Coulomb gap, Coulomb blockade, and dynamic activation energy in frustrated single-electron arrays
Daniel M. Kaplan, Victor A. Sverdlov, Konstantin K. Likharev
Abstract
We have used modern supercomputer facilities to carry out extensive numerical simulations of statistical properties of 1D and 2D arrays of single-electron islands with random background charges, in the limit of small island self-capacitance. In particular, the spectrum of single-electron addition energies shows a clear Coulomb gap that, in 2D arrays, obeys the Efros-Shklovskii theory modified for the specific electron-electron interaction law. The Coulomb blockade threshold voltage statistics for 1D arrays is very broad, with r.m.s. width
δ
V
t
growing as
<
V
t
>∝
N
1/2
with the array size
N
. On the contrary, in square 2D arrays of large size the distribution around
<
V
t
>∝N
becomes relatively narrow
(δ
V
t
/<
V
t
>∝1/N)
, and the dc
I
-
V
curves are virtually universal. At low voltages, the slope
G
0
(T)
of
I
-
V
curves obeys the Arrhenius law. The corresponding activation energy
U
0
grows only slowly with
N
and is considerably lower than the formally calculated "lowest pass" energy
E
max
of the potential profile, thus indicating the profile "softness".