For a general model of a mesoscopic multi-level quantum dot, we determine the necessary conditions for the existence of an anomalous Josephson current with spontaneously broken time-reversal symmetry. They correspond to a finite spin-orbit coupling, a suitably oriented Zeeman field, and the dot being a chiral conductor. We provide analytical expressions for the anomalous supercurrent covering a wide parameter regime.
We derive, via fourth order perturbation theory, an expression for the Josephson current through a gated interacting quantum dot. We analyze our expression for two different models of the superconductor-dot-superconductor (SDS) system. When the matrix elements connecting dot and leads are featureless constants, we compute the Josephson coupling J_c as a function of the gate voltage and Coulomb interaction. In the diffusive dot limit, we compute the probability distribution P(J_c) of Josephson couplings. In both cases, pi junction behavior (J_c < 0) is possible, and is not simply dependent on t…
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.
A double quantum dot coupled to an s-wave superconductor and subject to an inhomogeneous magnetic field can host a pair of zero-energy Majorana fermions when the dot properties are tuned appropriately. Here, we demonstrate the possibility to generate a fractional 4-pi Josephson effect in two such double dots tunnel-coupled to each other. We discuss the robustness of this effect with respect to perturbations away from the special point in parameter space where the uncoupled double dots host Majorana fermions. We demonstrate the possibility to generate Josephson effects with a period of 8-pi and…
We study a double quantum dot each dot of which is tunnel-coupled to superconducting leads. In the Coulomb blockade regime, a spin-dependent Josephson coupling between two superconductors is induced, as well as an antiferromagnetic Heisenberg exchange coupling between the spins on the double dot which can be tuned by the superconducting phase difference. We show that the correlated spin states-singlet or triplets-on the double dot can be probed via the Josephson current in a dc-SQUID setup.
We discuss the behavior of a two-level system coupled to a quantum dot contacted by superconducting source/drain electrodes, representing a simple model for the conformational degree of freedom of a molecular dot or a break junction. The Josephson current is shown to induce conformational changes, including a complete reversal. For small bias voltage, periodic conformational motions induced by Landau-Zener transitions between Andreev states are predicted.
The equilibrium Josephson current through a nanoscale multi-level quantum dot with Rashba or Dresselhaus spin-orbit coupling $α$ has been computed. The critical current can be drastically modified already by moderate $α$. In the presence of a Zeeman field, Datta-Das-like oscillatory dependencies on $α$ are predicted.
We present a theory of transport through interacting quantum dots coupled to normal and superconducting leads in the limit of weak tunnel coupling. A Josephson current between two superconducting leads, carried by first-order tunnel processes, can be established by non-equilibrium proximity effect. Both Andreev and Josephson current is suppressed for bias voltages below a threshold set by the Coulomb charging energy. A $π$-transition of the supercurrent can be driven by tuning gate or bias voltages.
We consider transport through a Josephson junction consisting of a conventional s-wave superconductor coupled via a double quantum dot to a noncentrosymmetric superconductor with both, singlet and triplet pairing. We calculate the Andreev bound state energies and the associated Josephson current. We demonstrate that the current-phase relation is a sensitive probe of the singlet-triplet ratio in the noncentrosymmetric superconductor. In particular, in the presence of an inhomogeneous magnetic field the system exhibits a $φ$-junction behavior.
The phase and thermal driven transport properties of the T-shaped uncorrelated double quantum dot Josephson junction are analyzed by using Keldysh non-equilibrium Green's function equation of motion technique. In this setup, we have shown that the side-attached quantum dot provides an additional route for electron transmission which is affecting the transport properties by adjusting the interdot hopping between the main dot and the side dot. We began with investigating the impact of interdot hopping on Andreev bound states and Josephson supercurrent. When a small thermal bias is applied across…
We present the theory of the Josephson effect in nanotube dots where an SU(4) symmetry can be realized. We find a remarkably rich phase diagram that significantly differs from the SU(2) case. In particular, π-junction behavior is largely suppressed. We analytically obtain the Josephson current in various parameter regions: (i) in the Kondo regime, covering the full crossover from SU(4) to SU(2), (ii) for weak tunnel couplings, and (iii) for large BCS gap. The transition between these regions is studied numerically.
We studied anomalous Josephson effect (AJE) in Josephson trijunctions fabricated on Bi$_2$Se$_3$, and found that the AJE in T-shaped trijunctions significantly alters the Majorana phase diagram of the trijunctions, when an in-plane magnetic field is applied parallel to two of the three single junctions. Such a phenomenon in topological insulator-based Josephson trijunction provides unambiguous evidence for the existence of AJE in the system, and might provide an additional knob for controlling the Majorana bound states in the Fu-Kane scheme of topological quantum computation.
An odd-occupied quantum dot in a Josephson junction can flip transmission phase, creating a π-junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a full-shell hybrid interferometer, using gate voltage to control dot-junction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zero-bias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zero-energy modes in the leads.
We study Josephson junctions made of semiconducting nanowires with Rashba spin-orbit coupling, where superconducting correlations are induced by the proximity effect. In the presence of a suitably directed magnetic field, the system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a phase bias between two superconductors. We show that this anomalous current can be increased significantly by tuning the nanowire into the helical regime. In particular, in a short junction, a large anomalous current is a signature for topologically nontrivial superconductivity in t…
We propose a model for resonant Josephson tunneling through quantum dots that accounts for Cooper pair-breaking processes in the superconducting leads caused by a magnetic field or spin-flip scattering. The pair-breaking effect on the critical supercurrent $I_c$ and the Josephson current-phase relation $I(ϕ)$ is largely due to the modification of the spectrum of Andreev bound states below the reduced (Abrikosov-Gorkov) quasiparticle gap. For a quantum dot formed in a quasi-one-dimensional channel, both $I_c$ and $I(ϕ)$ can show a significant magnetic field dependence induced by pair breaking d…
We consider a model of a Josephson junction of two topological superconducting wires mediated by an interacting quantum dot. An additional normal electrode coupled to the dot from the top allows to probe its density of states. The Majorana states adjacent to the dot hybridize across the junction and from a bound state in the dot. The dot is subjected to the effective magnetic field arising from the superposition of the fields driving each wire into topological states, which, dependent on the angle between the fields, introduces variable Zeeman splitting of the dot active level. We show that el…
A superconductor-semiconducting nanowire-superconductor heterostructure in the presence of spin orbit coupling and magnetic field can support a supercurrent even in the absence of phase difference between the superconducting electrodes. We investigate this phenomenon, the anomalous Josephson effect, employing a model capable of describing many bands in the normal region. We discuss geometrical and symmetry conditions required to have finite anomalous supercurrent and in particular we show that this phenomenon is enhanced when the Fermi level is located close to a band opening in the normal reg…
The anomalous proximity effect in dirty superconducting junctions is one of most striking phenomena highlighting the profound nature of Majorana bound states and odd-frequency Cooper pairs in topological superconductors. Motivated by the recent experimental realization of planar topological Josephson junctions, we describe the anomalous proximity effect in a superconductor/semiconductor hybrid, where an additional dirty normal-metal segment is extended from a topological Josephson junction. The topological phase transition in the topological Josephson junction is accompanied by a drastic chang…
We theoretically investigate the Fano effect in dc Josephson current at the absolute zero of temperature. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). Here the Kondo temperature is assumed to be much smaller than the superconducting gap, and the Coulomb interaction inside the QD is treated by the Hartree-Fock approximation. It is shown that the Josephson critical current exhibits an asymmetric resonance against the QD energy level. This behavior is caused by the interferenc…
We investigate the Josephson radiation emitted by a junction made of a quantum dot coupled to two conventional superconductors. Close to resonance, the particle-hole symmetric Andreev states that form in the junction are detached from the continuum above the superconducting gap in the leads, while a gap between them opens near the Fermi level. Under voltage bias, we formulate a stochastic model that accounts for non-adiabatic processes, which change the occupations of the Andreev states. This model allows calculating the current noise spectrum and determining the Fano factor. Analyzing the fin…
The anomalous ground state phase shift in S/AF/S Josephson junctions in the presence of the Rashba SO-coupling is predicted and numerically investigated. It is found to be a consequence of the uncompensated magnetic moment at the S/AF interfaces. The anomalous phase shift exhibits a strong dependence on the value of the SO-coupling and the sublattice magnetization with the simultaneous existence of stable and metastable branches. It depends strongly on the orientation of the Neel vector with respect to the S/AF interfaces via the dependence on the orientation of the interface uncompensated mag…
We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current $J$ flows without a phase difference across the junction $θ$. The phase shift $φ$ appealing in the current-phase relationship $J\propto \sin(θ-φ$) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains t…
We study the effect of Rashba spin-orbit interaction on the Josephson current through a double quantum dot in presence of Coulomb repulsion. In particular, we describe the characteristic effects on the magnetic-field induced singlet-triplet transition in the molecular regime. Exploring the whole parameter space, we analyze the effects of the device asymmetry, the orientation of the applied magnetic field with respect to the spin-orbit interaction, and finite temperatures. We find that at finite temperatures the orthogonal component of the spin-orbit interaction exhibits a similar effect as the…
We investigate anomalous Hall effect in a magnet coupled to a triplet superconductor under phase gradient. It is found that the anomalous Hall supercurrent arises from non-trivial structure of the magnetization. The magnetic structure manifested in the Hall supercurrent is characterized by even order terms of the exchange coupling, essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. We also discuss a possible candidate for magnetic structure to verify our prediction.
We analyze the magnetic and transport properties of a double quantum dot coupled to superconducting leads. In addition to the possible phase transition to a $π$ state, already present in the single dot case, this system exhibits a richer magnetic behavior due to the competition between Kondo and inter-dot antiferromagnetic coupling. We obtain results for the Josephson current which may help to understand recent experiments on superconductor-metallofullerene dimer junctions. We show that in such a system the Josephson effect can be used to control its magnetic configuration.
We consider a ballistic Josephson junction with a quantum point contact in a two-dimensional electron gas with Rashba spin-orbit coupling. The point contact acts as a spin filter when embedded in a circuit with normal electrodes. We show that with an in-plane external magnetic field an anomalous supercurrent appears even for zero phase difference between the superconducting electrodes. In addition, the external field induces large critical current asymmetries between the two flow directions, leading to supercurrent rectifying effects.
We investigate theoretically the Josephson junction of semiconductor nanowire with strong spin-orbit (SO) interaction in the presence of magnetic field. By using a tight-binding model, the energy levels $E_n$ of Andreev bound states are numerically calculated as a function of phase difference $φ$ between two superconductors in the case of short junctions. The DC Josephson current is evaluated from the Andreev levels. In the absence of SO interaction, a $0$-$π$ transition due to the magnetic field is clearly observed. In the presence of SO interaction, the coexistence of SO interaction and Zeem…
We study Josephson effect of $d$-wave superconductor (DS)/ferromagnet insulator(FI)/DS junctions on a surface of topological insulator (TI). We calculate Josephson current $I\left(φ\right) $ for various orientations of the junctions where $φ$ is the macroscopic phase difference between two DSs. In certain configurations, we find anomalous current-phase relation $I(φ)=-I\left( -φ+π\right)$ with $2π$ periodicity. In the case where the first order Josephson coupling is absent without magnetization in FI, $I(φ)$ can be proportional to $\cos φ$. The magnitude of the obtained Josephson current is en…
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…
Periodically driven Kitaev chains are known to exhibit novel Floquet Majorana fermions and anomalous Floquet end modes. The fact that `quasienergy in Floquet systems is periodic' poses a difficulty in defining the ground state in periodically driven systems. To overcome this problem, we start with the ground state of the undriven Kitaev chain and gradually switch on the periodic driving in chemical potential over a timescale $τ$. The extent to which the single particle eigenstates of the undriven system get distributed among the Floquet states upon driving can be characterized by inverse parti…
We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [Deacon, R. S. et al., Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tu…
We calculate the current-voltage (I-V) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The phase $ϕ$ across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase I-V characteristic. The number of voltage steps counts the number of Rabi oscillations per $2π$ increment of $ϕ$, providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the "Majora…
Josephson current of spin-entangled electrons through the two branches of a SQUID-like structure with two quantum dots exhibits a magnetic-flux response different from the conventional Josephson current. Due to their interference, the period of maximum Josephson current changes from $h/2e$ to $h/e$, which can be used for detecting the Cooper-pair splitting efficiency. The nonlocal spin entanglement provides a quantum mechanical functionale for switching on and off this novel Josephson current, and explicitly a switch is formulated by including a pilot junction. It is shown that the device can …
We consider a model for a single molecule with a large frozen spin sandwiched in between two BCS superconductors at equilibrium, and show that this system has a $π$ junction behavior at low temperature. The $π$ shift can be reversed by varying the other parameters of the system, e.g., temperature or the position of the quantum dot level, implying a controllable $π$ junction with novel application as a Josephson current switch. We show that the mechanism leading to the $π$ shift can be explained simply in terms of the contributions of the Andreev bound states and of the continuum of states abov…
We investigate dynamical transport aspects of a combined nanomechanical-superconducting device in which Cooper pair tunneling interfere with the mechanical motion of a vibrating molecular quantum dot embedded in a Josephson junction. Six different regimes for the tunneling dynamics are identified with respect to the electron level and the charging energy in the quantum dot. In five of those regimes new time-scales are introduced which are associated with the energies of the single electron transitions within the quantum dot, while there is one regime where the internal properties of the quantu…
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…
We discuss the response of an rf-SQUID formed by anomalous Josephson junctions embedded in a superconducting ring with a non-negligible inductance. We demonstrate that a properly sweeping in-plane magnetic field can cause both the total flux and the current circulating in the device to modulate and to behave hysteretically. The bistable response of the system is analyzed as a function of the anomalous phase shift at different values of the screening parameter, in order to highlight the parameter range within which a hysteretic behavior can be observed. The magnetic flux piercing the SQUID ring…
We propose a Josephson junction setup based on a topological insulator (TI) thin film to detect Majorana states, which exploits the unique helical and extended nature of the TI surface state. When the magnetic flux through the junction is close to an integer number of flux quanta, Majorana states, present on both surfaces of the film, give rise to a narrow peak-dip structure in the current- phase relation by hybridizing at the edge of the junction. Moreover, the maximal Majorana-state contribution to Josephson current takes a (nearly) universal value, approximately equal to the supercurrent ca…
Exerting control of the magnetic exchange interaction in heterostructures is of both basic interest and has potential for use in spin-based applications relying on quantum effects. We here show that the sign of the exchange interaction in a spin-valve, determining whether the ferro- or antiferromagnetic configuration is favored, can be controlled via an electric voltage. This occurs due to an interplay between a nonequilibrium quasiparticle distribution and the presence of spin-polarized Cooper pairs. Additionally, we show that a voltage-induced distribution controls the anomalous supercurrent…
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…
We study the combined effects of spin-orbit interaction, magnetic field, and Coulomb charging on the Josephson current-phase relation, I(φ), for a multi-level quantum dot tunnel-contacted by two conventional s-wave superconductors with phase difference φ. A general model is formulated and analyzed in the cotunneling regime (weak tunnel coupling) and in the deep subgap limit, fully taking into account interaction effects. We determine the conditions for observing a finite anomalous supercurrent I_a=I(φ=0). For a two-level dot with spin-orbit coupling and arbitrarily weak Zeeman field B, we find…
We characterize parallel double quantum dot Josephson junctions based on closely-grown double nanowires bridged by in-situ deposited superconductors. The parallel double dot behavior occurs despite the closeness of the nanowires and the potential risk of nanowire clamping during growth. By tuning the charge filling and lead couplings, we map out the simplest parallel double quantum dot Yu-Shiba-Rusinov phase diagram. Our quasi-independent two-wire hybrids show promise for the realization of exotic topological phases.
In spite of extended efforts, detecting thermoelectric effects in superconductors have proven to be a challenging task, due to the inherent superconducting particle-hole symmetry. Here we present a theoretical study of an experimentally attainable Superconductor -- Quantum Dot -- Superconductor (SC-QD-SC) Josephson Junction with highly tunable thermoelectric properties and a thermal response that is far larger than previous suggestions. The QD energy level between the SCs breaks particle-hole symmetry in a gradual manner, allowing, in the presence of a temperature gradient, for gate controlled…
In a standard Josephson junction the current is zero when the phase difference between the superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin-orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect -- the hallmark effect of superconducting spintronics --and can be characterized by the corresponding anomalous phase shift ($ϕ_0$). We report the observation of a tunable anomalous Jose…
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.
Serial double quantum dots created in semiconductor nanostructures provide a versatile platform for investigating two-electron spin quantum states, which can be tuned by electrostatic gating and an external magnetic field. In this work, we directly measure the supercurrent reversal between adjacent charge states of an InAs nanowire double quantum dot with superconducting leads, in good agreement with theoretical models. In the even charge parity sector, we observe a supercurrent blockade with increasing magnetic field, corresponding to the spin singlet to triplet transition. Our results demons…
Josephson junctions with topological insulator weak links can host low energy Andreev bound states giving rise to a current phase relation that deviates from sinusoidal behaviour. Of particular interest are zero energy Majorana bound states that form at a phase difference of $π$. Here we report on interferometry studies of Josephson junctions and superconducting quantum interference devices (SQUIDs) incorporating topological insulator weak links. We find that the nodes in single junction diffraction patterns and SQUID oscillations are lifted and independent of chemical potential. At high tempe…
We study the key features of the Josephson transport through a curved semiconducting nanowire. Based on numerical simulations and analytical estimates within the framework of the Bogoliubov-de Gennes equations we find the ground-state phase difference $φ_0$ between the superconducting leads tuned by the spin splitting field $h$ driving the system from the topologically trivial to the nontrivial superconducting state. The phase $φ_0$ vanishes for rather small $h$, grows in a certain field range around the topological transition, and then saturates at large $h$ in the Kitaev regime. Both the sub…
Despite the robustness of the chiral edge modes of quantum Hall systems against the superconducting proximity effect, Cooper pairs can penetrate into the chiral edge channels and carry the Josephson current in an appropriate setup. In our work, the Josephson junction of a spin-polarized quantum anomalous Hall insulator (QAHI) with a Chern number $ν=1$ connecting conventional superconductors is studied from the perspective of pairing symmetry consistent with the chiral edge mode. Induced pairing states are equal-spin triplet, a combination of the even- and odd-frequency components, nonlocally e…
