Ll. Sohn et M. Octavio, HALF-INTEGER SHAPIRO STEPS IN SINGLE-PLAQUETTE JOSEPHSON-JUNCTION ARRAYS IN A MAGNETIC-FIELD, Physical review. B, Condensed matter, 49(13), 1994, pp. 9236-9239
We derive an equation for a single-plaquette array of Josephson juncti
ons for an arbitrary number of flux quanta per unit cell f. We show th
at for f = 1/2 this equation is equivalent to one derived for a 2 X 2
Josephson-junction array in the f = 1/2 ground state. We show that in
the presence of an rf drive with frequency nu, the system exhibits, fo
r all nonzero values of f, integer and half-integer Shapiro steps at [
V] = nhnu/4e, where n = 1,2,3,... . In addition, very small subharmoni
c Shapiro steps at [V] = nhnu/2em, where m = 1,2,3,... and not equal t
o n, are observed for all f not equal to zero. These particular steps,
however, are found to be consistently smaller than the integer and ha
lf-integer steps concurrently present in the array I-V characteristics
. Contrary to recent suggestions, we show that single-plaquette array
behavior is not entirely consistent with that of large arrays of Josep
hson junctions and hence not responsible for the display of fractional
giant Shapiro steps in these large arrays. Such behavior may, however
, be responsible for the recent observation of half-integer steps in h
igh-T(c) grain-boundary junctions.