Midgap Andreev Resonant States Research Articles

Temperature dependence of zero-bias conductance in a normal metal/ferromagneticsuperconductor junction

In this study, we investigate the temperature dependence of zero-bias conductance (ZBC)in a normal metal/ferromagnetic superconductor (N/FS) junction where the ferromagneticsuperconductor (FS) is in three different Cooper pairing states: spin singlet s-wave pairing(SWP), spin triplet opposite spin pairing (OSP) and spin triplet equal spin pairing (ESP).We include the exchange field of the FS and effective mass mismatch (EMM) intwo sides of the junction. In the OSP case, the formation of mid-gap Andreevresonant states at the interface of the junction, extremely affects the ZBC withtemperature and exchange field. In the SWP and ESP cases, numerical results showvarious temperature dependences of the ZBC, depending on various exchange fields,h andx, wherex parameterizes the effect of the EMM. From the obtained results, not only can we estimatethe magnitude of the exchange field, but also we can learn more about the pairing of theFS. Also the results show that, in comparison with experimental data, the inclusion ofEMM is essential.

Midgap Andreev resonant state affected by superconducting proximity effect of high-Tc cuprate attached to diffusive normal metal

We report how a midgap Andreev resonant state (MARS) is affected by the superconducting proximity effect at an interface of diffusive normal metal/insulator/dx.2_y2-wave superconductor (DN/I/DS) junctions. A zero-bias conductance peak (ZBCP) was observed for the (110)-oriented interface in Ag/SiO/Bi2Sr2CaCu2O8+δ (Bi-2212) planar junctions. The experimental ZBCP was analyzed by the extended circuit theory, which was improved by the introduction of spatial variations of the pair potential in a DS electrode near the junction interface. Our experimental results are well explained by the extended circuit theory for DN/I/DS junctions.

Odd-frequency pairing state in superconducting junctions

Using a quasiclassical Green’s function formalism, we show that odd-frequency pairing state can be ubiquitously induced in the superconducting junctions. In ballistic normal metal–superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk, we show that odd-frequency pairing state can be induced at the interface. Even in the s-wave superconductor junction, the amplitude of the odd-frequency component is enhanced in the normal metal. The appearance of the midgap Andreev resonant states due to the sign change of the anisotropic pair potential at the interface is reinterpreted in terms of the generation of the odd-frequency pair amplitude.

Odd-frequency pairing in normal-metal/superconductor junctions

We theoretically study the induced odd-frequency pairing states in ballistic normal-metal/superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk and a normal-metal layer has an arbitrary length. Using the quasiclassical Green's function formalism, we demonstrate that, quite generally, the pair amplitude in the junction has an admixture of an odd-frequency component due to the breakdown of translational invariance near the N/S interface where the pair potential acquires spatial dependence. If a superconductor has an even-parity pair potential (spin-singlet $s$-wave or spin-singlet ${d}_{xy}$-wave state), the odd-frequency pairing component with odd parity is induced near the N/S interface, while in the case of an odd-parity pair potential (spin-triplet ${p}_{x}$ wave) the odd-frequency component with even parity is generated. We show that in conventional $s$-wave junctions, the amplitude of the odd-frequency pairing state is strongest in the case of a full-transparency N/S interface and is enhanced at energies corresponding to the peaks in the local density of states (LDOS). In ${p}_{x}$- and ${d}_{xy}$-wave junctions, the amplitude of the odd-frequency component on the S side of the N/S interface is enhanced at zero energy where the midgap Andreev resonant state (MARS) appears due to the sign change of the pair potential. The odd-frequency component extends into the N region and exceeds the even-frequency component at energies corresponding to the LDOS peak positions, including the MARS. At the edge of the N region the odd-frequency component is nonzero while the even-frequency one vanishes. We show that the concept of the odd-frequency pairing state plays a pivotal role to interpret a number of phenomena in nonuniform superconducting systems, like McMillan-Rowell and midgap Andreev resonance states.

Ubiquitous presence of odd-frequency pairing state in superconducting junctions

We predict generation of the odd-frequency pairing state near interfaces in conventional even-frequency superconductors. Using the quasiclassical Green's function formalism, we show that the pair amplitude can be decomposed into even and odd-frequency components. We demonstrate that, quite generally, the spin-singlet even-parity (spin-triplet odd-parity) pair potential in a superconductor induces the odd-frequency pairing component with spin-singlet odd-parity (spin-triplet even-parity) near interfaces. The magnitude of the induced odd-frequency component is enhanced in the presence of the midgap Andreev resonant state due to the sign change of the anisotropic pair potential at the interface. The Josephson effect should therefore occur between odd- and even-frequency superconductors, contrary to the standard wisdom. A method to probe the odd-frequency superconductors is proposed.

Andreev bound states in dirty unconventional superconductor junctions

We review the recent development in the theory of proximity effect in unconventional superconductor junctions. The low energy transport in the unconventional superconductor junction is governed by two interference effects of a quasiparticle: formation of a midgap Andreev resonant state (MARS) at the junction interface and the diffusion of Cooper pair into a normal-metal (proximity effect). Both of them are sensitive to the pairing symmetry of superconductivity. In a p-wave superconductor junction, the MARS penetrates from a superconductor into a normal-metal and drastically increases the conductance and the Josephson current. We will show that such anomalous quantum transport is the result of a cooperative effect between the MARS and the proximity effect. Experimental trials to detect the Josephson current between two p-wave superconductors are in progress.

Temperature dependence of tunneling conductance in diffusive normal metal/triplet superconductor junctions

The thermal broadening effect on the tunneling conductance in diffusive normal metal/triplet superconductor (DN/TS) junctions is studied based on the Usadel equation under the generalized boundary condition. The zero-bias conductance peak (ZBCP) enhances in the antinodal direction, due to the coexistence of the proximity effect and the midgap Andreev resonant states at the DN/TS junction interface. It is found that the ZBCP is affected by the thermal broadening effect especially for tunnel junctions with the low transparency and the small Thouless energy.

Anomalous Josephson current by odd frequency Cooper pairs

The Josephson effect in superconductor/diffusive normal metal/superconductor junctions is studied theoretically, where the p-wave pairing symmetry is assumed in superconductors. The amplitudes of the Josephson current become much larger than those in the s-wave junctions because of a cooperative effect between the midgap Andreev resonant states and the proximity effect. We show that the Josephson current is carried by the odd-frequency Cooper pairs in diffusive metals.

Josephson spin current in triplet superconductor junctions

This paper theoretically discusses the spin current in spin-triplet superconductor/insulator/spin-triplet superconductor junctions. At low temperatures, a midgap Andreev resonant state anomalously enhances not only the charge current but also the spin current. The coupling between the Cooper pairs and the electromagnetic fields leads to a Fraunhofer pattern in the direct current spin flow in magnetic fields and an alternative spin current under applied bias voltages.

Theory of Josephson effect in [formula omitted]-wave superconductor/diffusive ferromagnet/ [formula omitted]-wave superconductor junctions

We study Josephson effect in d -wave superconductor/diffusive ferromagnet/ d -wave superconductor junctions, changing the exchange field and the angles between the normal to the interfaces and the crystal axes of d -wave superconductors. We find a 0– π transition at a certain value of the exchange field. In the presence of midgap Andreev resonant states (MARS), the maximum Josephson current has a double peak structure as a function of temperature due to the exchange field and the competition between the proximity effect and the MARS.

Smearing origin of zero-bias conductance peak in Ag-SiO-Bi2Sr2CaCu2O8+δ planar tunnel junctions: influence of diffusive normal metal verified with the circuit theory

We propose a new approach of smearing origins of a zero-bias conductance peak (ZBCP) in high-Tc superconductor tunnel junctions through the analysis based on the circuit theory for a d-wave pairing symmetry. The circuit theory has been recently developed from conventional superconductors to unconventional superconductors. The ZBCP frequently appears in line shapes for this theory, in which the total resistance was constructed by taking account of the effects between a d-wave superconductor and a diffusive normal metal (DN) at a junction interface, including the midgap Andreev resonant states (MARS), the coherent Andreev reflection (CAR) and the proximity effect. Therefore, we have analyzed experimental spectra with the ZBCP of Ag-SiO-Bi2Sr2CaCu2O8+δ (Bi-2212) planar tunnel junctions for the {110}-oriented direction by using a simplified formula of the circuit theory for d-wave superconductors. The fitting results reveal that the spectral features of the ZBCP are well explained by the circuit theory not only excluding the Dynes's broadening factor but also considering only the MARS and the DN resistance. Thus, the ZBCP behaviors are understood to be consistent with those of recent studies on the circuit theory extended to the systems containing d-wave superconductor tunnel junctions.

Josephson current through superconductor/diffusive-normal-metal/superconductor junctions: Interference effects governed by pairing symmetry

The Josephson effect in superconductor/diffusive-normal-metal/superconductor junctions is studied numerically by using the recursive Green function method. In superconductors, we consider spin-singlet $s$- and $d$-wave and spin-triplet $p$-wave pairing symmetries. The pairing symmetry governs two interference effects in junctions: the formation of a midgap Andreev resonant state at junction interfaces and the proximity effect in diffusive normal metals. A cooperative effect between the two interference effects causes anomalous Josephson current in a $p$-wave symmetry.

Nonmonotonic temperature dependence of critical current in diffusived-wave junctions

We study the Josephson effect in D/I/DN/I/D junctions, where I, DN, and D denote an insulator, a diffusive normal metal, and a $d$-wave superconductor, respectively. The Josephson current is calculated based on the quasiclassical Green's function theory with a general boundary condition for unconventional superconducting junctions. In contrast to $s$-wave junctions, the product of the Josephson current and the normal-state resistance is enhanced by making the interface barriers stronger. The Josephson current has a nonmonotonic temperature dependence due to the competition between the proximity effect and the midgap Andreev resonant states.

Anomalous Josephson Effect inp-Wave Dirty Junctions

The Josephson effect in p-wave superconductor/diffusive normal metal/p-wave superconductor junctions is studied theoretically. Amplitudes of Josephson currents are several orders of magnitude larger than those in s-wave junctions. Current-phase (J-phi) relations in low temperatures are close to those in ballistic junctions such as J proportional to sin(phi/2) and J proportional to phi even in the presence of random impurity potentials. A cooperative effect between the midgap Andreev resonant states and the proximity effect causes such anomalous properties and is a character of the spin-triplet superconductor junctions.

Theory of charge transport in high-TC superconductor junctions from the view point of the mid gap Andreev resonant state

In this paper, we report important features about high-TC superconductor junctions. It has been clarified that the most important property of high-TC junctions is the sign change of the pair potential on the Fermi surface reflecting on the d-wave pair potential. This unique feature induces the formation of the mid gap Andreev resonant state (MARS) at the interface of the high-TC superconductor junctions. The MARS influences various physical quantities, e.g., quasiparticle current, Josephson effect and proximity effect. In d-wave superconductor, the MARS competes with the proximity effect. On the other hand, for triplet superconductor junctions, it can coexist. We can expect giant proximity effect enhanced by the MARS.

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).

Theory of charge transport in diffusive normal metal/unconventional superconductor junctions

Novel theory of charge transport which is available for both a diffusive normal metal/unconventional singlet superconductor (DN/USS) and a diffusive normal metal/triplet superconductor (DN/TS) junctions is presented based on the Keldysh–Nambu quasiclassical Green's function formalism. For DN/USS junctions, proximity effect in DN region and the mid gap Andreev resonant state (MARS) formed at the USS side of the DN/USS interface strongly compete each other. On the other hand, for DN/TS junctions, proximity effect is enhanced by the MARS. In DN/TS junction, the total resistance is drastically reduced and is completely independent of the resistance of the DN in the extreme case. We can also check this dramatic effect by numerical simulations without using quasiclassical formalism.

Theory of thermal and charge transport in diffusive normal metal/superconductor junctions

Thermal and charge transport in the diffusive normal metal(DN) / insulator / $s$-, $d$- and p-wave superconductor junctions are studied for various situations, where we have used the Usadel equation with Nazarov's generalized boundary condition. Thermal and electrical conductance of the junction and the Lorentz ratio are calculated by varying the magnitudes of the resistance, the Thouless energy and the magnetic scattering rate in DN, the transparency of the insulating barrier, and the angle between the normal to the interface and the crystal axis of d-wave superconductors or the angle between the normal to the interface and the lobe direction of the p-wave pair potential. New general expression is derived for the calculation of the thermal conductance. It is demonstrated that the proximity effect doesn't influence the thermal conductance while the mid gap Andreev resonant states suppress it. We have also discussed a possibility of distinguishing pairing symmetries based on the dependencies of the electrical and thermal conductance on temperatures.

Theory of anomalous charge transport and proximity effect in diffusive normal metal/triplet superconductor junctions

Charge transport and proximity effect of a diffusive normal metal/triplet superconductor (DN/TS) junction are studied based on the Keldysh-Nambu quasiclassical Green's function formalism. In triplet superconductor junctions, mid gap Andreev resonant state (MARS) and proximity effect can coexist each other. The local density of states of quasiparticles in DN region has a zero energy peak contrary to the case of singlet unconventional superconductor junctions. This property becomes a novel method to identify the triplet symmetry of unconventional superconductivity.

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.