Session B24: Focus Session: Transport in Nanostructures II: Strong Correlations

Symmetries and interaction effects in carbon nanotube quantum dots

By controlling the contact transparency within the same nanotube quantum dot, we observe the conductance evolving from the well- developed Coulomb blockade through the Kondo regime to the mixed valence regime. We work with high quality nanotubes, where energy subbands are doubly-degenerate, resulting in the SU(4) Kondo effect for one, two, and three electrons filling two degenerate orbitals. As the contacts are made more transparent, the sample enters the mixed valence regime, where different charge states within a pair of orbitals are hybridized. The hallmark of this regime in nanotube conductance is washing out of single-electron features at low temperature. In our measurement the level broadening is close to the charging energy and level spacing (both $\approx 10$ meV). Nevertheless, the low temperature regime is established only at temperatures of the order or less than 0.5 meV. The same low energy scale is also apparent from the width of the zero-bias peak in the tunneling density of states.   

SU(4) Kondo effect in coupled quantum dots in parallel: Evidence of marginal fixed point

We theoretically study the Kondo effect in coupled quantum dots in parallel, using the scaling and NRG methods. The double quantum dots are capacitively coupled to each other, whereas they are attached to separate leads.\footnote{A.\ Huebel, J.\ Weis and K.von Klitzing, 17th International Conference on the Electronic Properties of Two-Dimensional Systems (EP2DS, 2007).} The SU(4) Kondo effect is realized when the energy levels are matched between the quantum dots. We show that (i) the Kondo temperature $T_K$ decreases with increasing $|\Delta|$, where $\Delta$ is the level separation between the dots, obeying a power law [crossover from SU(4) to SU(2) Kondo effect]. (ii) The exponent of the power law is not a universal value in general.\footnote{M.\ Eto, J.\ Phys.\ Soc.\ Jpn.{\bf 74}, 95 (2005).} This is an evidence of the marginal fixed point of SU(4) Kondo effect.\footnote{L.\ Borda {\it et al}., Phys.\ Rev.\ Lett.\ {\bf 90}, 026602 (2003)} (iii) The conductance through one of the quantum dots may show a non-monotonic behavior as a function of temperature $T$ although the total conductance is a universal function of $T/T_K$.   

Exact-diagonalization treatment of the non-universal transport regime in few-electron quantum dots

Recently, experimental studies\footnote{M. Avinun-Kalish {\it et al.\/}, Nature {\bf 436}, 529 (2005)} have revealed a distinct second transport regime in the behavior of transmission phases obtained via Aharonov-Bohm interferometry using small quantum dots (QDs); namely, a non-universal regime for QDs with $N < 10$ electrons, in addition to the earlier known universal one for larger QDs with $N > 14$. Sophisticated (beyond-the-mean-field) many-body methods are needed for describing this non-universal regime. Here, we study the transport properties of small QDs using exact-diagonalization (EXD) calculations in conjunction with Bardeen's theory of quasiparticle mediated conductance.\footnote{For an adaptation of the formalism to QDs, see S.A. Gurvitz, arXiv:0704.1260v1} We will present EXD calculations\footnote{C. Yannouleas and U. Landman, Rep. Prog. Phys. {\bf 70}, 2067 (2007)} for anisotropic QDs, and for a wide range of anisotropies and strengths of inter-electron repulsion.   

Quantum dot in a Aharonov-Bohm interferometer: magnetic flux-dependent pseudogap in the Kondo regime.

We study a quantum dot embedded in one of the arms of a Aharonov-Bohm interferometer threaded by a magnetic flux $\Phi$. In the regime where a single resonant mode propagates in the interferometer's ``free arm", the system can be described by an effective one-channel Anderson impurity model coupled to a non-constant, flux-dependent density of states (DoS). We present numerical renormalization-group results for the Kondo temperature $T_K$, phase shift and finite-temperature linear conductance. For $\Phi\neq 0$, the ground state of the system is Kondo-like, with a renormalized $T_K$. For $\Phi=0$, the effective DoS \textit{vanishes} at the Fermi energy and the system maps into the pseudogap Anderson model, which displays a quantum critical transition between Kondo and non-Kondo phases [1]. Signatures of these effects appear in the conductance and transmission phase-shifts across the system. This setup constitutes an experimental realization of a tunable pseudogap Anderson Hamiltonian, allowing for an experimental probe into the non-trivial properties of such a model. \newline [1] L.G.G.V. Dias da Silva et al, PRL {\bf 97} 096603 (2006). \newline Supported by NSF-IMC/NIRT.   

Two-particle processes in quantum dots

Inelastic two-electron processes in transport through quantum dots can lead to unexpected effects. At the low temperature Kondo regime, transport is described by an effective low-temperature theory in terms of weakly interacting quasiparticles. Despite the weakness of the interaction, we find that the backscattering current and hence the shot noise are dominated by two-quasiparticle scattering. We show that the simultaneous presence of one- and two- quasiparticle scattering results in a universal average charge 5/3e as measured by shot-noise experiments. As will be presented, recent experimental data measured in the vicinity of the Kondo limit supports our findings. Furthermore, this experiment suggests that many-body effects are not restricted to the low temperature regime only. Extending our study to the high temperature regime, we found under general conditions in Coulomb blockaded quantum dots, signatures of transfer of electron pairs. Those results on many- body corrections to the cotunneling current will be discussed in a related talk by M.E. Raikh.   

Finite-temperature conductance signatures of a quantum-critical transition in a double quantum-dot device

We present conductance results for a quantum-dot system containing one dot in the Kondo regime coupled to two leads in parallel with a noninteracting resonant level. The system can be mapped onto a single-impurity Anderson model with a pseudogapped effective density of states [1]. The finite-temperature linear conductance $G(T)$ of this double-dot device is obtained via numerical renormalization-group calculations. The position of the single-particle levels can be controlled with gate voltages so that the effective density of states vanishes in power-law fashion at the Fermi energy of the leads; within this regime, further tuning can drive the system through a quantum critical point separating Kondo and unscreened phases. Signatures of both effects appear in $G(T)$, with a prominent feature at the scale $T^*$ marking the crossover from the high-temperature quantum-critical regime to a low-temperature Fermi liquid. These results open the way for experimental verification of the effect, and in principle allow access to a quantum critical point in a unique tunable system. [1] L.G.G.V. Dias da Silva et al., PRL {\bf 97}, 096603 (2006).   

Conductance signatures of quantum phase transitions in asymmetric double quantum dots

Double quantum dots (DQDs) are currently of great theoretical and experimental interest. A DQD device in which dot 1 is in the Kondo regime and dot 2 acts as a noninteracting resonant level can be tuned to access a pair of quantum phase transitions separating Kondo-screened and local-moment phases [1]. This talk focuses on the effects of introducing a nonzero Coulomb interaction $U_2$ on the second dot. For small $U_2$, the system continues to exhibit two quantum phase transitions, although their nature is markedly different than for $U_2=0$. However, stronger interactions $U_2 > U_{2,c}$ suppress the local-moment phase and destroy the quantum phase transitions. We use numerical renormalization-group techniques to identify signatures of these behaviors in the linear conductance of the DQD device. [1] L. G. G. V. Dias da Silva, N. P. Sandler, K. Ingersent, and S. E. Ulloa, Phys. Rev. Lett. {\bf 97}, 096603 (2006).   

Symmetries and conductance in Kondo quantum dots

The role of symmetries on nanoscale structures is essential for the different physical behavior exhibited in these systems while its understanding offers deeper insights into the observed properties. The ability to fabricate structures such as quantum dot arrays with tailored symmetries provides further motivation to understand the interplay of geometrical and orbital symmetries in interacting systems at low temperatures, where quantum coherence and Kondo correlations determine the electronic properties. In this work we study the transport properties of three interconnected quantum dots coupled to different leads in a triangular geometry. Conductance calculations carried out in a finite-U slave-boson mean field approximation show excellent agreement with results from the embedded cluster approximation (ECA), highlighting the rich features of the various physical regimes. We focus on and compare two important geometries with: {\em equilateral} (all couplings and leads identical) and {\em isosceles} (one lead and respective couplings different from the others) symmetries. In the first case, we show that only two degenerate orbitals contribute to the Kondo state conductance. Further, we show that the presence of an open third lead in all cases introduces dephasing which affects differently the various features of the conductance.   

Kondo correlations and transport in single and triple quantum dots with damped lead hoppings: a tDMRG study.

We study the transport properties of one and three quantum dot systems with the time-dependent Density Matrix Renormalization-Group method (tDMRG). As previously noted [1,2], finite-size effects make the tDMRG description of the strongly interacting Kondo regime a numerically demanding task. We address this issue by introducing an exponential decay in the hopping terms in the leads ($t_n \propto \Lambda^{-n/2}$), recently introduced in cluster embedding methods [3]. For a given system size, results for $\Lambda>1$ show several improvements over the undamped ($\Lambda=1$)[1,2] case: the Kondo plateau in the differential conductance is correctly obtained deeper in the strongly interacting regime; steady-state current plateaus remain well defined for longer time scales. These results show that, with the proposed modification, the characterization of Kondo correlations in the transport properties can be substantially improved, at less computational cost. [1] K. A. Al-Hassanieh et al. PRB, 73, 195304 (2006). [2] F. Heidrich-Meisner et al. arxiv:0705.1801 (2007). [3] E. Anda et al., pre-print (Nov. 2007).   

Comparative Study of Quantum Monte Carlo and GW methods of treating electronic correlations in nanoscale junctions

We analyze the impact of electronic correlation in nanoscale junctions, focusing on the on-molecule interactions. To discuss the essential physics, we restrict attention to a single resonance coupled to metallic leads and including the local Coulomb interaction, the single-impurity Anderson model. Self-consistent GW results for the linear response conductance, orbital filling and spectral function are compared to numerically exact Quantum Monte Carlo calculations. Our analysis suggests that while the GW approximation may be useful for molecular conductors in the non-resonant tunneling regime, it is not accurate for nanoscale junctions in intermediate to strongly correlated and Kondo regimes.