Figure 1
(a) Current
(
10) perpendicular to
versus time for
,
, and
[dark gray (blue) line] and
[light gray (red) line], assuming a valley-polarized situation
. For “Shapiro-step” conditions [Eq. (
16)] periodic oscillations can be seen [light gray (red)], while away from this condition aperiodic oscillations occur [dark gray (blue)]. (b) Same as (a) but for potential
with
,
,
, and frequencies
[light gray (red) line] and
[dark gray (blue) line]. Both currents are aperiodic. For the matching condition
[dark gray (blue)] a considerable enhancement followed by a saturation of the amplitude of the current oscillations occurs, while away from this resonance no enhancement is seen versus time. (c) Current
(
12) for
at
, using
. At Shapiro resonance [
, dark gray (blue) line] pronounced current enhancement occurs, cf. Eqs. (
17,
18), while away from the resonance [
, light gray (red) line] no enhancement is seen. (d) Time-dependent reflectivity
, calculated by numerical integration of Eq. (
17), solid blue line, and by using the approximation (
19), red dashed line, near resonance for
and
. (e)
at resonance (dashed green line,
,
) and near resonance (solid blue line,
,
). At the resonance,
increases with time
, in agreement with Eq. (
19). (f) Time-averaged reflectivity
as a function of
for
. Equidistant resonances occur at
(dashed blue vertical lines), cf. Eq. (
18). One of the resonance peaks is well fitted by the resonance equation (
20), as shown by short-dashed green line. (g)
as a function of the driving frequency
for
: resonance peaks are clearly seen at Shapiro-step conditions (
18)
, indicated as dashed magenta vertical lines.
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