Energy gap structure and tunneling characteristics of layered superconductors Page: 10 of 34
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The density-of-states in the superconducting state is calculated in the standard way:
N,(w) = - ImG(k,) (19)
where 6 = 0+. After integrating over k, we find
_ sdkz -iv c - e12 ce1
N,(w) = N(0)I--[ + ] . ,()
N'( ' N() f27r 2c t v2 +} a+ + v2 + a_ ---+ (+0
where the quantities c and af are defined in Eqs.(14) and (15). We show in Fig.3 a set
of total DOS curves at zero temperature for the same set of model parameters in Fig.1
with Ji/Teo ranging from a weak hopping value of 0.1 to a strong hopping value of 5.
The calculated A1,2 are marked on the graph with two kinds of arrows. The four curves
are displaced vertically by 2 units successively. It can be seen that in the weak hopping
case; the bottommost curve, the DOS. has two sets of peaks corresponding to the OP's.of
the two layers, in agreement with the conclusions of Refs. 1 -and 2. Each set resembles
the BCS result. The system may be regarded as two nearly independent superconductors,
each with its own energy gap. The strong hopping case, the topmost curve, the peaks are
situated halfway between A1 and A2, i.e. -the position of A+, in agreement with Refs. 3-5.
The two middle curves for intermediate hopping do not conform to either physical picture.
In particular, for J1ITeo = 1, we find N,(w) = 0 for w < w0 = A+ 1 _ A2 /(J1 - J2)2.
[In calculating the curves in Fig.3 we have put in a nonvanishing 6 = 0.3 - 0.5 in Eq.(20)
to smooth out the curves, and this results in a small and nonvanishing DOS inside of the
threshold]. The first peak. occurs at w = A+ 1 - A2 /(Jx + J2)2. In the limit of 6 = 0,
the peak is a logarithmic singularity, i.e.
N,(w) = A+In w - w' + B , (21)
where A+, B are nonsingular in w and refer to the high or low side of the singularity.
A second logarithmic singularity occurs at w = w+ = (J + J2)2 + A+ + A-, which is
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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/m1/10/: accessed January 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.