D-wave Superconductor Junction Research Articles

Zeeman effects on the tunneling spectra of a ferromagnetic d-wave superconductor in contact with a quantum wire

We study tunneling conductance in a quantum wire–insulator–ferromagnetic d-wave superconductor junction. The results show that exchange field of superconductor has a strong impact on tunneling spectra depending on the junction parameters. We have found a gap like structure in the tunneling limit when we have an interface normal to the (100) axis of superconductor. In the case of (110) axis of superconductor, there is not any zero- bias conductance peaks in tunneling spectra. For a metallic junction the dips disappear.

Andreev reflection and subgap conductance in monolayer MoS2 ferromagnet/s and d-wave superconductor junction

The accurate and proper form of electron-hole excitations and corresponding Dirac-like spinors of superconducting monolayer molybdenum disulfide are exactly obtained. Andreev reflection and resulting subgap conductance in a MoS2-based ferromagnet-superconductor (F/S) junction are particularly calculated in terms of dynamical characteristics of structure. Due to the spin-splitting energy gap in the valence band and also nondegenerate K and K′ valleys, the ferromagnetic exchange energy sh can cause a distinct behavior of Andreev reflection process between spin-up and spin-down charge carriers in the different valleys. In order to occur the retro Andreev reflection, the chemical potential is necessarily fixed in a determined range. Given here one-particle superconducting bispinors enable us to explicitly involve the anisotropic superconducting gap ΔS under electron-hole conversion, i.e., taking place in d-wave asymmetry. Dependence of the Andreev process on the electron incidence angle at the interface is explicitly explored in the presence of such superconducting pair potential.

Spin Polarization Dependence of Zero Bias Conductance in Ferromagnetic Quantum Wire/ D-wave Superconductor Junctions

A relation between the zero-bias conductance and spin polarization in a ferromagnetic quantum wire/ d-wave superconductor junction at finite temperature is studied, theoretically. In contrast to conventional d-wave superconductors which zero bias conductance peaks appear in tunneling spectra, we have found a disappearance of zero bias peak in tunneling spectra, in a way that it will be zero for all of barriers and polarizations parameters. Also, different temperature dependencies of zero bias conductance will be discussed.

Heat transport of graphene-based normal metal–ferromagnetic barrier-superconductor junctions

In this paper, the effect of ferromagnetic barrier (FB) on the thermal conductance of graphene-based normal metal/ferromagnetic barrier/s- and d-wave superconductor junction has been studied theoretically. The results show that the exchange energy (h) in the ferromagnetic barrier has a strong effect on the amplitude, phase and period of the thermal conductance oscillations in terms of the FB length. Also, we have discussed novel thermal conductance oscillations in a graphene-based NFBS junction that happened for maximum superconducting orientation α=π/4. This finding is arisen from the quantum nature of interference between spin states, up and down quasiparticles in FB region. Interestingly, at α=π/4 the h has also the highest effect on the thermal conductance and by increasing the exchange energy h, the thermal conductance enhances at this angle. The exchange energy h also affects the thermal conductance as a function of temperature for both s- and d-wave superconductor. At last, we propose an experimental setup to detect our predicted effects.

Josephson effect in ferromagnetic d-wave superconductor/ferromagnet/ferromagnetic d-wave superconductor junctions

By solving a self-consistent equation for the ferromagnetic d-wave superconducting gap and the exchange energy, we study the Josephson current in the ferromagnetic d-wave superconductor/ferromagnet/ferromagnetic d-wave superconductor junctions. In the Josephson critical current, there are two oscillation components with different periods. It is found that the short-period component can be separated from the long-period one by increasing the exchange energy in ferromagnet and the barrier strength at the ferromagnet/ferromagnetic d-wave superconductor interface, and vice versa. Under a certain thickness for the ferromagnet, exchange energy for the ferromagnetic d-wave superconductor may increase the critical current in the case of a parallel alignment of the magnetization in the ferromagnetic d-wave superconductor.

Tunneling conductance and magnetoresistance in topological insulator Fi/I/Fi/d-wave superconductor junctions

We investigate the tunneling conductance and tunneling magnetoresistance (TMR) in topological insulator ferromagnetic insulator/insulator/ferromagnetic insulator/d-wave superconductor (Fi/I/Fi/d-wave SC) junction, by applying the Blonder-Tinkham-Klapwijk approach. We find that the multiple scatterings in the middle ferromagnetic layer cause the conductance to exhibit an oscillatory behavior as a function of barrier strength even in the case where there is a large Fermi surface mismatch between ferromagnetic and superconductor regions. We find also that the conductance in antiparallel magnetization configuration can be larger than that in the parallel one, depending on the value of barrier strength. This, together with the magnetically induced phase shift of the antiparallel conductance relative to the parallel conductance, leads to a huge negative tunneling magnetoresistance.

Josephson current in d-wave superconductor junctions with ferromagnetic insulator

We investigate the temperature dependence of the critical current and current-phase relation by taking into account the ferromagnetic scattering effect at interface in a d-wave superconductor (S)/ferromagnetic insulator layer (FI)/d-wave superconductor (S) junction. It is shown that both the barrier scattering and the roughness scattering at the interface always suppress the Andreev reflection. The Josephson critical currents depend to a great extent on the effective exchange field of the interface and the crystal orientation of the d-wave superconductor. The exchange field can lead to the change of the junction from 0 to π states and the alteration of the oscillation periods. It can also enhance the Josephson critical current in the junction under certain conditions.

Tunneling conductance on surface of topological insulator ferromagnet/insulator/(s- or d-wave) superconductor junction: Effect of magnetically-induced relativistic mass

We investigate the tunneling conductance on the surface of topological insulator ferromagnet (F)/insulator (I)/superconductor (S) junction where superconducting type is either s- or d-wave paring. Topological insulators (TI) are insulating in bulk but conducting on the surface with the Dirac-fermion-like carriers. In contrast to the Dirac fermions in graphene, relativistic mass of the Dirac fermions in TI can be easily caused by applying magnetic field perpendicular to its surface. In this work, we emphatically focus on the effect of the magnetically-induced relativistic mass on the tunneling conductance of a TI-based F/I/S junction. We find that, due to the effect of spinless fermions as carriers in TI, the behavior of the tunneling conductance in a TI-based NIS junction resembles that in a nonmagnetic graphene-based NIS junction. In case of the d-wave paring F/I/S junction, increasing magnetically-induced relativistic mass changes the zero bias conductance dip (peak) to a zero bias conductance peak (dip). This behavior cannot be observed in a graphene-based F/I/S junction.

INTERFACE SCATTERING EFFECT ON JOSEPHSON CURRENT IN A d-WAVE SUPERCONDUCTOR/d-WAVE SUPERCONDUCTOR JUNCTION

By taking into account the interface scattering effect in a d-wave superconductor (S)/insulator layer (I)/d-wave superconductor (S) junction, the temperature dependence of the critical current and the current-phase relation are studied theoretically. It is found that both the barrier scattering and the roughness scattering at the interface always suppress the Andreev reflection and the current-phase relation is almost sinusoidal in the junction. The Josephson current strongly depends on the crystalline axis orientation of the d-wave superconductor in the junction. Some different phenomena appear depending on whether the crystal orientations of the superconductors on the two sides are the same or not, and this is mainly presented in the influence of the zero-energy states formation at the interface on the critical current which changes with temperature and phase.

Tunneling conductance in a gapped graphene-based normal metal–insulator–d-wave superconductor junction: Case of massive Dirac electrons

Using the extended Blonder–Tinkham–Klapwijk formalism, the normal conductance spectra in a normal/insulator/d-wave superconductor gapped graphene junction, considering effect of asymmetric pairing potential (anisotropic d-wave) is investigated in the limit of a thin barrier. The charged Dirac carriers in this structure are treated as massive relativistic particles. The exact solutions of Dirac–Bogoliubov–de Gennes Hamiltonain for three normal gapped graphene, insulator and superconductor region of junction and related normal and Andreev reflection coefficients are obtained. In this work, we focus to study in detail the effect of rotated angle α caused by d-wave order parameter of superconductor in tunneling conductance behavior in our system. In particular, the conductance spectra in terms of the bias voltage eV, the d-wave superconducting orientation angular α and also the electrostatic potentials U 0 and V 0 is plotted. It is shown that by increasing rotated angle α in that case of U 0 → ∞ and mv 2 F / E F =0.99, the maximum of resonant peak of normal conductance decreases and also the position of peak shifts from eV / Δ = 1 to progressively lower values. We also observe an oscillatory behavior of conductance versus insulator potential V 0.

Quantum point contact conductance in normal metal/insulator/ metal/ [formula omitted] mixed wave superconductor junctions

The tunneling conductance in a normal metal/insulator/metal/ d x 2 − y 2 + i d x y mixed wave superconductor (N/I/N/ d x 2 − y 2 + i d x y ) junction is calculated, where the N/I/N region is a quantum wire. It is found in the single-mode case that the magnitude of the tunneling conductance near zero voltage is enhanced due to the Andreev bound state by quasiparticles with perpendicular and horizontal injection, and the zero-bias conductance varies with L ( L is the distance from insulating layer to the interface of N/ d x 2 − y 2 + i d x y mixed wave superconductor). Splitting of the zero-bias conductance peak appears in the quantum point contact tunneling spectra for an N/I/N/ d x 2 − y 2 + i d x y junction, and several subgap peaks can split at the same time. On increasing both L and the magnitude ratio of the two components for the d x 2 − y 2 + i d x y mixed wave, the subgap resonances exhibit an alternately high and low behavior inside the energy gap. These results are different from those in d-wave and p-wave superconductor junctions.

Shot noise in the semiconductor/ferromagnetic d-wave superconductor tunnel junction

Considering the dependence of the gap on the exchange energy in ferromagnetic d-wave superconductor, we use an extended Blonder-Tinkham-Klapwijk approach to investigate the shot noise in semiconductor/ferromagnetic d-wave superconductor junction by solving the Bogoliubov-de Gennes（BdG） equation. It is shown that the exchange energy h0 in the ferromagnetic d-wave superconductor may induce a split of the shot noise double-peak at zero-bias and the energy gap peak, and the interval between the two split peaks is equal to 2h0; furthermore, with the increasing exchange energy h0, the shot noise and the ratio of shot noise power to average current are restrained.

Differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent

This paper applies the Bogoliubov–de Gennes equation and the Blonder–Tinkham–Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent Is. We find that (i) a three-humped structure appears at a nearly critical supercurrent Is and z ≈ 0.5 for the normal metal/insulator/metal/dx2+y2-wave superconductor junction; (ii) the zero-bias conductance peak splits into two peaks with sufficiently large applied current for the normal metal/insulator/metal/dxy-wave superconductor junction; (iii) the conductance spectrum exhibits oscillating behaviour with the bias voltage and the peaks of the resonances are suppressed by increasing supercurrent Is.

SQUID-Based Investigation of D-Wave Superconductor Junctions

SQUID-Based Investigation of D-Wave Superconductor Junctions

Anomalous conductance spectrum in ferromagnet/d-wave superconductor junctionscarrying a supercurrent

The Blonder–Tinkham–Klapwijk approach is exploited to study the conductancespectrum in ferromagnet(F)/d-wave superconductor(S) junctions with a transversesupercurrent in S. In the absence of exchange energy with (110) contact(α = π/4), when the supercurrent , we find that the conductance coherence peaks split into subpeaks atZ = 0.5 and 1.0. The energy difference between the two subpeaks corresponding to a single coherence peak isfound to increase as the supercurrent increases. For the F/S junctions with (110) contact atZ = 0.5 and 1.0, when the supercurrent the subpeaks split again: in this the exchange energy plays adominant role, similar to the Zeeman effect. At certain values ofh0/EF, we found that the two Zeeman-like peaks around zero energy could merge into a singleone.

Spin-polarized transport in ferromagnetic semiconductor/ferromagnetic d-wave superconductor tunnel junction

By solving a self-consistent equation for the d-wave superconducting gap and the magnetization, and applying an extended Blonder-Tinkham-Klapwijk approach, we study the spin-polarized quasiparticle transport coefficients and the differential conductance in ferromagnetic semiconductor/ferromagnetic d-wave superconductor junction. It is shown that (1) the exchange energy h0 in the ferromagnetic d-wave superconductor may make the zero-bias conductance peak and energy gap peak split into two peaks, and the energy difference between the two splitting peaks is equal to 2h0; (2) the exchange energy hFS in the ferromagnetic semiconductor can decrease the height of the two peaks resulting from splitting of the zero-bias conductance peak. For the splitting of the energy gap conductance peak, however, with hFS increased the left-hand peak is lowered and the right-hand peak is raised in the parallel configuration, but the left-hand peak is raised and the right-hand peak is lowered in the antiparallel configuration.

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks, however, neither of them can influence the Zeeman effect.

Resonant proximity effect in normal metal/diffusive ferromagnet/superconductor junctions

Resonant proximity effect in the normal metal / insulator / diffusive ferromagnet / insulator / $s$- and d-wave superconductor (N/I/DF/I/S) junctions is studied for various regimes by solving the Usadel equation with the generalized boundary conditions. It is shown that the resonant proximity effect originating from the exchange field in DF layer strongly modifies the tunneling conductance and density of states.

Spin-polarized proximity effect in superconducting junctions

We study spin dependent phenomena in superconducting junctions in both ballistic and diffusive regimes. For ballistic junctions we study both ferromagnet/ s- and d-wave superconductor junctions and two-dimensional electron gas/ s-wave superconductor junctions with Rashba spin-orbit coupling. It is shown that the exchange field always suppresses the conductance while the Rashba spin-orbit coupling can enhance it. In the latter part of the article we study the diffusive ferromagnet/insulator/ s- and d-wave superconductor (DF/I/S) junctions, where the proximity effect can be enhanced by the exchange field in contrast to common belief. This resonant proximity effect in these junctions is studied for various situations: conductance of the junction and density of states of the DF are calculated by changing the heights of the insulating barriers at the interfaces, the magnitudes of the resistance in DF, the exchange field in DF, the transparencies of the insulating barriers and the angle between the normal to the interface and the crystal axis of d-wave superconductors α. It is shown that the resonant proximity effect originating from the exchange field in DF strongly influences the tunneling conductance and density of states. We clarify the followings: for s-wave junctions, a sharp zero bias conductance peak (ZBCP) appears due to the resonant proximity effect. The magnitude of this ZBCP can exceed its value in normal states in contrast to that observed in diffusive normal metal/superconductor junctions. We find similar structures to the conductance in the density of states. For d-wave junctions at α = 0 , we also find a result similar to that in s-wave junctions. The magnitude of the resonant ZBCP at α = 0 can exceed that at α / π = 0.25 due to the formation of the mid gap Andreev resonant states. To cite this article: T. Yokoyama, Y. Tanaka, C. R. Physique 7 (2006).

Meissner effect in diffusive normal metal/ d-wave superconductor junctions

The Meissner effect in diffusive normal metal/insulator/ d-wave superconductor junctions is studied theoretically in the framework of the Usadel equation under the generalized boundary condition. The effect of midgap Andreev resonant states (MARS) formed at the interface of d-wave superconductor is taken into account. It is shown that the formation of MARS suppresses the susceptibility of the diffusive normal metal.