Unconventional Superconductor Junctions Research Articles

Theory of proximity effect in s+p -wave superconductor junctions

We derive a boundary condition for the Nambu Keldysh Green's function in diffusive normal metal / unconventional superconductor junctions applicable for mixed parity pairing. Applying this theory to a 1d model of $s+p$-wave superconductor, we calculate LDOS in DN and charge conductance of DN / $s+p$-wave superconductor junctions. When the $s$-wave component of the pair potential is dominant, LDOS has a gap like structure at zero energy and the dominant pairing in DN is even-frequency spin-singlet $s$-wave. On the other hand, when the $p$-wave component is dominant, the resulting LDOS has a zero energy peak and the dominant pairing in DN is odd-frequency spin-triplet $s$-wave. We show the robustness of the quantization of the conductance when the magnitude of $p$-wave component of the pair potential is larger than that of $s$-wave one. These results show the robustness of the anomalous proximity effect specific to spin-triplet superconductor junctions.

Anomalous inverse proximity effect in unconventional superconductor junctions

We investigate the effects of Andreev bound states due to the unconventional pairing on the inverse proximity effect of ferromagnet/superconductor junctions. Utilizing quasiclassical Eilenberger theory, we obtain the magnetization penetrating into the superconductor. We show that in a wide parameter range the direction of the induced magnetization is determined by two factors: whether Andreev bound states are present at the junction interface and the sign of the spin-mixing angle. In particular, when Andreev bound states appear at the interface, the direction of the induced magnetization is opposite to that without Andreev bound states. We also clarify the conditions under which the inverted induced magnetization appears. Applying this novel effect helps distinguishing the pairing symmetry of a superconductor.

Study of spin polarization in graphene-based unconventional superconductor junctions

In this paper, we study spin polarization in ferromagnetic-unconventional superconductor graphene junction, where we consider three different Cooper pairing states: one unconventional dx2-y2-wave and two time-reversal symmetry broken dx2-y2+is and dx2-y2+idxy . In the absence of Fermi wave mismatch (FWM), a high-spin polarization is achievable if we increase the exchange field of ferromagnet close to the Fermi energy values in the ferromagnetic region. In the presence of FWM, the angle between the normal to the interface and the x-axis of superconducting crystal, i. e. β plays a crucial role in spin polarization. For β=π/8, the polarization is totally negative especially in the sub-gap region when modified conventional Andreev reflection (MCAR) governs, and it is completely positive when modified specular Andreev reflection (MSAR) dominates on the tunneling junction. If we rotate β from β=π/8 to β=π/4, the spin polarization shows three different behaviors for the mentioned Cooper pairing states. Therefore, not only is it possible to discriminate MCAR from MSAR which is significant especially from a condensed-matter perspective but also one can find high spin polarization by tuning the junction parameters which is important in spintronic applications.

Theory of Surface Andreev Bound States and Odd-Frequency Pairing in Superconductor Junctions

In this review, we mention about the theoretical achievement of physics of surface Andreev bound state (SABS) and odd-frequency pairing during this quarter century based on our research. Currently, topological superconductors with Majorana edge state have become a central issue in condensed matter physics. It is noted that Majorana edge state is nothing but a zero energy surface Andreev bound state (ZESABS) and the study of ZESABS has started in the context of the pairing symmetry of high Tc cuprate. We mention our obtained conductance formula of quasiparticle tunneling and Josephson current in unconventional superconductor junctions through ZESABS have already captured the essence of the charge transport profile via the Majorana fermion. We also mention that in the presence of ZESABS, odd-frequency pairing like spin-triplet s-wave or spin-singlet p-wave is hugely enhanced near the surface or interface. We further analyze the spectroscopy of the induced odd-frequency pairings by extending bulk-boundary correspondence in ZESABS. If we consider a semi-infinite superconductor with ZESABS, the induced odd-frequency pair amplitude can be expressed by a c-number defined in bulk, which we call spectral bulk-boundary correspondence. The odd-frequency pair amplitude is classified into singular part and regular one, the former part is proportional to $\sim 1/z$ (z is a complex frequency) reflecting the presence of ZESABS, and the latter one is proportional to $\sim z$ . The coefficient of the latter one diverges at the topological phase transition point. Analyzing the spectral behavior of the odd-frequency pairing is useful to understand the critical phenomena near topological transition points.

Theory of the proximity effect in two-dimensional unconventional superconductors with Rashba spin-orbit interaction

We study the anomalous proximity effect in diffusive normal metal (DN)/unconventional superconductor junctions, where the local density of states (LDOS) in the DN has a zero-energy peak due to the penetration of the odd-frequency spin-triplet $s$-wave pairing. In this study, we consider a two-dimensional unconventional superconductor on the substrate in the presence of a Rashba spin-orbit coupling (RSOC) $\lambda$, where the Rashba vector is parallel to the $z$-direction. The anomalous proximity effect, originally predicted in spin-triplet $p$-wave superconductor junctions, is sensitive to the RSOC. It disappears with the increase of $\lambda$. On the other hand, the anomalous proximity effect can be switched on by the large $\lambda$ values in the spin-singlet $d_{xy}$-wave superconductor junctions. The resulting zero-energy LDOS and the magnitude of the odd-frequency spin-triplet $s$-wave pair amplitude increase with the increase of $\lambda$.

Current fluctuations in unconventional superconductor junctions with impurity scattering

The order parameter of bulk two-dimensional superconductors is classified as nodal, if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Non-magnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between a normal-metal and unconventional superconductors by solving the quasi-classical Eilenberger equation self-consistently, including the presence of non-magnetic impurities in the superconductor. As the impurity strength increases, we find that superconductivity is suppressed for almost all order parameters since (i) at zero applied bias, the effective transferred charge calculated from the noise-current ratio tends to the electron charge $e$ and (ii) for finite bias, the current-voltage characteristics follows that of a normal state junction. There are notable exceptions to this trend. First, gapful nontrivial (chiral) superconductors are very robust against impurity scattering due to the linear dispersion relation of their surface Andreev bound states. Second, for nodal nontrivial superconductors, only p_x-wave pairing is almost immune to the presence of impurities due to the emergence of odd-frequency s-wave Cooper pairs near the interface. Owing to their anisotropic dependence on the wave vector, impurity scattering is an effective pair breaking mechanism for the rest of nodal superconductors. All these behaviors are neatly captured by the noise-current ratio, providing a useful guide to find experimental signatures for unconventional superconductivity.

Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors

We study the surface Andreev bound states (SABSs) and quasiparticle tunneling spectroscopy of three-dimensional (3D) chiral superconductor by changing the surface (interface) misorientation angle of chiral superconductors. We obtain analytical formula of the energy dispersion of SABS for general pair potential when an original 4$\times$4 BdG Hamiltonian can be reduced to be two 2$\times$2 blocks. The resulting SABS for 3D chiral superconductors with pair potential given by $k_z(k_x + ik_y)^{\nu}$ $({\nu} = 1, 2)$ has a complicated energy dispersion due to the coexistence of both point and line nodes. We focus on the tunneling spectroscopy of this pairing in the presence of applied magnetic field which induces Doppler shift of quasiparticle spectra. By contrast to previous known Doppler effect in unconventional superconductors, zero bias conductance dip can change into zero bias conductance peak by external magnetic field. We also study SABSs and tunneling spectroscopy for possible pairing symmetries of UPt$_3$ . For this purpose, we extend a standard formula of tunneling conductance of unconventional superconductor junctions in order to treat spin-triplet non-unitary pairings. The magneto tunneling spectroscopy, i.e., tunneling spectroscopy in the presence of magnetic field, can serve as a guide to determine the pairing symmetry of this material.

Influence of the impurity scattering on charge transport in unconventional superconductor junctions

We study the influence of non-magnetic impurity scatterings on the tunneling conductance of a junction consisting of a normal metal and a disordered unconventional superconductor by solving the quasiclassical Eilenberger equation self-consistently. We find that the impurity scatterings in both the Born and unitary limits affect the formation of the Andreev bound states and modify strongly the tunneling spectra around zero bias. Our results are interpreted well by the appearance of odd-frequency Cooper pairs near the interface and by the divergent behavior of the impurity self-energy. The present paper provides a useful tool to identify the pairing symmetry of unconventional superconductors in experiments.

Effect of d-wave pair coupling on evanescent type of Andreev reflection

In this paper, we investigate the current resulted from virtual Andreev process, passing through a N/S gapped graphene-based junction, where superconductivity in the S-region is induced by depositing unconventional d-wave superconductor. It is shown that the evanescent type of Andreev reflections occurs above the critical electron incident angle, and needs to take into account its effect when calculating the tunneling conductance in the both conventional and unconventional superconductor junctions. In the evanescent wave regime, the new pure imaginary wavevector of hole-like quasiparticle is obtained, and consequently, the tunneling conductance formalism is modified. We show that due to the nature of pair interaction in d-wave superconductivity, considering the virtual Andreev process affects significantly the behavior of charge carriers in the structure. In particular, the conductance in the virtual regime is more sensitive to the superconductor gap characterized by orbital rotated angle, so that with increasing α the width of zero conductance versus bias energy decreases and above α=0.1π the current in junction is supplied just by virtual Andreev process.

Current-Phase Relation of YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7-X</sub>/Nb Unconventional Superconductor Junctions

The knowledge of the current-phase relation (CPR) in superconducting junctions is essential in many applications like low-dissipative superconducting electronics or superconducting qubits for quantum computation. Theory predicts that unconventional superconductivity induces a significant second harmonic J2 in the CPR. Consequently, anomalies such as half-integer Shapiro steps should be observed in the microwave assisted current-voltage characteristics of the junctions. We performed electric transport measurements in YBa2Cu3O7-x/Nb unconventional superconductor junctions for 72 different tunneling directions in the ab plane and found no trace of such anomalies. This suggest that J2 is insignificantly small so that YBa2Cu3O7-x/Nb junctions have a purely sinusoidal CPR.

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.

Superharmonic Josephson relations in unconventional superconductor junctions with a ferromagnetic barrier

For misorientation of $45\ifmmode^\circ\else\textdegree\fi{}$ in the $a\text{\ensuremath{-}}b$ plane of Josephson junctions between two $d$-wave superconductors separated by a ferromagnet, unusual superharmonic current-phase relations (CPR) are predicted in the clean case and for high barrier transparency. Depending on the strength of the magnetic barrier influence, junctions with triply degenerate $0$, $\ensuremath{\pi}∕2$, and $\ensuremath{\pi}$ equilibrium states exhibit CPR similar to $I\ensuremath{\sim}{I}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}\phantom{\rule{0.2em}{0ex}}4\ensuremath{\phi}$ at low temperature, whereas junctions with doubly degenerate $0$ and $\ensuremath{\pi}$ states or junctions with a nondegenerate state $\ensuremath{\pi}∕2$ have CPR close to $I\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}{I}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\phi}$, respectively, at all temperatures. In the presence of an external magnetic field, the corresponding critical currents oscillate with periods of ${\ensuremath{\phi}}_{0}∕4$ and ${\ensuremath{\phi}}_{0}∕2$.

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.

Circuit theory of unconventional superconductor junctions.

We extend the circuit theory of superconductivity to cover transport and proximity effect in mesoscopic systems that contain unconventional superconductor junctions. The approach fully accounts for zero-energy Andreev bound states forming at the surface of unconventional superconductors. As a simple application, we investigate the transport properties of a diffusive normal metal in series with a d-wave superconductor junction. We reveal the competition between the formation of Andreev bound states and proximity effect that depends on the crystal orientation of the junction interface.

Andreev bound state and charge transport in unconventional superconductors

The Andreev bound state which is formed at the surface or the interface of the unconventional superconductor junctions arouses many novel interference effect which cannot be expected for conventional superconductor junctions. Physical meaning of the zero bias tunneling conductance peak, zero bias dip of shot noise, and anomalous temperature dependence of Josephson current are discussed.

Phase Dependent Energy Levels of Bound States and D.C. Josephson Current in Unconventional Superconductor / Ferromagnetic Insulator / Unconventional Superconductor Junctions

Properties of the DC Josephson effects in unconventional-superconductors under the presence of an exchange field in the insulator are studied theoretically. The current-phase relation of the DC Jos...

DC Josephson current in S/F/S jucntions

The d. c. Josephson current in unconventional-superconductor / ferromagnet / unconventional-superconductor junctions is calculated for various cases to reveal the influence of the exchange interaction on the Josephson effect. When the two superconductors have d-wave symmetry, the Josephson current is drastically suppressed with the increase of the exchange interaction. On the other hand, when the two superconductors have different parities, e.g. s-wave and p-wave, an enhancement of the Josephson current is obtained with the increment of the exchange interaction in Ferromagnet. The direction of the Josephson current is reversed by the flip of the magnetization axis.