Edson Vernek

Subtle leakage of a Majorana mode into a quantum dot

We investigate quantum transport through a quantum dot connected to source and drain leads and side coupled to a topological superconducting nanowire (Kitaev chain) sustaining Majorana end modes. Using a recursive Green’s-function approach, we determine the local density of states of the system and find that the end Majorana mode of the wire leaks into the dot, thus, emerging as a unique dot level pinned to the Fermi energy eF of the leads. Surprisingly, this resonance pinning, resembling, in this sense, a “Kondo resonance,” occurs even when the gate-controlled dot level edot(Vg) is far above or far below eF . The calculated conductance G of the dot exhibits an unambiguous signature for the Majorana end mode of the wire: In essence, an off-resonance dot [edot(Vg) � eF ], which should have G = 0, shows, instead, a conductance e 2 /2h over a wide range of Vg due to this pinned dot mode. Interestingly, this pinning effect only occurs when the dot level is coupled to a Majorana mode; ordinary fermionic modes (e.g., disorder) in the wire simply split and broaden (if a continuum) the dot level. We discuss experimental scenarios to probe Majorana modes in wires via these leaked/pinned dot modes.

Suppression of Kondo screening by the Dicke effect in multiple quantum dots

Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute,Ohio University, Athens, Ohio 45701-2979(Dated: September 21, 2010)The interplay between the coupling of an interacting quantum dot to a conduction band and itsconnection to localized levels has been studied in a triple quantum dot arrangement. The electronicDicke effect, resulting from quasi-resonant states of two side-coupled non-interacting quantum dots,is found to produce important effects on the Kondo resonance of the interacting dot. We studyin detail the Kondo regime of the system by applying a numerical renormalization group analysisto a finite-U multi-impurity Anderson Hamiltonian model. We find an extreme narrowing of theKondo resonance, as the single-particle levels of the side dots are tuned towards the Fermi level and“squeeze” the Kondo resonance, accompanied by a strong drop in the Kondo temperature, due tothe presence of a supertunneling state. Further, we show that the Kondo temperature vanishes inthe limit of the Dicke effect of the structure. By analyzing the magnetic moment and entropy ofthe three-dot cluster versus temperature, we identify a different local singlet that competes with theKondo state, resulting in the eventual suppression of the Kondo temperature and strongly affectingthe spin correlations of the structure. We further show that system asymmetries in couplings, levelstructure or due to Coulomb interactions, result in interesting changes in the spectral function nearthe Fermi level. These strongly affect the Kondo temperature and the linear conductance of thesystem.

Kondo screening suppression by spin-orbit interaction in quantum dots

We study the transport properties of a quantum dot embedded in an Aharonov-Bohm ring in the presence of spin-orbit interactions. Using a numerical renormalization-group analysis of the system in the Kondo regime, we find that the competition of Aharonov-Bohm and spin-orbit dynamical phases induces a strong suppression of the Kondo state singlet, somewhat akin to an effective intrinsic magnetic field in the system. This effective field breaks the spin degeneracy of the localized state and produces a finite magnetic moment in the dot. By introducing an in-plane Zeeman field we show that the Kondo resonance can be fully restored, re-establishing the spin singlet and a desired spin-filtering behavior in the Kondo regime, which may result in full spin polarization of the current through the ring.

Spin-polarized conductance in double quantum dots: Interplay of Kondo, Zeeman, and interference effects

We study the effect of a magnetic field in the Kondo regime of a double-quantum-dot system consisting of a strongly correlated dot (the “side dot”) coupled to a second, noninteracting dot that also connects two external leads. We show, using the numerical renormalization group, that application of an in-plane magnetic field sets up a subtle interplay between electronic interference, Kondo physics, and Zeeman splitting with nontrivial consequences for spectral and transport properties. The value of the side-dot spectral function at the Fermi level exhibits a nonuniversal field dependence that can be understood using a form of the Friedel sum rule that appropriately accounts for the presence of an energy- and spin-dependent hybridization function. The applied field also accentuates the exchange-mediated interdot coupling, which dominates the ground state at intermediate fields leading to the formation of antiparallel magnetic moments on the dots. By tuning gate voltages and the magnetic field, one can achieve complete spin polarization of the linear conductance between the leads, raising the prospect of applications of the device as a highly tunable spin filter. The system’s low-energy properties are qualitatively unchanged by the presence of weak on-site Coulomb repulsion within the second dot.

Enhanced photon-assisted spin transport in a quantum dot attached to ferromagnetic leads

We investigate real-time dynamics of spin-polarized current in a quantum dot coupled to ferromagnetic leads in both parallel and antiparallel alignments. While an external bias voltage is taken constant in time, a gate terminal, capacitively coupled to the quantum dot, introduces a periodic modulation of the dot level. Using non equilibrium Greens function technique we find that spin polarized electrons can tunnel through the system via additional photon-assisted transmission channels. Owing to a Zeeman splitting of the dot level, it is possible to select a particular spin component to be photon-transfered from the left to the right terminal, with spin dependent current peaks arising at different gate frequencies. The ferromagnetic electrodes enhance or suppress the spin transport depending upon the leads magnetization alignment. The tunnel magnetoresistance also attains negative values due to a photon-assisted inversion of the spin-valve effect.

Capacitively coupled double quantum dot system in the Kondo regime

A detailed study of the low-temperature physics of an interacting double quantum dot system in a T-shape configuration is presented. Each quantum dot is modeled by a single Anderson impurity and we include an inter-dot electron-electron interaction to account for capacitive coupling that may arise due to the proximity of the quantum dots. By employing a numerical renormalization group approach to a multi-impurity Anderson model, we study the thermodynamical and transport properties of the system in and out of the Kondo regime. We find that the two-stage-Kondo effect reported in previous works is drastically affected by the inter-dot Coulomb repulsion. In particular, we find that the Kondo temperature for the second stage of the two-stage-Kondo effect increases exponentially with the inter-dot Coulomb repulsion, providing a possible path for its experimental observation.

Spin filtering in a double quantum dot device: Numerical renormalization group study of the internal structure of the Kondo state

A double quantum dot device, connected to two channels that only interact through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. Using a two-impurity Anderson model, and realistic parameter values [S. Amasha, A. J. Keller, I. G. Rau, A. Carmi, J. A. Katine, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Phys. Rev. Lett. 110, 046604 (2013)], it is shown that, by applying a moderate magnetic field and independently adjusting the gate potential of each quantum dot at half-filling, a spin-orbital SU(2) Kondo state can be achieved where the Kondo resonance originates from spatially separated parts of the device. Our results clearly link this spatial separation effect to currents with opposing spin polarizations in each channel, i.e., the device acts as a spin filter. In addition, an experimental probe of this polarization effect is suggested, pointing to the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.

Kondo regime of a quantum dot molecule: A finite-U slave boson approach

We study the electronic transport in a double quantum dot structure connected to leads in the Kondo regime for both series and parallel arrangements. By applying a finite-U slave boson technique in the mean field approximation we explore the effect of level degeneracy in the conductance through the system. Our results show that for the series connection, as the energy difference of the localized dot levels increases, the tunneling via the Kondo state is destroyed. For the parallel configuration, we find an interesting interplay of state symmetry and conductance. Our results are in good agreement with those obtained with other methods, and provide additional insights into the physics of the Kondo state in the double dot system.

Conductance and Kondo Interference beyond Proportional Coupling

The transport properties of nanostructured systems are deeply affected by the geometry of the effective connections to metallic leads. In this work we derive a conductance expression for a class of interacting systems whose connectivity geometries do not meet the Meir-Wingreen proportional coupling condition. As an interesting application, we consider a quantum dot connected coherently to tunable electronic cavity modes. The structure is shown to exhibit a well-defined Kondo effect over a wide range of coupling strengths between the two subsystems. In agreement with recent experimental results, the calculated conductance curves exhibit strong modulations and asymmetric behavior as different cavity modes are swept through the Fermi level. These conductance modulations occur, however, while maintaining robust Kondo singlet correlations of the dot with the electronic reservoir, a direct consequence of the lopsided nature of the device.

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

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 the 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 density matrix renormalization group (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 under way to improve the numerical accuracy of its DRMG calculation and explore different definitions.