Spectrum and thermodynamic currents in one-dimensional Josephson elements

Abstract

The dc Josephson effect is considered from the thermodynamic point of view. Universal thermodynamic equations, relating both bound and continuum contributions to the Josephson current with the normal electron scattering amplitudes are derived for the single mode case. To derive these equations we use and further develop the method of spatial separation between the superconducting and normal parts of the junction. We also use this method to find the Andreev bound states in structures containing superconducting components. The general thermodynamic formulas are applied to the calculation of the current in various Josephson-type structures. In particular, the crucial role of the continuum contribution is demonstrated, even for short junctions (where it is usually neglected). We also find structures where the bound states supporting the giant currents are well separated; thus they can, hopefully, be populated nonuniformly and such current can be measured.

Scattering matrix approach to the description of quantum electron transport

“…The critical current increases by I c with the appearance of each new open channel (Fig. The discrete and continuous spectra can be simultaneously taken into account by using the Crane theorem, as in [254,255]. In the case of strong scattering Z 1, an Andreev quantum dot is formed.…”

Josephson quantum spin thermodynamics

“…Andreev approximation [35] gives q + = q − = k F , with k F being Fermi wavevector, and E F >> ∆. Imposing boundary conditions on (3,4) at x = 0, gives…”

Tuning the 0 − π Josephson junction with a magnetic impurity: Role of tunnel contacts, exchange coupling, e − e interactions and high-spin states

“…For | E | ≪ E F , we can write , where ξ 0 = E F /( k F Δ 0 ) is the BCS coherence length 10 . By using the boundary conditions mentioned in supplementary material section I.B one can get the different scattering amplitudes.…”

“…In the section on Josephson current in presence of a HSM, we use the Furusaki-Tsukuda formalism to calculate the total Josephson current. To calculate the individual contribution-(i) the bound state we take the derivative of bound state energy with respect to phase difference and (ii) for the continuum contributions use the formalism developed in Refs 9 and 10 . Following this we plot the Andreev bound states as a function of phase difference for different values of spin and magnetic moment of the HSM in the section on Andreev bound states.…”