In s-wave superconductors the Cooper pair wave function is isotropic in momentum space. This property may also be expected for Cooper pairs entering a normal metal from a superconductor due to the proximity effect. We show, however, that such a deduction is incorrect and the pairing function in a normal metal is surprisingly anisotropic because of quasiparticle interference. We calculate angle resolved quasiparticle density of states in NS bilayers which reflects such anisotropic shape of the pairing function. We also propose a magneto-tunneling spectroscopy experiment which could confirm our predictions.
We investigate the coupling between ferromagnet and superconducting phase dynamics in superconductor-ferromagnet-superconductor Josephson junction. The current-voltage characteristics of the junction demonstrate a pattern of subharmonic current steps which forms a devil's staircase structure. We show that a width of the steps becomes maximal at ferromagnetic resonance. Moreover, we demonstrate that the structure of the steps and their widths can be tuned by changing the frequency of the external magnetic field, ratio of Josephson to magnetic energy, Gilbert damping and the junction size.
We develop a theory of current-voltage (I-U) characteristics for superconductor-normal metal-superconductor (SNS) junctions. At small voltages and sufficiently low temperatures the I-U characteristics of the junction is controlled by the inelastic relaxation time, τ_{in}. In particular, the linear conductance is proportional to, τ_{in}. In this regime the I-U characteristics can be expressed solely in terms of dependence of the density of states in the normal region, ν(χ), on the phase difference of the order parameter across the the junction. In contrast, at large voltages the I-U characteris…
We consider a finite-size topological Josephson junction formed at the edge of a two-dimensional topological insulator in proximity to conventional superconductors and study the impact of Cooper pair symmetries on the electron transport. We find that, due to the finite junction size, electron transport is highly tunable by the superconducting phase difference $ϕ$ across the junction. At zero frequency and $ϕ=π$, the setup exhibits vanishing local Andreev reflection and perfect normal transmission due to the interplay of finite junction size and formation of topological Andreev bound states in …
We investigate phase-coherent thermal transport in Josephson junctions made from unconventional superconductors or superfluids. The thermal conductance is evaluated for one- and two-dimensional junctions within the Bogoliubov-de Gennes formalism. We analyze three different scenarios of junctions between two triplet superconductors with (i) helical pairing, (ii) unitary chiral and (iii) nonunitary chiral pairing. We find that the phase-dependent thermal conductance allows us to distinguish the different pairings and provides insight into the formation of topologically nontrivial Andreev bound s…
The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4π$ (rather than a $2π$) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short- and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and f…
We demonstrate that antiferromagnet-superconductor (AF-S) junctions show qualitatively different transport properties than normal metal-superconductor (N--S) and ferromagnet-superconductor (F-S) junctions. We attribute these transport features to presence of two new scattering processes in AF--S junctions, i.e., specular reflection of holes and retroreflection of electrons. Using the Blonder-Tinkham-Klapwijk formalism, we find that the electrical and thermal conductance depend nontrivially on antiferromagnetic exchange strength. Furthermore, we show that the interplay between the Néel vector d…
We study theoretically a junction of a $\mathcal{PT}$-symmetric non-Hermitian superconductor (PTS) placed between two conventional superconductors. We show that due to non-Hermitian electron-electron interaction in the PTS region and the combination of symmetries, only discrete values of phases of the conventional superconductors yield solutions for Andreev bound states. Remarkably, in the case of $0$ and $π$, we obtain growing and decaying in time Andreev bound states. For $π/2$ and $3π/2$, there is a Majorana zero mode penetrating through the junction in only one direction forming a quasipar…
We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanishes in such an i-Josephson junction, the second order coupling from tunneling always generates chiral superconductivity orders with broken time reversal symmetry. Josephson frequency in the i-junction is doubled, namely $ω= 4eV /h$. The result provides a way to engineer topological superconductivity such as the d + id' -wave superconducting state ch…
We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal-superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflecti…
We study Josephson junctions based on second-order topological superconductors (SOTSs) which can be realized in quantum spin Hall insulators with large inverted gap in proximity to unconventional superconductors. We find that tuning the chemical potential in the superconductor strongly modifies the induced pairing of the helical edge states, resulting in topological phase transitions. In a corresponding Josephson junction, a $0$-$π$ transition is realized by tuning the chemical potentials in the superconducting leads. This striking feature is stable in junctions with respect to different sizes…
We study a junction between two time-reversal-invariant topological superconductors and show this system goes through a series of multiple transitions between a $0$-junction phase, where the free energy has its minimum for a superconducting phase difference of zero, and a $π$-junction phase, where the free energy has its minimum for a superconducting phase difference of $π$. These transitions occur in the absence of Coulomb blockade or magnetic impurities. Rather, they are driven by the spin orbit coupling in the junction, and can be probed, for example, by measuring the tunneling density of s…
The phase difference $ϕ$, between the superconducting terminals in superconductor-normal metal-superconductor tunnel junctions (SINIS), incorporates the phase differences $χ_{1,2}$ across thin interfaces of constituent $SIN$ junctions and the phase incursion $φ$ between the side faces of the central electrode of length $L$. It is demonstrated here that $χ_{1,2}$ pass through over their proximity-reduced domain twice, there and back, while $ϕ$ changes over the single period. Two corresponding solutions, that describe the double-valued order-parameter dependence on $χ_{1,2}$, jointly form the si…
An in-plane magnetic field applied to an Ising superconductor converts spin-singlet Cooper pairs to spin-triplet ones. In this work, we study a Josephson junction formed by two Ising superconductors that are proximitized by ferromagnetic layers. This leads to highly tunable spin-triplet pairing correlations which allow to modulate the charge and spin supercurrents through the in-plane magnetic exchange fields. For a junction with a nonmagnetic barrier, the charge current is switchable by changing the relative alignment of the in-plane exchange fields, and a $π$-state can be realized. Furthermo…
We determine the current-phase relation (CPR) of two-terminal configurations of Josephson junctions containing two-dimensional (2D) time-reversal invariant topological superconductors (TRITOPS), including TRITOPS-TRITOPS, as well as junctions between topological and non-topological superconductors (TRITOPS-S). We focus on long junctions for which several channels intervene in the tunneling coupling through the junction. We present a description of the topological edge modes for different TRITOPS models including $p$-wave pairing and the combination of $s$-wave pairing with spin-orbit coupling.…
We report on the fabrication of Josephson junction devices with weak links utilizing the Weyl and higher-order topological semimetal $\text{WTe}_2$. We show that $\text{WTe}_2\text{/Pd}$ contact annealed at a low temperature of 80°C did not exhibit superconducting properties because neither $\text{WTe}_2$ nor Pd are superconductors in the ground state. Upon 180°C annealing, spontaneous formation of superconducting $\text{PdTe}$ due to Pd diffusion enabled us to obtain the interface between $\text{WTe}_2$ and superconductor suitable for the Josephson junction. This result is a facile technique …
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…
Proximity-driven source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor voltage-biased Josephson junction
