We study the out-of-equilibrium current through an interacting quantum dot modelled as an Anderson impurity contacted by two BCS superconductors held at fixed voltage bias. In order to account for multiple Andreev reflections, we develop a Keldysh Green's function scheme perturbative in the dot's interaction strength. We find an unexpected enhancement of the current due to repulsive interactions for small lead-to-dot couplings.
We present a theory of non-equilibrium superconducting proximity effect in an interacting quantum dot induced by a time-dependent tunnel coupling between dot and a superconducting lead. The proximity effect, that is established when the driving frequency fulfills a gate-voltage-dependent resonance condition, can be probed through the tunneling current into a weakly-coupled normal lead. Furthermore, we propose to generate and manipulate coherent superpositions of quantum-dot states with electron numbers differing by two, by applying pulsed oscillatory variations to the couplings between dot and…
We consider the energetics of a superconducting double dot, comprising two superconducting islands coupled in series via a Josephson junction. The periodicity of the stability diagram is governed by the competition between the charging energy and the superconducting gap, and the stability of each charge state depends upon its parity. We also find that, at finite temperatures, thermodynamic considerations have a significant effect on the stability diagram.
Electrons in a quantum-dot spin valve, consisting of a single-level quantum dot coupled to two ferromagnetic leads with magnetizations pointing in arbitrary directions, experience an exchange field that is induced on the dot by the interplay of Coulomb interaction and quantum fluctuations. We show that a third, superconducting lead with large superconducting gap attached to the dot probes this exchange field very sensitively. In particular, we find striking signatures of the exchange field in the symmetric component of the supercurrent with respect to the bias voltage applied between the ferro…
The superconducting reservoir effect on the current carrying transport of a double quantum dot in Markovian regime is investigated. For this purpose, a quantum master equation (QME) at finite temperature is derived for the many-body density matrix of an open quantum system. The dynamics and the steady-state properties of the double quantum dot system for arbitrary bias are studied. We will show that how the populations and coherencies of the system states are affected by superconducting leads. The energy parameter of system contains essentially four contributions due to dots system-electrodes …
We study subgap transport from a superconductor through a double quantum dot with large on-site Coulomb repulsion to two normal leads. Non-local superconducting correlations in the double dot are induced by the proximity to the superconducting lead, detectable in non-local Andreev transport that splits Cooper pairs in locally separated, spin-entangled electrons. We find that the $I$--$V$ characteristics are strongly asymmetric: for a large bias voltage of certain polarity, transport is blocked by populating the double dot with states whose spin symmetry is incompatible with the superconductor.…
We investigate the thermoelectric properties of a quantum dot coupled to ferromagnetic and superconducting electrodes. The combination of spin polarized tunneling at the ferromagnetic-quantum dot interface and the application of an external magnetic field that Zeeman splits the dot energy level leads to large values of the thermopower (Seebeck coefficient). Importantly, the thermopower can be tuned with an external gate voltage connected to the dot. We compute the figure of merit that measures the efficiency of thermoelectric conversion and find that it attains high values. We discuss the diff…
We analyze the heat current traversing a quantum dot sandwiched between a ferromagnetic and a superconducting electrode. The heat flow generated in response to a voltage bias presents rectification as a function of the gate potential applied to the quantum dot. Remarkably, in the thermally driven case the heat shows a strong diode effect with large asymmetry ratios that can be externally tuned with magnetic fields or spin-polarized tunneling. Our results thus demonstrate the importance of hybrid systems as promising candidates for thermal applications.
We present a microscopic theory of transport through quantum dot set-ups coupled to superconducting leads. We derive a master equation for the reduced density matrix to lowest order in the tunneling Hamiltonian and focus on quasiparticle tunneling. For high enough temperatures transport occurs in the subgap region due to thermally excited quasiparticles, which can be used to observe excited states of the system for low bias voltages. On the example of a double quantum dot we show how subgap transport spectroscopy can be done. Moreover, we use the single level quantum dot coupled to a normal an…
We investigate subgap quasiparticles of a single level quantum dot coupled to the superconducting and normal leads, whose energy level is periodically driven by external potential. Using the Floquet formalism we determine the quasienergies and analyze redistribution of their spectral weights between individual harmonics upon varying the frequency and amplitude of the driving potential. We also propose feasible spectroscopic methods for probing the in-gap quasiparticles observable in the differential conductance of the charge current averaged over a period of oscillations.
We report direct detection of charge-tunneling between a quantum dot and a superconducting island through radio-frequency gate sensing. We are able to resolve spin-dependent quasiparticle tunneling as well as two-particle tunneling involving Cooper pairs. The quantum dot can act as an RF-only sensor to characterize the superconductor addition spectrum, enabling us to access subgap states without transport. Our results provide guidance for future dispersive parity measurements of Majorana modes, which can be realized by detecting the parity-dependent tunneling between dots and islands.
We have studied the Waiting Time Distributions (WTDs) for sub-gap transport through a single-level quantum dot tunnel coupled to one normal and one superconducting lead. The WTDs reveal the internal dynamics of the system in particular the coherent transfer of Cooper pairs between the dot and the superconductor. The WTDs exhibit oscillations that can be directly associated to the coherent oscillation between the empty and doubly occupied dot. The oscillation frequency is equal to the energy splitting between the Andreev bound states. These effects are more pronounced when the empty state and d…
We measure the non-dissipative supercurrent in a single InAs self-assembled quantum dot (QD) coupled to superconducting leads. The QD occupation is both tuned by a back-gate electrode and lateral side-gate. The geometry of the side-gate allows tuning of the QD-lead tunnel coupling in a region of constant electron number with appropriate orbital state. Using the side-gate effect we study the competition between Kondo correlations and superconducting pairing on the QD, observing a decrease in the supercurrent when the Kondo temperature is reduced below the superconducting energy gap in qualitati…
Epitaxial semiconductor-superconductor hybrid materials are an excellent basis for studying mesoscopic and topological superconductivity, as the semiconductor inherits a hard superconducting gap while retaining tunable carrier density. Here, we investigate double-quantum-dot devices made from InAs nanowires with a patterned epitaxial Al two-facet shell that proximitizes two gate-defined segments along the nanowire. We follow the evolution of mesoscopic superconductivity and charging energy in this system as a function of magnetic field and voltage-tuned barriers. Inter-dot coupling is varied f…
We investigate transport and thermoelectric properties of hybrid systems based on a single-level quantum dot and one superconducting lead. The other lead is generally normal-metallic ferromagnet. In the latter case single-particle transport is spin-polarized. Our main interest is in the interplay of Andreev tunneling of Cooper pairs and single-particle tunneling. The latter is responsible for relatively large thermopower and figure of merit due to a diverging density of single-particle states at the superconducting gap edges. System with ferromagnetic and superconducting leads can also reveal …
We propose a highly efficient thermoelectric diode device built from the coupling of a quantum dot with a normal or ferromagnetic electrode and a superconducting reservoir. The current shows a strongly nonlinear behavior in the forward direction (positive thermal gradients) while it almost vanishes in the backward direction (negative thermal gradients). Our discussion is supported by a gauge-invariant current-conserving transport theory accounting for electron-electron interactions inside the dot. We find that the diode behavior is greatly tuned with external gate potentials, Zeeman splittings…
We consider different configurations of ac driven quantum dots coupled to superconductor leads where Majorana fermions can exist as collective quasiparticles. The main goal is to tune the existence, localization and properties of these zero energy quasiparticles by means of periodically driven external gates. In particular, we analyze the relevance of the system and driving symmetry. We predict the existence of different sweet spots with Floquet Majorana fermions in configurations where they are not present in the undriven system.
Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Sta…
We investigate the origin of matching effect observed in disordered superconducting NbN thin films with periodic array of holes. In addition to the periodic variation in the electrical resistance just above the superconducting transition temperature, Tc0, we find pronounced periodic variations with magnetic field in all dynamical quantities which can be influenced by flux-line motion under an external drive such as the magnetic shielding response and the critical current which survive in some samples down to temperatures as low as 0.09Tc0. In contrast, the superconducting energy gap, D which i…
We report conductance and supercurrent measurements for InAs single and parallel double quantum dot Josephson junctions contacted with Nb or NbTiN superconducting electrodes. Large superconducting gap energy, high critical field and large switching current are observed, all reflecting the features of Nb-based electrodes. For the parallel double dots we observe an enhanced supercurrent when both dots are on resonance, which may reflect split Cooper pair tunneling.
We report on the study of the non-trivial Berry phase in superconducting multiterminal quantum dots biased at commensurate voltages. Starting with the time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model in the Floquet space, and we solve these equations in the semiclassical limit. We observe that the parameter space defined by the contact transparencies and quartet phase splits into two components with a non-trivial Berry phase. We use the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if the quantum dot level sits at zero energy, then the Ber…
We discuss the nonlinear Andreev current of an interacting quantum dot coupled to spin-polarized and superconducting reservoirs when voltage and temperature biases are applied across the nanostructure. Due to the particle-hole symmetry introduced by the superconducting (S) lead, the subgap spin current vanishes identically. Nevertheless, the Andreev charge current depends on the degree of polarization in the ferromagnetic (F) contact since the shift of electrostatic internal potential of the conductor depends on spin orientation of the charge carrier. This spin-dependent potential shift charac…
We study the full counting statistics of charge transport through a quantum dot tunnel-coupled to one normal and one superconducting lead with a large superconducting gap. As function of the level detuning, there is a crossover from a regime with strong superconducting correlations in the quantum dot to a regime in which the proximity effect on the quantum dot is suppressed. We analyze the current fluctuations of this crossover in the shot-noise regime. In particular, we predict that the full counting statistics changes from Poissonian with charge 2e, typical for Cooper pairs, to Poissonian wi…
We study the nonlinear cotunneling current through a spinful quantum dot contacted by two superconducting leads. Applying a general nonequilibrium Green function formalism to an effective Kondo model, we study the rich variation in the IV-characteristics with varying asymmetry in the tunnel coupling to source and drain electrodes. The current is found to be carried respectively by multiple Andreev reflections in the symmetric limit, and by spin-induced Yu-Shiba-Russinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different IV…
A normal metal source reservoir can load two electrons onto a double quantum dot in the spin-triplet configuration. We show that if the drain lead of the dot is a spin-singlet superconductor, these electrons cannot form a Cooper pair and are blockaded on the double dot. We call this phenomenon Andreev blockade because it arises due to suppressed Andreev reflections. We identify transport characteristics unique to Andreev blockade. Most significantly, it occurs for any occupation of the dot adjacent to the superconductor, in contrast with the well-studied Pauli blockade which requires odd occup…
Hanbury Brown Twiss effects in channel mixing normal-superconducting systems
本文研究了邻近效应在多端、通道混合、正常超导系统中电流互相关中的作用。所提出的实验是光学Hanbury Brown Twiss强度互相关实验的电学模拟。混沌量子点通过量子点接触连接到两个正常和一个超导水库。为了控制点到超导储层的耦合，点中的通量量子量级的磁通量抑制邻近效应并将互相关的符号从正反转为负。在相反的限制，对于一个占主导地位的耦合到正常的水库，邻近效应是弱的，交叉相关是积极的点和超导水库之间的非理想接触。我们表明，在这个限制的相关性可以解释粒子计数参数。
We present a derivation of Markovian master equation for the out of equilibrium quantum dot connected to two superconducting reservoirs, which are described by the Bogoliubov-de Gennes Hamiltonians and have the chemical potentials, the temperatures, and the complex order parameters as the relevant quantities. We consider a specific example in which the quantum dot is represented by the Anderson impurity model and study the transport properties, proximity effect and Andreev bound states in equilibrium and far from equilibrium setups.
We theoretically study the superconducting proximity effect in a quantum dot coupled to two superconducting leads when the intradot interaction between electrons is made attractive. Because of the superconducting proximity effect, the electronic states for the embedded quantum dot are either spin-polarized states with an odd occupation number or BCS-like states with an even occupation number. We show that in the presence of an external magnetic field, the system can exhibit quantum phase transitions of fermion parity associated with the occupation number. In this work, we adopt a self-consiste…
Andreev bound states (ABSs) are studied in quantum dot coupled to conventional BCS superconducting leads on the basis of effective slave boson Hamiltonian in an infinite-U (Coulomb interaction) limit followed by Green's function technique. From the relevant Green's function, density of states (DOS) is analyzed at different superconducting phase differences. On the basis of numerical computation, it is pointed out from DOS plot that ABSs (sub-gap states) arise due to the phase difference between left and right superconducting leads. Due to the dependence on superconducting phase difference, ABS…
We investigate the Fano-type spectroscopic lineshapes of the T-shape double quantum dot coupled between the conducting and superconducting electrodes and analyze their stability on a decoherence. Because of the proximity effect the quantum interference patterns appear simultaneously at +/- epsilon_2, where epsilon_2 is an energy of the side-attached quantum dot. We find that decoherence gradually suppresses both such interferometric structures. We also show that at low temperatures another tiny Fano-type structure can be induced upon forming the Kondo state on the side-coupled quantum dot due …
The proximity effect (PE) between superconductor and confined electrons can induce the effective pairing phenomena of electrons in nanowire or quantum dot (QD). Through interpreting the PE as an exchange of virtually quasi-excitation in a largely gapped superconductor, we found that there exists another induced dynamic process. Unlike the effective pairing that mixes the QD electron states coherently, this extra process leads to dephasing of the QD. In a case study, the dephasing time is inversely proportional to the Coulomb interaction strength between two electrons in the QD. Further theoret…
We analyze heat and charge transport through a single-level quantum dot coupled to two BCS superconductors at different temperatures to first order in the tunnel coupling. In order to describe the system theoretically, we extend a real-time diagrammatic technique that allows us to capture the interplay between superconducting correlations, strong Coulomb interactions, and nonequilibrium physics. We find that a thermoelectric effect can arise due to the superconducting proximity effect on the dot. In the nonlinear regime, the thermoelectric current can also flow at the particle-hole symmetric p…
Sub-gap transport properties of a quantum dot (QD) coupled to two superconducting and one metallic leads are studied theoretically, solving the time-dependent equation of motion by the Laplace transform technique. We focus on time-dependent response of the system induced by a sudden switching on the QD-leads couplings, studying the influence of initial conditions on the transient currents and the differential conductance. We derive analytical expressions for measurable quantities and find that they oscillate in time with the frequency governed by the QD-superconducting lead coupling and acquir…
We investigate non-linear transport in a double quantum dot connected to two normal electrodes and a central superconducting finger. By this means, we perform a transport spectroscopy of such a system which implements a Cooper pair splitter. The non-linear conductance exhibits strong subgap features which can be associated with the coherence of the injected Cooper pairs. Our findings are well accounted for by the recently developed microscopic theory of Cooper pairs splitters made in SWNTs.
We present in this letter a theoretical analysis of the current-voltage (I-V) characteristics of a hybrid normal-superconducting device consisting of a quantum dot and two electrodes that can be either normal or superconducting. We show that voltage drops at two different contacts that have been regarded unimportant in literature play essential roles in the Andreev tunneling process when at least one of electrodes is superconducting. A differential-conductance-anomaly caused by the aforementioned voltage drops is predicted. We also propose a new spectroscopy method to measure the energy levels…
We study a hybrid device defined in an InAs nanowire with an epitaxial Al shell that consists of a quantum dot in contact with a superconducting island. The device is electrically floating, prohibiting transport measurements, but providing access to states that would otherwise be highly excited and unstable. Radio-frequency reflectometry with lumped-element resonators couples capacitatively to the quantum dot, and detects the presence of discrete subgap states. We perform a detailed study of the case with no island states, but with quantum-dot-induced subgap states controlled by the tunnel cou…
We study the in-gap states of the quantum dot hybridized to a conducting and superconducting electrode. The usual proximity effect suppresses electronic states over the entire subgap regime $|ω| < Δ$, where $Δ$ denotes the energy gap of superconductor. Owing to the Andreev scattering there can, however, emerge additional in-gap states whose line-broadening (inverse life-time) depends on the coupling to a normal electrode. We show that even number of such bound states appears in the quantum dot spectrum, depending on a competition between the Coulomb repulsion and the induced on-dot pairing. We…
We investigate the AC Josephson current through a quantum dot with strong Coulomb interaction attached to two superconducting and one normal lead. To this end, we perform a perturbation expansion in the tunneling couplings within a diagrammatic real-time technique. The AC Josephson current is connected to the reduced density matrix elements that describe superconducting correlations induced on the quantum dot via proximity effect. We analyze the dependence of the AC signal on the level position of the quantum dot, the charging energy, and the applied bias voltages.
We study the Josephson current through a resonant level coupled to a vibration mode (local Holstein model) in the adiabatic limit of low oscillator frequency. A semiclassical theory is then appropriate and allows us to consider the oscillator dynamics within the Born-Oppenheimer approximation for arbitrary electron-vibration couplings. The resulting Fokker-Planck equation has been solved in the most relevant underdamped limit and yields the oscillator distribution function and the Josephson current. Remarkably, a transition from single-well to double-well behavior of the effective oscillator p…
We study the interplay of spin and charge coherence in a single-level quantum dot. A tunnel coupling to a superconducting lead induces superconducting correlations in the dot. With full spin symmetry retained, only even-singlet superconducting correlations are generated. An applied magnetic field or attached ferromagnetic leads partially or fully reduce the spin symmetry, and odd-triplet superconducting correlations are generated as well. For single-level quantum dots, no other superconducting correlations are possible. We analyze, with the help of a diagrammatic real-time technique, the inter…
We study the entanglement of a two-qubit system in a superconducting quantum dot (SQD) lattice in the presence of magnetic flux and gate voltage inhomogeneity. We observe a universal feature for the half-integer magnetic flux quantum which completely washes out the entanglement of the system both at zero and finite temperature. We observe that the ground state is always in a maximally entangled Bell state when there is no inhomogeneity in gate voltage in the superconducting quantum dot lattice. We find an important constraint in magnetic flux for ground state entanglement. We also observe few …
Dynamical processes induced by the external time-dependent fields can provide valuable insight into the characteristic energy scales of a given physical system. We investigate them here in a nanoscopic heterostructure, consisting of the double quantum dot coupled in series to the superconducting and the metallic reservoirs, analyzing its response to (i)~abrupt bias voltage applied across the junction, (ii) sudden change of the energy levels, and imposed by (iii)~their periodic driving. We explore subgap properties of this setup which are strictly related to the in-gap quasiparticles and discus…
The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., a system with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the pr…
