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Register a new userOdd-frequency pairing effect on the superfluid density and the Pauli spin susceptibility in spatially nonuniform spin-singlet superconductors
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S. Higashitani
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A theoretical study is presented on the odd-frequency spin-singlet pairing that arises in nonuniform even-frequency superconductors as a consequence of broken translation symmetry. The effect of the odd-frequency pairing on the superfluid density and the spin susceptibility is analyzed by using the quasiclassical theory of superconductivity. It is shown that (1) the superfluid density is reduced by the formation of the odd-frequency singlet pairs and (2) the odd-frequency pairing increases the spin susceptibility even though its spin symmetry is singlet. The two unusual phenomena are related to each other through a generalized Yosida formula by taking into account both the even- and odd-frequency pairing effects.
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The spin transport inside an odd-frequency spin-triplet superconductor differs from that of a conventional superconductor due to its distinct symmetry properties. We show that the peculiar nature of the density of states allows for an even larger spin injection than in the normal-state. Moreover, when the odd-frequency pairing inherits its temperature dependence from a conventional superconductor through the proximity effect, the density of states can transition from gapless to gapped as the temperature decreases. At the transition point, there is a massive spin accumulation inside the odd-frequency superconductor. While the spin-flip scattering time is known to decrease below the superconducting transition temperature in conventional superconductors, we find that the same is true for the spin-orbit scattering time in odd-frequency superconductors. This renormalization is particularly large for energies close to the gap edge, if such a gap is present.
The effects of spin independent hybridization potential and spin orbit coupling on two band superconductor with equal time s-wave inter band pairing order parameter is investigated theoretically. To study symmetry classes in two band superconductors the Gorkov equations are solved analytically. By defining spin singlet and spin triplet s wave order parameter due to two band degree of freedom the symmetry classes of Cooper pair are studied. For spin singlet case it is shown that spin independent hybridization generates Cooper pair belongs to even frequency spin singlet even momentum even band parity (ESEE) symmetry class for both intraband and interband pairing correlations. For spin triplet order parameter, intraband pairing correlation generates odd frequency spin triplet even momentum even band parity (OTEE) symmetry class whereas, interband pairing correlation generates even frequency spin triplet even momentum odd band parity ETEO) class. For the spin singlet, spin orbit coupling generates pairing correlation that belongs to odd frequency spin singlet odd momentum even band parity (OSOE) symmetry class and even frequency spin singlet even momentum even band parity (ESEE) for intraband and interband pairing correlation respectively. In the spin triplet case for itraband and interband correlation, spin orbit coupling generates even-frequency spin triplet odd momentum even band parity (ETOE) and even frequency spin triplet even momentum odd band parity (ETEO) respectively.
We show that mixed-parity superconductors may exhibit equal-spin pair correlations that are odd-in-time and can be tuned by means of an applied field. The direction and the amplitude of the pair correlator in the spin space turn out to be strongly dependent on the symmetry of the order parameter, and thus provide a tool to identify different types of singlet-triplet mixed configurations. We find that odd-in-time spin-polarized pair correlations can be generated without magnetic inhomogeneities in superconducting/ferromagnetic hybrids when parity mixing is induced at the interface.
The proximity effect from a spin-triplet $p_x$-wave superconductor to a dirty normal-metal has been shown to result in various unusual electromagnetic properties, reflecting a cooperative relation between topologically protected zero-energy quasiparticles and odd-frequency Cooper pairs. However, because of a lack of candidate materials for spin-triplet $p_x$-wave superconductors, observing this effect has been difficult. In this paper, we demonstrate that the anomalous proximity effect, which is essentially equivalent to that of a spin-triplet $p_x$-wave superconductor, can occur in a semiconductor/high-$T_c$ cuprate superconductor hybrid device in which two potentials coexist: a spin-singlet $d$-wave pair potential and a spin--orbit coupling potential sustaining the persistent spin-helix state. As a result, we propose an alternative and promising route to observe the anomalous proximity effect related to the profound nature of topologically protected quasiparticles and odd-frequency Cooper pairs.
Superconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. This offers a fascinating arena to study the physics of broken gauge symmetry. However, the important symmetries in superconductors are not only the gauge invariance. Especially, the symmetry properties of the pairing, i.e., the parity and spin-singlet/spin-triplet, determine the physical properties of the superconducting state. Recently it has been recognized that there is the important third symmetry of the pair amplitude, i.e., even or odd parity with respect to the frequency. The conventional uniform superconducting states correspond to the even-frequency pairing, but the recent finding is that the odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously. Especially, this is the case in the Andreev bound state (ABS) appearing at the surface/interface of the sample. The other important recent development is on the nontrivial topological aspects of superconductors. As the band insulators are classified by topological indices into (i) conventional insulator, (ii) quantum Hall insulator, and (iii) topological insulator, also are the gapped superconductors. The influence of the nontrivial topology of the bulk states appears as the edge or surface of the sample. In the superconductors, this leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs of the superconductors are the place where the symmetry and topology meet each other which offer the stage of rich physics. In this review, we discuss the physics of ABS from the viewpoint of the odd-frequency pairing, the topological bulk-edge correspondence, and the interplay of these two issues. It is described how the symmetry of the pairing and topological indices determines the absence/presence of the ZEABS, its energy dispersion, and properties as the Majorana fermions.
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