Theory of the tunneling spectroscopy of ferromagnetic superconductors

Abstract

We study tunneling conductance in normal metal / insulator / ferromagnetic superconductor junctions. The tunneling spectra show a clear difference between spin-singlet s-wave pairing, spintriplet opposite spin pairing and spin-triplet equal spin pairing: These pairings exhibit, respectively, gap struture, double peak structure and zero bias peak in the spectra. The obtained result may serve as a tool for determining the pairing symmetry of ferromagnetic superconductors.Magnetism and superconductivity have been under intensive pursuit in the field of low temperature physics. Recently the interplay of them has also attracted much attention because nontrivial phenomena are predicted or found experimentally. Such phenomena are expected to occur in ferromanget/superconductor junctions 1,2,3 and also in ferromangnetic superconductors (FS). Up to now, several bulk materials, e.g., UGe 2 4 , ZrZn 2 5 and URhGe 6 , are identified as FS. How Cooper pairs are formed in FS or under the coexistence of ferromagnetism and superconductivity is an interesting problem. However the pairing symmetries of FS are still controversial.Ferromagnetic superconductors seem to be triplet superconductors because singlet pairing and ferromagnetism are antagonist while triplet pairing have a uniform magnetic moment. However the possibility of swave pairing cannot be excluded. 7,8,9,10,11,12,13,14 For example it is predicted that UGe 2 can have s-wave superconductivity mediated by local ferromagnetic spins. 10,11The study of the nuclear relaxation rate cannot rule out the possibility of s-wave pairing in UGe 2 .12,13 A weak ferromagnetic Fermi liquid theory also suggests the possibility of s-wave superconductivity.14 Therefore detailed comparison between theoretical predictions and experimantal data is required to settle this problem. Then the properties of thermodynamic quantities should be noted: For example equilibrium thermodynamic quantities for Balian-Werthamer state of p-wave pairing, which is realized in B phase of 3 He, are expected to show swave property because its gap is constant.15 In this way, equilibrium thermodynamic quantities for p-wave pairing could not be clearly distinguished from those of s-wave pairing. Therefore nonequilibrium quantities are more desirable to compare with experimental data. Although some predictions are made on the properties of junctions with equal spin pairing(ESP) FS, 16,17,18,19 the study of tunneling spectra for possible candidate pairings of FS is insufficient.Tunneling spectroscopy provides an important information on the superconducting gap and its pairing symmetry. In normal metal / supercunductor junctions, Andreev reflection (AR) 20 is a key concept for low energy transport. Blonder, Tinkham and Klapwijk (BTK) formulated the tunneling conductance where the AR is taken into account 21 . This enables us to study the energy gap of superconductors. The generalization of the BTK formula for normal metal / unconventional superconductor junctions are also useful to study the properties of unconvent...

Current-Phase Relation in FSIFS Josephson Junction

“…This is because the increase of exchange fields decreases Andreev reflection coefficient and the Josephson current. Also, as it is mentioned in [23,24], the wave functions of P wave in antiparallel case depend on exchange field. Comparing Figs.…”

“…3a, b that Josephson current does not depend on exchange field. This is due to the fact that the wave functions in the case of parallel P wave symmetry do not depend on exchange fields [23,24]. In order to discuss with more details, we obtain Josephson current from (5) which is as follows:…”

“…Also, we examine antiparallel pair potential (AP) in which the − → dvector of FS is considered to be parallel with exchange field and parallel pair potential (PP) in which the FS − → dvector and the exchange field perpendicular to each other [22][23][24]. To illustrate our model in a simple case, we apply a two-dimensional calculation in the framework developed by Furusaki and Tsukada [4].…”

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

“…The homogeneous spin splitting in the superconductor can be realized in the systems such as thin F/S junctions [9,10] or thin superconductor films under the application of an in-plane magnetic field [11]. It has been shown that N/ZS junctions, where N stands for a normal metal, can generate highly spin-polarized current [12][13][14][15]. Josephson junctions with spin-split superconductors have been also studied in various types of structures.…”

Unconventional superconductors with spin-orbit interaction

“…The homogeneous spin splitting in the superconductor can be realized in the systems such as thin F/S junctions [200,201] or thin superconductor films under the application of an in-plane magnetic field [202]. It has been shown that N/ZS junctions, where N stands for a normal metal, can generate highly spin-polarized current [203][204][205][206]. Josephson junctions with spin-split superconductors have been also studied in various types of structures.…”