Green function theory of dirty two-band superconductivity

We study the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor, where we assume the equal-time spin-singlet s-wave pair potential in each conduction band and the hybridization between the two bands as well as the band asymmetry. In the clean limit, the phase of hybridization determines the stability of two states: called $s_{++}$ and $s_{+-}$. The interband impurity scatterings decrease $T_c$ of the two states exactly in the same manner when the Hamiltonian preserves time-reversal symmetry. We find that a superconductor with larger hybridization shows more moderate suppression of $T_c$. This effect can be explained by the presence of odd-frequency Cooper pairs which are generated by the band hybridization in the clean limit and are broken by impurities.Comment: 11 pages, 2 figure

Properties of rough interfaces in superconductors with d-wave pairing

Theoretical model of a rough interface in a superconductor with d-wave symmetry of the order parameter is proposed. The surface roughness is introduced by means of a surface layer with small electronic mean free path. The proximity effect between such a layer and a bulk d-wave superconductor is studied theoretically in the framework of the quasiclassical Eilenberger theory. It is shown that as a result of strong scattering in the interlayer the d-wave component of the order parameter near the interface is reduced while the s-wave component localized near the interface is generated. Angular and spatial structure of the pair potential and the electronic density of states near the interface is calculated. The interplay of the zero-energy (midgap) and finite-energy bound states leads to peculiarities in the energy dependence of the angle-averaged density of states. We argue that the model is relevant for the description of rough interfaces in high Tc superconductors. In the framework of the present approach we calculate the Josephson critical current for several types of junctions with rough interface

Dirty two-band superconductivity with interband pairing order

We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order as well as a spin-singlet s-wave order parameter due to the two-band degree of freedom. In a spin-singlet superconductor, $T_c$ is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in a spin-triplet superconductor, $T_c$ decreases with the increase of the impurity concentration. We conclude that Cooper pairs belonging to odd-band-parity symmetry class are fragile under the random impurity potential even though they have s-wave pairing symmetry.Comment: 7 pages, 2 figures embedde

Josephson Effect due to Odd-Frequency Pairs in Diffusive Half Metals

Motivated by a recent experiment [Keizer et al., Nature (London) 439, 825 (2006)], we study the Josephson effect in superconductor/diffusive half metal/superconductor junctions using the recursive Green function method. The spin-flip scattering at the junction interfaces opens the Josephson channel of the odd-frequency spin-triplet Cooper pairs. As a consequence, the local density of states in a half metal has a large peak at the Fermi energy. Therefore the odd-frequency pairs can be detected experimentally by using the scanning tunneling spectroscopy

Electron transport in a ferromagnet-superconductor junction on graphene

In a usual ferromagnet connected with a superconductor, the exchange potential suppresses the superconducting pairing correlation. We show that this common knowledge does not hold in a ferromagnetsuperconductor junction on a graphene. When the chemical potential of a graphene is close to the conical point of energy dispersion, the exchange potential rather assists the charge transport through a junction interface. The loose-bottomed electric structure causes this unusual effec

Microscopic theory of tunneling spectroscopy in Sr2_2RuO4_4

We study the surface Andreev bound state (ABS) of superconducting Sr$_2$RuO$_4$, which is a candidate material for the realization of the chiral $p$-wave superconducting state. In order to clarify the role of chiral edge modes as ABSs, the surface density of states and the tunneling conductance is calculated in the normal metal/Sr$_2$RuO$_4$ junction within the framework of recursive Green's function method, while taking into account the orbital degrees of freedom (including Spin-Orbit interactions) with realistic material parameters. In Sr$_2$RuO$_4$, there are two bands $\alpha$ and $\beta$ originating from quasi-one-dimensional orbitals $d_{yz}$ and $d_{zx}$ and a two-dimensional band $\gamma$ originating from $d_{xy}$ orbital. We discuss about the contributions of various electronic bands to LDOS and the influence of atomic spin-orbit interaction (SOI). In the light of our calculations, quasi-one-dimensional model with dominant pair potentials in $\alpha$ and $\beta$ bands is consistent with conductance measurements in Au/Sr$_{2}$RuO$_{4}$ junctions.Comment: to be published in J. Phys. Soc. Jpn., 10 pages, 12 figure

Tunability of Andreev levels via spin-orbit coupling in Zeeman-split Josephson junctions

We study Andreev reflection and Andreev levels $\varepsilon$ in Zeeman-split superconductor/Rashba wire/Zeeman-split superconductor junctions by solving the Bogoliubov de-Gennes equation. We theoretically demonstrate that the Andreev levels $\varepsilon$ can be controlled by tuning either the strength of Rashba spin-orbit interaction or the relative direction of the Rashba spin-orbit interaction and the Zeeman field. In particular, it is found that the magnitude of the band splitting is tunable by the strength of the Rashba spin-orbit interaction and the rength of the wire, which can be interpreted by a spin precession in the Rashba wire. We also find that if the Zeeman field in the superconductor has the component parallel to the direction of the junction, the $\varepsilon$-$\phi$ curve becomes asymmetric with respect to the superconducting phase difference $\phi$. Whereas the Andreev reflection processes associated with each pseudospin band are sensitive to the relative orientation of the spin-orbit field and the exchange field, the total electric conductance interestingly remains invariant.Comment: 10 pages, 8 figure

Effects of the phase coherence on the local density of states in superconducting proximity structures

We theoretically study the local density of states in superconducting proximity structure where two superconducting terminals are attached to a side surface of a normal-metal wire. Using the quasiclassical Green's function method, the energy spectrum is obtained for both of spin-singlet $s$-wave and spin-triplet $p$-wave junctions. In both of the cases, the decay length of the proximity effect at the zero temperature is limited by a depairing effect due to inelastic scatterings. In addition to the depairing effect, in $p$-wave junctions, the decay length depends sensitively on the transparency at the junction interfaces, which is a unique property to odd-parity superconductors where the anomalous proximity effect occurs.Comment: 11 pages, 9 figure

Conductance Spectroscopy of Spin-triplet Superconductors

We propose a novel experiment to identify the symmetry of superconductivity on the basis of theoretical results for differential conductance of a normal metal connected to a superconductor. The proximity effect from the superconductor modifies the conductance of the remote current depending remarkably on the pairing symmetry: spin-singlet or spin-triplet. The clear-cut difference in the conductance is explained by symmetry of Cooper pairs in a normal metal with respect to frequency. In the spin-triplet case, the anomalous transport is realized due to an odd-frequency symmetry of Cooper pairs.Comment: 4pages, 3 figures embedde

Josephson effect in two-band superconductors

We study theoretically the Josephson effect between two time-reversal two-band superconductors, where we assume the equal-time spin-singlet $s$-wave pair potential in each conduction band. %as well as the band asymmetry and the band hybridization in the normal state. The superconducting phase at the first band $\varphi_1$ and that at the second band $\varphi_2$ characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green's function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band $\delta\varphi_1$, the phase difference at the second band $\delta\varphi_2$, and the difference at the center-of-mass phase $\delta(\varphi_1+\varphi_2)/2$. A Cooper pairs generated by the band hybridization carries the last current component. In some cases, the current-phase relationship deviates from the sinusoidal function as a result of time-reversal symmetry breaking down.Comment: 6 page, 2 figure