Transport in carbon nanotubes: Two-level SU(2) regime reveals subtle competition between Kondo and intermediate valence states

Abstract

In this work, we use three different numerical techniques to study the charge transport properties of a system in the two-level SU(2) (2LSU2) regime, obtained from an SU(4) model Hamiltonian by introducing orbital mixing of the degenerate orbitals via coupling to the leads. SU(4) Kondo physics has been experimentally observed, and studied in detail, in Carbon Nanotube Quantum Dots. Adopting a two molecular orbital basis, the Hamiltonian is recast into a form where one of the molecular orbitals decouples from the charge reservoir, although still interacting capacitively with the other molecular orbital. This basis transformation explains in a clear way how the charge transport in this system turns from double-to single-channel when it transitions from the SU(4) to the 2LSU2 regime. The charge occupancy of these molecular orbitals displays gate-potential-dependent occupancy oscillations that arise from a competition between the Kondo and Intermediate Valence states. The determination of whether the Kondo or the Intermediate Valence state is more favorable, for a specific value of gate potential, is assessed by the definition of an energy scale T0, which is calculated through DMRG. We speculate that the calculation of T0 may provide experimentalists with a useful tool to analyze correlated charge transport in many other systems. For that, a current work is underway to improve the numerical accuracy of its DRMG calculation and explore different definitions.

Capacitively coupled double quantum dot system in the Kondo regime

“…This drop signals the transitioning of QD1 from the Kondo to the IV regime, as described above and in Ref. 54. The small peak (of height ≈ 0.3 G 0 ) observed at V g /U ≈ −1 corresponds to the discontinuous jump of the renormalized levelε 1 ≈ ε 1 + U ′ n 2 , caused by the discontinuous change in n 2 from 1 to 0, leading QD1 from a low occupancy ( n 1 ≈ 0.0) IV regime, to a high ( n 1 ≈ 2.0) IV regime, completely skipping the Kondo regime (with occupancy n 1 ≈ 1.0).…”

“…It is important to note the differences and similarities between this model and the one studied in Ref. 54: in the latter, one has a two channel system, where the dark state, for small values of t − , acquires a finite broadening and smoothens out the discontinuities seen in the n 1 and n 2 curves in Fig. 9.…”

“…8 in Ref. 54). On the other hand, it is interesting to notice the emergence of a sharp small peak at the p-h symmetric point for a higher temperature such as T /T K = 1.66 × 10 −1 [(red) ▽ curve].…”

“…The dark state ε 2 acts like a switch between the two regimes and may have applications in quantum computation. 54,56 For example, when the first discontinuity occurs, for V g /U ≈ −0.5, QD1 is in a Kondo state, however, a further decrease of V g makes it energetically more favorable for QD1 to be in an IV state, which can be accomplished by charging QD2 (by exactly one electron), this, due to the capacitive coupling, increases the effective gate potential of QD1, discharging it, and bringing it back to the IV regime. 57 As V g /U further decreases below −0.5, QD1 starts to transition from an IV to a Kondo state; when V g /U ≈ −1, again the IV state for QD1 is more favorable; this regime can now be achieved by completely avoiding the Kondo regime through the discontinuous charging of QD1 by one extra electron.…”

Kondo behavior and conductance through 3d impurities in gold chains doped with oxygen

“…In fact the low-energy effective Hamiltonian for a molecule of iron(II) phtalocyanine on Au(111) has SU(4) symmetry [12,26]. This is also the case for quantum dots in carbon nanotubes [27,28,29,30,31,32,33,34,35]. Recently, the SU(4) Kondo effect has been argued to correspond to experimental observations of a system of two quantum dots for a certain range of parameters [7,36,37,38,39,40,41].…”