Effects of neglected terms in Josephson junctions

It took over 40 years to develop a consistent theory (BCS-Bogoliubov) of superconductivity after its experimental discovery, in the simplest case of spin-singlet, s-wave orbital symmetry. The investigation of other types of symmetry in superconducting and superfluid systems was stimulated after the discovery of A and B phases of 3 He and unconventional pairings in heavy fermion and cuprate high temperature superconductors (HTS). The non-BCS pairing mechanisms underlying superconducting phases with unconventional symmetry remain one of the most intriguing problems in condensed matter physics. In high temperature superconductors, the pairing symmetry is solidly established as spin-singlet, orbital d-wave, while in different superconductors other symmetries are observed as well. While the nodal lines of the superconducting gap dx2-y2 attracted much attention, because they allowed as unusual (for BCS case) combination of superconductivity with low-energy excitations, a no less interesting consequence of d-wave symmery followed from the order parameter changing sign, thus producing an intrinsic, direction-dependent -shift of the superconducting phase. This phenomenon is particularly well manifested in the properties of Josephson junctions with high temperature superconducting materials, leading to the appearance of spontaneous currents and bistabilities, Andreev bound states and zero-bias anomalies in the normal conductance of Josephson junctions produced by the existance of these bound states. The latter was instrumental in establishing their d-wave pairing symmetry and remains the subject of an intensive theoretical and experimental research over the years. The process of Andreev reflection converts the quasi particle current to the supercurrent via the incoming electron-like quasiparticle is being reflected by the off-diagonal superconductor potential (order parameter) as a hole-like quasiparticle and vice versa. The effect takes place not only on SNS junctions but also in weak links and whenever two superconductors with different amplitudes of the order parameter are brought in contact. In Josephson junctions this leads to the formation of Andreev levels. The Andreev reflection amplitude depends on the superconducting phase; therefore, the Andreev levels are phase-sensitive. This allows to express both the superconducting and quasiparticle contributions of the Josephson current in terms of transport through the Andreev levels. The Andreev bound state with energy zero appears in junctions containing a superconductor with direction dependent -phase shift of the order parameter, which leads to canceling the energy-dependent terms in the quantization condition for this level. Its existance produces the specific zero-bias conductance peak (ZBCP) in the differential conductance of the Josephson junction. A convenient method of calculationg conductance of restricted quantum structures is based on the Landauer-Büttiker approach, expressing it through the scattering coefficients. In the following we will show that the appearance of ZBCP in HTS Josephson junctions may drastically change if certain terms, which are usually neglected in such calculations, are properly considered.