplet Kondo effect, can be associated instead to an SU(4) Kondo effect at half-filling. Besides presenting spin-charge Kondo screening similar to the quarter-filling SU(4), the half-filling SU(4) has been recently associated to very rich physical behavior, including a non-Fermi-liquid state (M. R. Galpin et al., Phys. Rev. Lett. 94, 186406 (2005)).Comment: 7 pages, 7 figure

A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.Comment: 17 pages, 13 figure

Full electrostatic control over polarized currents through spin-orbital Kondo effect

Numerical calculations indicate that by suitably controlling the individual gate voltages of a capacitively coupled parallel double quantum dot, with each quantum dot coupled to one of two independent non-magnetic channels, this system can be set into a spin-orbital Kondo state by applying a magnetic field. This Kondo regime, closely related to the SU(4) Kondo, flips spin from one to zero through cotunneling processes that generate almost totally spin-polarized currents with opposite spin orientation along the two channels. Moreover, by appropriately changing the gate voltages of both quantum dots, one can simultaneously flip the spin polarization of the currents in each channel. As a similar zero magnetic field Kondo effect has been recently observed by Y. Okazaki {\it et al.} [Phys. Rev. B {\bf 84}, (R)161305 (2011)], we analyze a range of magnetic field values where this polarization effect seems robust, suggesting that the setup may be used as an efficient bipolar spin filter, which can generate electrostatically reversible spatially separated spin currents with opposite polarizations.Comment: 6 pages, 8 figures (including supplemental material

Unexpected Conductance Dip in the Kondo Regime of Linear Arrays of Quantum Dots

Using exact-diagonalization of small clusters and Dyson equation embedding techniques, the conductance $G$ of linear arrays of quantum dots is investigated. The Hubbard interaction induces Kondo peaks at low temperatures for an odd number of dots. Remarkably, the Kondo peak is split in half by a deep minimum, and the conductance vanishes at one value of the gate voltage. Tentative explanations for this unusual effect are proposed, including an interference process between two channels contributing to $G$, with one more and one less particle than the exactly-solved cluster ground-state. The Hubbard interaction and fermionic statistics of electrons also appear to be important to understand this phenomenon. Although most of the calculations used a particle-hole symmetric Hamiltonian and formalism, results also presented here show that the conductance dip exists even when this symmetry is broken. The conductance cancellation effect obtained using numerical techniques is potentially interesting, and other many-body techniques should be used to confirm its existence

Electron Transport through a Molecular Conductor with Center-of-Mass Motion

The linear conductance of a molecular conductor oscillating between two metallic leads is investigated numerically both for Hubbard interacting and noninteracting electrons. The molecule-leads tunneling barriers depend on the molecule displacement from its equilibrium position. The results present an interesting interference which leads to a conductance dip at the electron-hole symmetry point, that could be experimentally observable. It is shown that this dip is caused by the destructive interference between the purely electronic and phonon-assisted tunneling channels, which are found to carry opposite phases. When an internal vibrational mode is also active, the electron-hole symmetry is broken but a Fano-like interference is still observed

Kondo regime in triangular arrangements of quantum dots: Molecular orbitals, interference and contact effects

Transport properties of an interacting triple quantum dot system coupled to three leads in a triangular geometry has been studied in the Kondo regime. Applying mean-field finite-U slave boson and embedded cluster approximations to the calculation of transport properties unveils a set of rich features associated to the high symmetry of this system. Results using both calculation techniques yield excellent overall agreement and provide additional insights into the physical behavior of this interesting geometry. In the case when just two current leads are connected to the three-dot system, interference effects between degenerate molecular orbitals are found to strongly affect the overall conductance. An S=1 Kondo effect is also shown to appear for the perfect equilateral triangle symmetry. The introduction of a third current lead results in an `amplitude leakage' phenomenon, akin to that appearing in beam splitters, which alters the interference effects and the overall conductance through the system.Comment: 14 pages, 9 figures, submitted to PR

Interference Effects in the Conductance of Multi-Level Quantum Dots

Using exact-diagonalization techniques supplemented by a Dyson equation embedding procedure, the transport properties of multilevel quantum dots are investigated in the Kondo regime. The conductance can be decomposed into the contributions of each level. It is shown that these channels can carry a different phase, and destructive interference processes are observed when the phase difference between them is $\pm\pi$. This effect is very different from those observed in bulk metals with magnetic impurities, where the phase differences play no significant role. The effect is also different from other recent studies of interference processes in dots, as discussed in the text. In particular, no external magnetic field is here introduced, and the hopping amplitudes dot-leads for all levels are the same. However, conductance cancellations induced by interactions are still observed. Another interesting effect reported here is the formation of localized states that do not participate in the transport. When one of these states crosses the Fermi level, the electronic occupation of the quantum dot changes, modifying the many-body physics of the system and indirectly affecting the transport properties. Novel discontinuities between two finite conductance values can occur as the gate voltage is varied, as discussed here