We have theoretically studied the supercurrent profiles in three-dimensional normal metal and ferromagnetic Josephson configurations, where the magnitude of the superconducting gaps in the superconducting leads are unequal, i.e., $Δ_1\neq Δ_2$, creating asymmetric $S_1NS_2$ and $S_1FS_2$ systems. Our results reveal that by increasing the ratio of the superconducting gaps $Δ_2/Δ_1$, the critical supercurrent in a ballistic $S_1NS_2$ system can be enhanced by more than $100\%$, and reaches a saturation point, or decays away, depending on the junction thickness, magnetization strength, and chemical potential. The total critical current in a diffusive $S_1NS_2$ system was found to be enhanced by more than $50\%$ parabolically, and reaches saturation by increasing one of the superconducting gaps. In a uniform ferromagnetic junction, the supercurrent undergoes reversal by increasing $Δ_2/Δ_1>1$. Through decomposing the total supercurrent into its supergap and subgap components, our results illustrate their crucial relative contributions to the Josephson current flow. It was found that the competition of subgap and supergap currents in a $S_1FS_2$ junction results in the emergence of second harmonics in the current-phase relation. In contrast to a diffusive asymmetric Josephson configuration, the behavior of the supercurrent in a ballistic system with $Δ_2/Δ_1=1$ can be properly described by the subgap current component only, in a wide range of parameter sets, including Fermi level mismatch, magnetization strength, and junction thickness. Interestingly, when $Δ_2/Δ_1>1$, our results have found multiple parameter sets where the total supercurrent is driven by the supergap component. Therefore, our comprehensive study highlights the importance of subgap and supergap supercurrent components in both the ballistic and diffusive regimes.
We demonstrate how potential impurities are a very powerful tool for determining the pairing symmetry in graphene proximity-coupled to a spin-singlet superconductor. All d-wave states are characterized by subgap resonances, with spatial patterns clearly distinguishing between nodal and chiral d-wave symmetry, while s-wave states have no subgap resonances. We also find strong supergap impurity resonances associated with the normal state Dirac point. Sub- and supergap resonances only interact at very low doping levels, then causing suppression of the supergap resonances.
We consider two-dimensional superconductor/ferromagnet/superconductor junctions and investigate the subgap modes along the junction interface. The subgap modes exhibit characteristics similar to the Yu-Shiba-Rusinov states that originate form the interplay between superconductivity and ferromagnetism in the magnetic junction. The dispersion relation of the subgap modes shows qualitatively different profiles depending on the transport state (metallic, half-metallic, or insulating) of the ferromagnet. As the spin splitting in the ferromagnet is increased, the subgap modes bring about a $0$-$π$ t…
We theoretically study superconducting islands based on semiconductor-nanowire Josephson junctions and take into account the presence of subgap quasiparticle excitations in the spectrum of the junction. Our method extends the standard model Hamiltonian for a superconducting charge qubit and replaces the Josephson potential by the Bogoliubov--de Gennes Hamiltonian of the nanowire junction, projected onto the relevant low-energy subgap subspace. This allows to fully incorporate the coherent dynamics of subgap levels in the junction. The combined effect of spin-orbit coupling and Zeeman energy in…
We study theoretically the current-voltage characteristics (IVCs) of the Josephson field effect transistor - a ballistic SNINS junction with superconducting (S) electrodes confining a planar normal metal region (N), which is controlled by the gate induced potential barrier (I). The calculations were performed using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflections (MAR) regime. We find significant difference of the subgap current structure in these junctions compared to the subharmonic gap structure in tunnel junctions an…
We study the quasiparticle current in clean ferromagnetic Josephson structures of the form $S_1/F_1/N/F_2/S_2$, where $S$, $F$, and $N$ denote superconducting, ferromagnetic or normal layers respectively. Our focus is on the structure of the conductance $G$ as a function of bias $V$, emphasizing the subgap region. We use a fully self consistent numerical method, coupled to a transfer matrix procedure to extract $G(V)$. We choose material parameters appropriate to experimentally realized Co Cu Nb structures. We find a resonance peak structure as a function of the intermediate layer thickness an…
We study theoretically the large variations of the supercurrent through a normal dot that are induced by a small quasiparticle injection current from normal leads connected to the dot. We find that the supercurrent decomposes into a subgap contribution, which depends on the voltages applied to the normal leads, as well as a contribution with opposite sign from energies outside the gap, which is insensitive to the voltages. As the voltages gradually suppress the subgap contribution, a critical voltage exists above which the contribution from energies outside the gap dominates, leading to a sign…
We study a Cooper-pair transistor realized by two Josephson weak links that enclose a superconducting island in an InSb-Al hybrid nanowire. When the nanowire is subject to a magnetic field, isolated subgap levels arise in the superconducting island and, due to the Coulomb blockade,mediate a supercurrent by coherent co-tunneling of Cooper pairs. We show that the supercurrent resulting from such co-tunneling events exhibits, for low to moderate magnetic fields, a phase offset that discriminates even and odd charge ground states on the superconducting island. Notably,this phase offset persists wh…
Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to $\leq3$ dimensions. Here we demonstrate that $n$-terminal Josephson junctions with conventional superconductors may provide a straightforward realization of tunable topological materials in $n-1$ dimensions. For $n\geq 4$, the Andreev subgap spectrum of the junction can accommodate Weyl singularit…
We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The correspondin…
We investigate the charge transport property of superconductor (S) /normal metal (N) / ferromagnet insulator (FI) /(normal metal) N' and S/N/FI/N'/S Josephson junctions on a three-dimensional topological insulator surface. We find asymmetric local density of states (LDOSs) in a S/N/FI/N' junction and show that the finite length of the N interlayer gives rise to subgap resonant spikes in the differential conductance and LDOSs. In a S/N/FI/N'/S junction, the Josephson current shows a non-sinusoidal current-phase relation and the N (or N') interlayer decreases the magnitude of the critical curren…
We study the evolution of averaged transconductances in three-terminal Josephson junctions when the superconducting leads are led throughout a topological phase transition from an $s$-wave to a $p$-wave (Majorana) phase by an in-plane magnetic field $B_x$. We provide a complete description of this transition as a function of $B_x$ and a magnetic flux $Φ$ threading the junction. For that we use a spinful model within a formalism that allows to treat on equal footing the contribution to the transconductance from both the Andreev subgap levels and the continuum spectrum. We unveil a fractionaliza…
We investigate the Josephson effcet in superconductor-normal-superconductor junction (SNS) base on the doped unbiased silicene under the perpendicular electric field and off-resonance circularly polarized light. The Andreev reflection (including the retroreflection and specular one) during the subgap transport, the free energy, and the reversal of the Josephson effect as well as the emergence of $ϕ_{0}$-junction are exploited. The Andreev reflection is complete in the NS interface even for the clean interface and without the Fermi wave vector mismatch, which is opposite to the case of ferromag…
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…
We study the emergent band topology of subgap Andreev bound states in the three-terminal Josephson junctions. We scrutinize the symmetry constraints of the scattering matrix in the normal region connecting superconducting leads that enable the topological nodal points in the spectrum of Andreev states. When the scattering matrix possesses time-reversal symmetry, the gap closing occurs at special stationary points that are topologically trivial as they carry vanishing Berry fluxes. In contrast, for the time-reversal broken case we find topological monopoles of the Berry curvature and correspond…
Using a Josephson junction interferometer (DC SQUID) as a microwave source for irradiating a single-electron trap, both devices fabricated on the same chip, we study the process of photon-assisted tunneling as an effective mechanism of single photon detection. High sensitivity down to a very small oscillation amplitude $v_{\rm J} \sim$ 10 nV$\ll E_{\rm act} \lesssim hf_{\rm J}$ and down to low photon absorption rates $Γ_{\rm ph} \sim$ (1--50)Hz, as well as a clear threshold type of operation with an activation energy $E_{\rm act} \sim$ 400 $μ$eV, are demonstrated for the trap with respect to t…
We study a superconductor-normal state-superconductor (SNS) Josephson junction along the edge of a quantum spin Hall insulator (QSHI) with a superconducting $π$-phase across the junction. We solve self-consistently for the superconducting order parameter and find both real junctions, where the order parameter is fully real throughout the system, and junctions where the order parameter has a complex phase winding. Real junctions host two Majorana zero modes (MZMs), while phase-winding junctions have no subgap states close to zero energy. At zero temperature we find that the phase-winding soluti…
Interfacial spin-orbit coupling in Josephson junctions offers an intriguing way to combine anomalous Hall and Josephson physics in a single device. We study theoretically how the superposition of both effects impacts superconductor/ferromagnetic insulator/superconductor junctions' transport properties. Transverse momentum-dependent skew tunneling of Cooper pairs through the spin-active ferromagnetic insulator interface creates sizable transverse Hall supercurrents, to which we refer as anomalous Josephson Hall effect currents. We generalize the Furusaki-Tsukada formula, which got initially est…
