Josephson effect in hybrid superconductor-normal metal structures
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The clean SNS junction, with a phase difference x across the normal metal barrier and without Fermi level mismatch between the components, is modeled by a step like pair potential. The quasiclassical equations are obtained from the Gorkov equations by the elimination of crystal momenta and are valid in the existence of only the off-diagonal potential(pair potential). Then for the SNS junction, the quasiclassical Green functions are obtained. At zero temperature, in the long barrier limit(d ^ ^o)> the current is found to have a sawtooth dependence on the phase difference, the amplitude of which is inversely proportional to the thickness of the normal layer. At finite temperatures in the limits d and Tc T, the current is found to have exponential dependence on the thickness of the normal layer, T exp(—d/^7’) sin y, .where = vfI2ttT. An extension of single SNS structures is the periodic SNS structure which may as well exhibit Josephson effect. It is simulated by a periodic step-wise pair potential, where the phase of the pair potential changes by some constant value in subsequent superconducting islands. Bogoliubov equations in the semicla.ssical limit are employed, yielding the density of states(DOS). In the DOS, there appears some forbidden energy regions, which point out to a band structure.
Quasiclassical Green Functions
Bogoliubov-de Gennes Equations