Angular dependence of Josephson currents in unconventional superconducting junctions

Abstract

Josephson effect in junctions between unconventional superconductors is studied theoretically within the model describing the effects of interface roughness. The particularly important issue of applicability of the frequently used Sigrist-Rice ͑SR͒ formula for Josephson current in d-wave superconductor/insulator/d-wave superconductor junctions is addressed. We show that although the SR formula is not applicable in the ballistic case, it works well for rough interfaces when the diffusive normal metal regions exist between the d-wave superconductor and the insulator. It is shown that the SR approach only takes into account the component of the d-wave pair potential symmetric with respect to an inversion around the plane perpendicular to the interface. Similar formula can be derived for general unconventional superconductors with arbitrary angular momentum l. [1][2][3][4] Because of such unconventional symmetry, the study of Josephson effect in high-T C superconducting ͑HTS͒ junctions attracted a lot of interest. A while ago, a simple formula for the Josephson current of d-wave superconductor/insulator/d-wave superconductor ͑DID͒ junctions was proposed by Sigrist and Rice ͑SR͒. 5 According to the SR formula, the Josephson current is proportional to cos 2␣ cos 2␤, where the ␣͑␤͒ denotes the angle between the normal to the interface and the crystal axis of the left͑right͒ d-wave superconductor. 5 Although the SR formula can explain experiments with the so-called junctions, 1,2 this formula does not take into account the effect of midgap Andreev resonant states ͑MARS͒ formed at junction interfaces. 6,7 Actually, as shown in Ref. 8, SR formula does not work in ballistic d-wave junctions for ␣ 0 and ␤ 0 where MARS influence severely the charge transport at low temperatures. It was shown both theoretically 9,10 and experimentally 11,12 that MARS induce a nonmonotonic temperature dependence of the maximum Josephson current in DID junctions. On the other hand, SR formula has been extensively used to analyze experiments with various types of HTS Josephson junctions. [13][14][15] Experiments with HTS junctions are of high importance for basic understanding of high-T c superconductivity since they may provide information on possible subdominant admixtures to the d-wave symmetry. [16][17][18] Therefore it is of fundamental interest to understand the physical mechanisms that determine the angular dependence of Josephson current in HTS junctions. For this reason, the determination of the conditions of applicability of the SR formula is an important issue which is addressed in the present paper.In the following, we study the Josephson current in D /DN/I /DN/D junctions, where DN denotes diffusive normal metal and could be formed between the insulator and d-wave superconductors. The calculations are based on the quasiclassical Green's function method applicable to unconventional superconductor junctions. 19,20 We find that the resulting Josephson current in D /DN/I /DN/D junctions is well fitted by the SR formula. Near the transi...

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