Energy gap structure and tunneling characteristics of layered superconductors Page: 9 of 34
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The critical temperature T, is solved from the linearized version of Eq.(14). A brief
summary of the results, which are discussed in detail in Ref. 6 and 8, is as follows. In the
limit of zero hopping the critical temperature is solved from
A>N(0)ajj(Teo) = 1, (17)
where A> is the larger of the two Ao, and all(T) = ln(2-ywgj/rT),7 = 1.78. With increasing
hopping T, is lowered steadily from the zero hopping limit Teo. In the limit of strong
hopping, i.e. Ja w, the critical temperature is solved from
A+N(0)all(T,) = 1, (18)
with A+ defined in Eq.(12).
The OP's at zero temperature depend also on the hopping strengths. In .the zero.
hopping limit the equations separate into two -independent equations whose solutions are
the gaps for the individual layers. With increasing hopping the larger of the two solutions,
which is designated as A1, decreases while the smaller one, A2 increases.. Thus, the two
layers are more similar to each other in their superconducting properties.: In the strong
hopping limit, we find that the ratio of the gaps satisfies A1/A2 = A1/A2. The average gap
A+ defined in Eq.(12) is the energy gap of the energy bands. These results are summarized
in Fig.1 for a set of parameters A02/Aoi = 0.7, A01N(0) = 0.5, J2/J1 = 0.3, and J/Teo
ranging from 0.1 to 10.
In Fig.2 we show A.(T), n = 1,2, for the same of mpodel parameters except that
Ji/Teo = 1. For these parameters the critical temperature T, = 0.92Teo. The dominant
OP A1 has the typical BCS behavior. The lesser OP A2 initially behaves as if it is heading
toward a critical temperature lower than T, but turns around to follow Ai above 0.6Tc,
where superconductivity in layer 2 is induced by the proximity effect. This result is typical
for systems with two or more coupled order parameters.
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Liu, S.H. & Klemm, R.A. Energy gap structure and tunneling characteristics of layered superconductors, report, June 1, 1993; Illinois. (digital.library.unt.edu/ark:/67531/metadc682733/m1/9/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.