The modern physics of superconductivity can be called the physics of unconventional superconductivity. The discovery of the d-wave symmetry of the order parameter in high-temperature superconductors and the triplet superconductivity in compound Sr2RuO4 has caused a huge stream of theoretical and experimental investigations of unconventional superconductors. In this review we discuss some novel aspects of the Josephson effect which are related to the symmetry of the order parameter. The most intriguing of them is spontaneous current generation in an unconventional weak link. The example of a Josephson junction in the form of a grain boundary between two disorientated d-wave or f-wave superconductors is considered in detail. Josephson current–phase relations and the phase dependences of the spontaneous current that flows along the interface are analyzed. The spontaneous current and spontaneous phase difference are manifestations of the time-reversal symmetry (𝒯 ) breaking states in the system. We analyzed the region of appearance of 𝒯-breaking states as function of temperature and mismatch angle. A review of the basics of superconducting qubits with emphasis on specific properties of d-wave qubits is given. Recent results in the problem of decoherence in d-wave qubits, which is the major concern for any qubit realization, are presented.
Josephson effects were predicted theoretically by B. D. Josephson in 1962. Josephson effects occur in weak links, structures which link two bulk superconductors 1 and 2, capable of carrying a supercurrent but not as strongly superconducting as the bulk materials. This chapter applies a specified voltage to the weak link, but many weak links have impedances at the relevant microwave frequencies of a few ohms or less. The surprising appearance of the oscillatory current is the d.c. Josephson effect. The ability of weak links to provide tunable oscillator power at very high frequencies can be very useful, but the power available from a single junction is of order RIJ2 typically less than 1 μW, and from a low-impedance source which is difficult to match; practical applications usually therefore make use of a suitable array of weak links.
Calibrated measurements of both the real and imaginary parts of the microwave impedance of proximity coupled superconducting weak links have been made. The measurements were compared with analytic calculations based on several different models for the supercurrent Is and quasiparticle current. For dc bias currents I1 less than the critical current Ic, the experimental results are consistent with the Josephson relation Is=Ic sinφ, where φ is the quantum phase angle. However, for I1≳Ic, the Fourier component of Is at the Josephson frequency is found to be significantly less (∼0.65±0.1) than would be predicted from Is=Ic sinφ, and consistent with Tinkham’s analysis of a phase slip process. The experimental results indicate that the phase-dependent part of the quasiparticle current, if it exists at all, is no more than 10% of the total quasiparticle current. These results do not necessarily contradict previous measurements made on true tunnel junctions because of the fundamental differences between the two types of devices.
We show that superconductors have a thin spectrum associated with spontaneous symmetry breaking similar to that of antiferromagnets, while still being in full agreement with Elitzur's theorem, which forbids the spontaneous breaking of local (gauge) symmetries. This thin spectrum in the superconductors consists of in-gap states that are associated with the spontaneous breaking of a global phase symmetry. In qubits based on mesoscopic superconducting devices, the presence of the thin spectrum implies a maximum coherence time which is proportional to the number of Cooper pairs in the device. Here we present the detailed calculations leading up to these results and discuss the relation between spontaneous symmetry breaking in superconductors and the Meissner effect, the Anderson-Higgs mechanism, and the Josephson effect. Whereas for the Meissner effect a symmetry breaking of the phase of the superconductor is not required, it is essential for the Josephson effect.
The BCS-like pairing in ultracold fermionic atomic (
UCFAG) gases is studied in the model of "isotopic-spin" pairing proposed in 1991 \cite% {Ku-Hof-SSC}. This model assumes a mismatch (
δ) in chemical potentials of pairing fermionic atoms. It is shown that a
π-Josephson junction can be realized in
UCFAG systems, where the left and right banks
are the
UCFAG superfluids. The weak link
M consists from the normal
with the finite mismatch
δ. If the
π-junction is a part of a closed ring the superfluid mass-current flows spontaneously in the ring, i.e., the time-reversal symmetry is broken spontaneously. This is realized if the radius of the ring
R is larger than the critical one $% R_{c} $. All these effects exist also in the case when
δ≫Δ, where
Δ is the superfluid gap, but with the reduced thickness of the weak link. It is also discussed, that if junctions
SM1M2S and trilayers
from
UCFAG are realizable this renders a possibility for a novel electronics - \textit{hypertronics}.
he BCS-like pairing in ultracold fermionic atomic (
UCFAG) gases is studied in the model of "isotopic-spin" pairing proposed in 1991 \cite% {Ku-Hof-SSC}. This model assumes a mismatch (
δ) in chemical potentials of pairing fermionic atoms. It is shown that a
π-Josephson junction can be realized in
UCFAG systems, where the left and right banks
are the
UCFAG superfluids. The weak link
M consists from the normal
with the finite mismatch
δ. If the
π-junction is a part of a closed ring the superfluid mass-current flows spontaneously in the ring, i.e., the time-reversal symmetry is broken spontaneously. This is realized if the radius of the ring
R is larger than the critical one $% R_{c} $. All these effects exist also in the case when
δ≫Δ, where
Δ is the superfluid gap, but with the reduced thickness of the weak link. It is also discussed, that if junctions
SM1M2S and trilayers
from
UCFAG are realizable this renders a possibility for a novel electronics - \textit{hypertronics}.