Center for Materials Theory, Department of Physics
and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019
(Received 20 September 1999)
Using a time-dependent Anderson Hamiltonian, a quantum dot with an ac voltage
applied to a nearby gate is investigated. A rich dependence of the
linear response conductance on the external frequency and driving
amplitude is demonstrated. At low frequencies a sufficiently strong ac
potential produces sidebands of the Kondo peak in the spectral density
of the dot, and a slow, roughly logarithmic decrease in conductance
over several decades of frequency. At intermediate frequencies, the
conductance of the dot displays an oscillatory behavior due to the
appearance of Kondo resonances of the satellites of the dot level. At
high frequencies, the conductance of the dot can vary rapidly due to
the interplay between photon-assisted tunneling and the Kondo
resonance. ©2000 The American Physical Society
PACS: 72.15.Qm, 73.50.Mx, 85.30.Vw
[e.g., Phys. Rev. D 40, 2172 (1989)]
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efficient using a second
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For the Hamiltonian (1) the time average dot(epsilon,t)>[equivalent]Im<Adot(epsilon,t)>/pi,
where Adot(epsilon,t) is the retarded and
hence causal function defined in Ref. 13, Eq. (28).
Hence in an experiment one may also expect peaks spaced by [h-bar]Omega
in the differential conductance.
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In contrast, an ac bias voltage of order TK/e
can produce significant effects such as Kondo sidebands, cf. Refs.
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To derive Eq. (6), we note that the full retarded propagators g
for the lead electrons are given in terms of their bare values g0
by g = g0 + g0Tg0
with matrix multiplication implied in the time and lead quantum number k.
The transition matrix T is given by Tkk[prime]
where Adot is the corresponding propagator for
the dot. The above two relations may be obtained directly from Eq. (1)
for arbitrary U (via the equations of motion for the c's,
for example). The total transition rate is then just 2 Im Tkk
from the optical theorem, which then implies for the time averaged
rate wleads(epsilon) = 2|Vk|2Im<Adot(epsilon,t)>.
Finally, using the relation between A and rhodot
given in Ref. 14 and the definition of Gammadot(epsilon)
given in Ref. 8, we arrive at Eq. (6).
A.A. Abrikosov, Physics (N.Y.) 2, 5 (1965).