Low-Temperature Anomaly in the Josephson Critical Current of Junctions in d-Wave Superconductors

φ Josephson Junction Induced by Altermagnetism

We study the Josephson effect in a superconductor-altermagnet-superconductor junction. We find anomalous phenomena, including 0-π transition and multinodal current-phase relations. Similar to a d-wave superconductor, a d-wave altermagnet can support a φ junction where free-energy minima locate neither φ=0 nor ±π with double degeneracy. These properties can be tunable by parameters, e.g., the exchange energy, the orientation of crystal axis, the length, and the chemical doping of the altermagnet. These rich features lead to accessible functionality of superconductor-altermagnet-superconductor junctions.

Decentralized Global Optimization Based on a Growth Transform Dynamical System Model

Conservation principles, such as conservation of charge, energy, or mass, provide a natural way to couple and constrain spatially separated variables. In this paper, we propose a dynamical system model that exploits these constraints for solving nonconvex and discrete global optimization problems. Unlike the traditional simulated annealing or quantum annealing-based global optimization techniques, the proposed method optimizes a target objective function by continuously evolving a driver functional over a conservation manifold, using a generalized variant of growth transformations. As a result, the driver functional asymptotically converges toward a Dirac-delta function that is centered at the global optimum of the target objective function. In this paper, we provide an outline of the proof of convergence for the dynamical system model and investigate different properties of the model using a benchmark nonlinear optimization problem. Also, we demonstrate how a discrete variant of the proposed dynamical system can be used for implementing decentralized optimization algorithms, where an ensemble of spatially separated entities (for example, biological cells or simple computational units) can collectively implement specific functions, such as winner-take-all and ranking, by exchanging signals only with its immediate substrate or environment. The proposed dynamical system model could potentially be used to implement continuous-time optimizers, annealers, and neural networks.

Study on Green's function on topological insulator surface

In the theory of superconducting junctions, Green's function has an important role for obtaining Andreev bound states, local density of states and Josephson current in a systematic way. In this article, we show how to construct Green's function on the surface of a topological insulator following McMillan's formalism where the energy spectrum of electrons obeys a linear dispersion. For a model of a superconductor (S)/ferromagnet (F)/normal metal (N) junction, we show that the generation of a Majorana fermion gives rise to the enhanced local density of states and pair amplitude of odd-frequency pairing. We also derive an extended Furusaki-Tsukada's formula of DC Josephson current in S/F/S junctions. The obtained Josephson current depends on the direction and magnitude of the magnetization.This article is part of the theme issue 'Andreev bound states'.

Quasiparticle conductance-voltage characteristics for break junctions involving d-wave superconductors: charge-density-wave effects

Quasiparticle tunnel conductance-voltage characteristics (CVCs), [Formula: see text], were calculated for break junctions (BJs) made up of layered d-wave superconductors partially gapped by charge-density waves (CDWs). The current is assumed to flow in the ab-plane of electrodes. The influence of CDWs is analyzed by comparing the resulting CVCs with CVCs calculated for BJs made up of pure d-wave superconductors with relevant parameters. The main CDW-effects were found to be the appearance of new CVC peculiarities and the loss of CVC symmetry with respect to the V-sign. Tunnel directionality was shown to be one of the key factors in the formation of [Formula: see text] dependences. In particular, the orientation of electrodes with respect to the current channel becomes very important. As a result, [Formula: see text] can acquire a large variety of forms similar to those for tunnel junctions between superconductors with s-wave, d-wave, and mixed symmetry of their order parameters. The diversity of peculiarities is especially striking at finite temperatures. In the case of BJs made up of pure d-wave superconductors, the resulting CVC can include a two-peak gap-driven structure. The results were compared with the experimental BJ data for a number of high-T _c oxides. It was shown that the large variety of the observed current-voltage characteristics can be interpreted in the framework of our approach. Thus, quasiparticle tunnel currents in the ab-plane can be used as an additional mean to detect CDWs competing with superconductivity in cuprates or other layered superconductors.

Degeneracy of Majorana bound states and fractional Josephson effect in a dirty SNS junction

We theoretically study the stability of more than one Majorana fermion appearing in a p-wave superconductor/dirty normal metal/p-wave superconductor junction in two-dimensions by using the chiral symmetry of a Hamiltonian. At the phase difference across the junction φ being π, we will show that all of the Majorana bound states in the normal metal belong to the same chirality. Due to this pure chiral feature, the Majorana bound states retain their high degree of degeneracy at zero energy even in the presence of a random potential. As a consequence, the resonant transmission of a Cooper pair via the degenerate Majorana bound states carries the Josephson current at [Formula: see text], which explains the fractional current-phase relationship discussed in a number of previous papers.

Symmetry protected topological superfluid (3)He-B

Owing to the richness of symmetry and well-established knowledge of bulk superfluidity, the superfluid (3)He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of (3)He in a multifaceted manner, including symmetry considerations, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the (3)He-B confined in a slab geometry. The (3)He-B under a magnetic field is separated to two different sub-phases: the symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of the (3)He nucleus. It is also demonstrated that odd-frequency even-parity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt3 and Rashba superconductors as examples.

The magnetic penetration depth influenced by the proximity to the surface

The effect of smooth inhomogeneities near a superconductor boundary on the magnetic penetration depth λ is studied with emphasis on the proximity-induced spatial dependence of the Cooper pair amplitude. The influence of surface pair breaking or pair formation on λ is described within the Ginzburg-Landau theory, with no model assumptions, for both strongly type-II and strongly type-I homogeneous superconductors. Generic values of λ, which can differ greatly from the London penetration depth, are identified and demonstrated to be induced by large-scale inhomogeneities, when superconductivity is strongly suppressed on the surface.

Spin and charge currents in SNS Josephson junction with f-wave pairing symmetry

We study transport properties and local density of states in a clean superconductor-normal metal-superconductor Josephson junction with triplet f-wave superconductors, based on the Eilenberger equation. Effects of the thickness of normal metal and a misorientation between the gap vector of the superconductors on the spin and charge currents are investigated. A spin current, which arises from the misalignment of the d-vectors, in the absence of charge current for some values of phase difference between the superconductors is found. We also find unconventional behavior of the spin current associated with the 0-π transition. The misalignment of the d-vectors also gives rise to a zero energy peak in the density of states in the normal metal.

Novel Josephson effect in triplet-superconductor-ferromagnet-triplet-superconductor junctions

We predict a novel type of Josephson effect to occur in triplet-superconductor-ferromagnet-triplet-superconductor Josephson junctions. We show that the Josephson current, IJ, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional sign change of IJ with increasing temperature.

Spin-dependent quasiparticle reflection and bound States at interfaces with itinerant antiferromagnets

We find a novel channel of quasiparticle reflection from the simplest two-sublattice antiferromagnet (AF) on a bipartite lattice. Low-energy quasiparticles in a normal metal (N) experience spin-dependent retroreflection at AF/N interfaces. As a combined effect of antiferromagnetic and Andreev reflections, subgap Andreev states arise at an AF/superconductor (SC) interface. When the antiferromagnetic reflection dominates the specular one, Andreev bound states have almost zero energy on AF/s-wave superconductor (sSC) interfaces, whereas there are no low-energy subgap states on AF/d-wave superconductor (dSC) boundaries. For an sSC/AF/sSC junction, the bound states are found to split, due to the finite width of the AF interlayer, and carry the supercurrent. The theory developed in the present Letter is based on a novel quasiclassical approach, which applies to interfaces involving itinerant antiferromagnets.

Quasiparticle decoherence in d-wave superconducting qubits

It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response nonequilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be detectable in a qubit containing a d-wave junction with appropriate parameters.

Experimental test for subdominant superconducting phases with complex order parameters in cuprate grain boundary junctions

We propose and implement a direct experimental test for subdominant superconducting phases with broken time-reversal symmetry in d-wave superconductors. The critical current of 45 degrees -asymmetric grain boundary junctions is shown to be extremely sensitive to the predicted onset of a complex order parameter at (110) surfaces and near magnetic impurities. Measurements in pure Ni-doped YBa2Cu3O7-x junctions indicate that the symmetry at the surface is consistent with pure d-wave at all temperatures, putting limits on the magnitude and chiral domain structure of any subdominant symmetry component.