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 ${\varepsilon }_F$ of the leads. Surprisingly, this resonance pinning, resembling, in this sense, a “Kondo resonance,” occurs even when the gate-controlled dot level ${\varepsilon }_{\mathrm{dot}}\left(V_g\right)$ is far above or far below ${\varepsilon }_F$. 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 [${\varepsilon }_{\mathrm{dot}}\left(V_g\right)\ne {\varepsilon }_F$], which should have $G=0$, shows, instead, a conductance $e^2/2h$ over a wide range of $V_g$ 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.

We have recently shown [ Phys. Rev. B 89, 165314 (2014)] that a noninteracting quantum dot coupled to a one-dimensional topological superconductor and to normal leads can sustain a Majorana mode even when the dot is expected to be empty, i.e., when the dot energy level is far above the Fermi level of the leads. This is due to the Majorana bound state of the wire leaking into the quantum dot. Here we extend this previous work by investigating the low-temperature quantum transport through an interacting quantum dot connected to source and drain leads and side coupled to a topological wire. We explore the signatures of a Majorana zero mode leaking into the quantum dot for a wide range of dot parameters, using a recursive Green's function approach. We then study the Kondo regime using numerical renormalization group calculations. We observe the interplay between the Majorana mode and the Kondo effect for different dot-wire coupling strengths, gate voltages, and Zeeman fields. Our results show that a “0.5” conductance signature appears in the dot despite the interplay between the leaked Majorana mode and the Kondo effect. This robust feature persists for a wide range of dot parameters, even when the Kondo correlations are suppressed by Zeeman fields and/or gate voltages. The Kondo effect, on the other hand, is suppressed by both Zeeman fields and gate voltages. We show that the zero-bias conductance as a function of the magnetic field follows a well-known universality curve. This can be measured experimentally, and we propose that the universal conductance drop followed by a persistent conductance of $0.5e^2/h$ is evidence of the presence of Majorana-Kondo physics. These results confirm that this “0.5” Majorana signature in the dot remains even in the presence of the Kondo effect.

The spatial length of the Kondo screening is still a controversial issue related to Kondo physics. While renormalization-group and Bethe-Ansatz solutions have provided detailed information about the thermodynamics of magnetic impurities, they are insufficient to study the effect on the surrounding electrons, i.e., the spatial range of the correlations created by the Kondo effect between the localized magnetic moment and the conduction electrons. The objective of this work is to present a quantitative way of measuring the extension of these correlations by studying their effect directly on the local density of states (LDOS) at arbitrary distances from the impurity. The numerical techniques used, the embedded cluster approximation, the finite-U slave bosons, and numerical renormalization group, calculate the Green's functions in real space. With this information, one can calculate how the local density of states away from the impurity is modified by its presence, below and above the Kondo temperature, and then estimate the range of the disturbances in the noninteracting Fermi sea due to the Kondo effect, and how it changes with the Kondo temperature TK. The results obtained agree with results obtained through spin-spin correlations, showing that the LDOS captures the phenomenology of the Kondo cloud as well.

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.

Transport properties of an interacting triple quantum dot system coupled to three leads in a triangular geometry have 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.

The interplay between the coupling of an interacting quantum dot to a conduction band and its connection to localized levels has been studied in a triple quantum-dot arrangement. The electronic Dicke effect, resulting from quasiresonant states of two side-coupled noninteracting quantum dots, is found to produce important effects on the Kondo resonance of the interacting dot. We study in detail the Kondo regime of the system by applying a numerical renormalization-group analysis to a finite-$U$ multi-impurity Anderson Hamiltonian model. We find an extreme narrowing of the Kondo resonance, as the single-particle levels of the side dots are tuned toward the Fermi level and “squeeze” the Kondo resonance, accompanied by a strong drop in the Kondo temperature, due to the presence of a supertunneling state. Further, we show that the Kondo temperature vanishes in the limit of the Dicke effect of the structure. By analyzing the magnetic moment and entropy of the three-dot cluster versus temperature, we identify a different local singlet that competes with the Kondo state, resulting in the eventual suppression of the Kondo temperature and strongly affecting the spin correlations of the structure. We further show that system asymmetries in couplings, level structure or due to Coulomb interactions, result in interesting changes in the spectral function near the Fermi level. These strongly affect the Kondo temperature and the linear conductance of the system.