In-gap states of a quantum dot coupled between a normal and a superconducting lead

Nonlocal correlations transmitted between quantum dots via short topological superconductor

We study the quasiparticle states and nonlocal correlations of a hybrid structure, comprising two quantum dots interconnected through a short-length topological superconducting nanowire hosting overlaping Majorana modes. We show that the hybridization between different components of this setup gives rise to the emergence of molecular states, which are responsible for nonlocal correlations. We inspect the resulting energy structure, focusing on the inter-dependence between the quasiparticles of individual quantum dots. We predict the existence of nonlocal effects, which could be accessed and probed by crossed Andreev reflection spectroscopy. Our study would be relevant to a recent experimental realization of the minimal Kitaev model [T. Dvir et al., Nature 614, 445 (2023) ], by considering its hybrid structure with side-attached quantum dots.

Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices

Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.

Quench dynamics of Fano-like resonances in the presence of the on-dot superconducting pairing

We explore the electron dynamics of a system composed of double quantum dot embedded between metallic and superconducting leads in a "T-shape" geometry. In nanoscopic systems, where electron transfer between electrodes can be realized via different paths, interference effects play an important role. For double quantum dot system in the chosen geometry, interference of electrons transferred between electrodes via the interfacial quantum dot and electrons scattered on the side dot gives rise to Fano-like interference. If such a system is additionally coupled to a superconducting electrode, together with the well-understood Fano resonance an additional resonance appears on the opposite side of the Fermi level. In the recent work (Barański et al. in Sci Rep 10:2881, 2020), we showed that this resonance occurs solely as a result of the local pairing of non-scattered electrons with scattered ones. In this work, considering the quench dynamics, we explore how much time is required for formation of each of these resonances. In particular, (i) we analyze the charge oscillations between subsystems; (ii) we estimate the time required for each resonance to achieve stable equilibrium upon an abrupt change of interdot connection; (iii) we discuss a typical energy and time scales for experiments on similar architectures.

Topological isoconductance signatures in Majorana nanowires

We consider transport properties of a hybrid device composed by a quantum dot placed between normal and superconducting reservoirs, and coupled to a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. It is demonstrated that if highly nonlocal and nonoverlapping MBSs are formed in the system, the zero-bias Andreev conductance through the dot exhibits characteristic isoconductance profiles with the shape depending on the spin asymmetry of the coupling between the dot and the topological superconductor. Otherwise, for overlapping MBSs with less degree of nonlocality, the conductance is insensitive to the spin polarization and the isoconductance signatures disappear. This allows to propose an alternative experimental protocol for probing the nonlocality of the MBSs in Majorana nanowires.

Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states

A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks-features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.

Influence of superconductivity on the magnetic moment of quantum impurity embedded in BCS superconductor

We study the influence of superconductivity on the formation of the localized magnetic moment for a single-level quantum impurity embedded in an s-wave Bardeen-Cooper-Schrieffer (BCS) superconducting medium, modeled by single-impurity Anderson Hamiltonian. We have combined Bogoliubov transformation with Green's function method within self-consistent Hartree-Fock Mean Field approximation to analyze the conditions necessary in metal (in the superconducting) for the formation of the magnetic moment at the impurity site for the low-frequency limit $|\omega|<<\Delta_{sc}$ as well as for the finite superconducting gap $\Delta_{sc}$. We have compared these results with other theoretical results and with the single-level quantum impurity embedded in the normal metallic host. Further we analyze the electronic spectral density of the quantum impurity embedded in superconducting host with the finite superconducting gap to study the sub-gap states as a function of impurity parameters.

Magnetic field effect on trivial and topological bound states of superconducting quantum dot

We investigate the properties of a quantum dot embedded between the normal and superconducting leads which is additionally side-attached to the topological superconducting nanowire, hosting the Majorana modes. This setup enables formation of the trivial (finite-energy) bound states induced in the quantum dot through the superconducting proximity effect, coexisting/competing with the topological (zero-energy) mode transmitted from the topological superconductor. We analyze their interplay, focusing on a role played by the external magnetic field. To distinguish between these bound states we analyze the qualitative and quantitative features manifested in the subgap charge tunneling originating under nonequilibrium conditions from the Andreev (particle to hole) scattering processes.

Anomalous Fano Resonance in Double Quantum Dot System Coupled to Superconductor

We analyze the influence of a local pairing on the quantum interference in nanoscopic systems. As a model system we choose the double quantum dot coupled to one metallic and one superconducting electrode in the T-shape geometry. The analysis is particularly valuable for systems containing coupled objects with considerably different broadening of energy levels. In such systems, the scattering of itinerant electrons on a discrete (or narrow) energy level gives rise to the Fano-type interference. Systems with induced superconducting order, along well understood Fano resonances, exhibit also another features on the opposite side of the Fermi level. The lineshape of these resonances differs significantly from their reflection on the opposite side of the Fermi level, and their origin was not fully understood. Here, considering the spin-polarized tunneling model, we explain a microscopic mechanism of a formation of these resonances and discuss the nature of their uncommon lineshapes. We show that the anomalous Fano profiles originate solely from the pairing of nonscattered electrons with scattered ones. We investigate also the interplay of each type of resonances with the Kondo physics and discuss the resonant features in differential conductivity.

Leakage of Majorana mode into correlated quantum dot nearby its singlet-doublet crossover

We study quasiparticle spectrum of the correlated quantum dot (QD) deposited on superconducting (SC) substrate which is side-coupled to the Rashba nanochain, hosting Majorana end modes. Ground state of an isolated QD proximitized to SC reservoirs is represented either by the singly occupied site or BCS-type superposition of the empty and doubly occupied configurations. Quantum phase transition between these distinct ground states is spectroscopically manifested by the in-gap Andreev states which cross each other at the Fermi level. This qualitatively affects leakage of the Majorana mode from the side-attached nanowire. We inspect the spin-selective relationship between the trivial Andreev states and the leaking Majorana mode, considering (i) perfectly polarized case, when tunneling of one spin component is completely prohibited, and (ii) another one when both spins are hybridized with the nanowire but with different couplings.

Zeeman Tunability of Andreev Bound States in van der Waals Tunnel Barriers

Quantum dots proximity coupled to superconductors are attractive research platforms due to the intricate interplay between the single-electron nature of the dot and the many body nature of the superconducting state. These have been studied mostly using nanowires and carbon nanotubes, which allow a combination of tunability and proximity. Here we report a new type of quantum dot which allows proximity to a broad range of superconducting systems. The dots are realized as embedded defects within semiconducting tunnel barriers in van der Waals layers. By placing such layers on top of thin NbSe_{2}, we can probe the Andreev bound state spectra of such dots up to high in-plane magnetic fields without observing the effects of a diminishing superconducting gap. As tunnel junctions defined on NbSe_{2} have a hard gap, we can map the subgap spectra without a background related to the rest of the junction. We find that the proximitized defect states invariably have a singlet ground state, manifest in the Zeeman splitting of the subgap excitation. We also find, in some cases, bound states that converge to zero energy and remain there. We discuss the role of the spin-orbit term, present both in the barrier and the superconductor, in the realization of such topologically trivial zero-energy states.

Interplay between correlations and Majorana mode in proximitized quantum dot

We study the low energy spectrum and transport properties of a correlated quantum dot coupled between normal and superconducting reservoirs and additionally hybridized with a topological superconducting nanowire, hosting the Majorana end-modes. In this setup the Majorana quasiparticle leaking into the quantum dot can be confronted simultaneously with the on-dot pairing and correlations. We study this interplay, focusing on the quantum phase transition from the spinless (BCS-type) to the spinful (singly occupied) configuration, where the subgap Kondo effect may arise. Using the selfconsistent perturbative treatment for correlations and the unbiased numerical renormalization group calculations we find that the Majorana mode has either constructive or destructive effect on the low-energy transport behavior of the quantum dot, depending on its spin. This spin-selective influence could be verified by means of the polarized STM spectroscopy.

Interplay between pairing and correlations in spin-polarized bound states

We investigate single and multiple defects embedded in a superconducting host, studying the interplay between the proximity-induced pairing and interactions. We explore the influence of the spin-orbit coupling on energies, polarization and spatial patterns of the bound (Yu-Shiba-Rusinov) states of magnetic impurities in a two-dimensional square lattice. We also address the peculiar bound states in the proximitized Rashba chain, resembling the Majorana quasiparticles, focusing on their magnetic polarization that has been recently reported by S. Jeon et al. (Science2017,358, 772). Finally, we study leakage of these polarized Majorana quasiparticles into side-attached nanoscopic regions and confront them with the subgap Kondo effect near to the singlet-doublet phase transition.

Spin-sensitive interference due to Majorana state on the interface between normal and superconducting leads

We investigate the subgap spectrum and transport properties of the quantum dot on the interface between the metallic and superconducting leads and additionally side-coupled to the edge of the topological superconducting (TS) chain, hosting the Majorana quasiparticle. Due to the chiral nature of the Majorana states only one spin component of the quantum dot electrons (say [Formula: see text]) is directly affected, however the proximity induced on-dot pairing transmits its influence on the opposite spin as well. We investigate the unique interferometric patterns driven by the Majorana quasiparticle that are different for each spin component. We also address the spin-sensitive interplay with the Kondo effect manifested at the same zero-energy and we come to the conclusion that quantum interferometry can unambiguously identify the Majorana quasiparticle.

Andreev and Majorana bound states in single and double quantum dot structures

We present a numerical study of the emergence of Majorana and Andreev bound states in a system composed of two quantum dots, one of which is coupled to a conventional superconductor, SC1, and the other connects to a topological superconductor, SC2. By controlling the interdot coupling we can drive the system from two single (uncoupled) quantum dots to double (coupled) dot system configurations. We employ a recursive Green's function technique that provides us with numerically exact results for the local density of states of the system. We first show that in the uncoupled dot configuration (single dot behavior) the Majorana and the Andreev bound states appear in an individual dot in two completely distinct regimes. Therefore, they cannot coexist in the single quantum dot system. We then study the coexistence of these states in the coupled double dot configuration. In this situation we show that in the trivial phase of SC2, the Andreev states are bound to an individual quantum dot in the atomic regime (weak interdot coupling) or extended over the entire molecule in the molecular regime (strong interdot coupling). More interesting features are actually seen in the topological phase of SC2. In this case, in the atomic limit, the Andreev states appear bound to one of the quantum dots while a Majorana zero mode appears in the other one. In the molecular regime, on the other hand, the Andreev bound states take over the entire molecule while the Majorana state remains always bound to one of the quantum dots.

Constructive influence of the induced electron pairing on the Kondo state

Superconducting order and magnetic impurities are usually detrimental to each other. We show, however, that in nanoscopic objects the induced electron pairing can have constructive influence on the Kondo effect originating from the effective screening interactions. Such situation is possible at low temperatures in the quantum dots placed between the conducting and superconducting reservoirs, where the proximity induced electron pairing cooperates with the correlations amplifying the spin-exchange potential. The emerging Abrikosov-Suhl resonance, which is observable in the Andreev conductance, can be significantly enhanced by increasing the coupling to superconducting lead. We explain this intriguing tendency within the Anderson impurity model using: the generalized Schrieffer-Wolff canonical transformation, the second order perturbative treatment of the Coulomb repulsion, and the nonperturbative numerical renormalization group calculations. We also provide hints for experimental observability of this phenomenon.

Enhancements of the Andreev conductance due to emission/absorption of bosonic quanta

We predict that the subgap spectrum and transport properties of the quantum dot embedded between superconducting and metallic reservoirs can be substantially enhanced by emission/absorption of external bosonic quanta. Upon tuning the gate voltage the in-gap Andreev states eventually interfere with each other. We explore the measurable signatures of such interference appearing in the differential conductance for both linear and nonlinear regimes.