Odd-frequency pairing in normal metal/superconductor junctions

Abstract

We 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 even-parity pair potential (spin-singlet s-wave state), the odd-frequency pairing component with odd-parity is induced near the N/S interface, while in the case of odd-parity pair potential (spin-triplet $p_x$-wave or spin-singlet $d_{xy}$-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 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.

27 pages, 12 figures

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• A spin triplet supercurrent through the half-metallic ferromagnet CrO2
• Theory of the proximity effect in junctions with unconventional superconductors
• Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
• Triplet proximity effect in FSF trilayers
• Manifestation of the odd-frequency spin-triplet pairing state in diffusive ferromagnet / superconductor junctions
• Anomalous Josephson effect in p-wave dirty junctions
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