69 research outputs found
Metastable Voltage States of Coupled Josephson Junctions
We investigate a chain of capacitively coupled Josephson junctions in the
regime where the charging energy dominates over the Josephson coupling,
exploiting the analogy between this system and a multi-dimensional crystal. We
find that the current-voltage characteristic of the current-driven chain has a
staircase shape, beginning with an (insulating) non-zero voltage plateau at
small currents. This behavior differs qualitatively from that of a single
junction, which should show Bloch oscillations with vanishing dc voltage. The
simplest system where this effect can be observed consists of three grains
connected by two junctions. The theory explains the results of recent
experiments on Josephson junction arrays.Comment: 5 pages, 4 figures include
Resistance of Josephson Junction Arrays at Low Temperatures
We study motion of vortices in arrays of Josephson junctions at zero
temperature where it is controlled by quantum tunneling from one plaquette to
another. The tunneling process is characterized by a finite time and can be
slow compared to the superconducting gap (so that ). The
dissipation which accompanies this process arises from rare processes when a
vortex excites a quasiparticle above the gap while tunneling through a single
junction. We find that the dissipation is significant even in the case , in particular it is not exponentially small in this parameter. We
use the calculated energy dissipation for the single vortex jump to estimate
the physical resistance of the whole array.Comment: 24 pages, LaTeX references added, to appear in PR
Nonlinear Viscous Vortex Motion in Two-Dimensional Josephson-Junction Arrays
When a vortex in a two-dimensional Josephson junction array is driven by a
constant external current it may move as a particle in a viscous medium. Here
we study the nature of this viscous motion. We model the junctions in a square
array as resistively and capacitively shunted Josephson junctions and carry out
numerical calculations of the current-voltage characteristics. We find that the
current-voltage characteristics in the damped regime are well described by a
model with a {\bf nonlinear} viscous force of the form , where is the vortex velocity,
is the velocity dependent viscosity and and are
constants for a fixed value of the Stewart-McCumber parameter. This result is
found to apply also for triangular lattices in the overdamped regime. Further
qualitative understanding of the nature of the nonlinear friction on the vortex
motion is obtained from a graphic analysis of the microscopic vortex dynamics
in the array. The consequences of having this type of nonlinear friction law
are discussed and compared to previous theoretical and experimental studies.Comment: 14 pages RevTex, 9 Postscript figure
Dynamics of An Underdamped Josephson Junction Ladder
We show analytically that the dynamical equations for an underdamped ladder
of coupled small Josephson junctions can be approximately reduced to the
discrete sine-Gordon equation. As numerical confirmation, we solve the coupled
Josephson equations for such a ladder in a magnetic field. We obtain
discrete-sine-Gordon-like IV characteristics, including a flux flow and a
``whirling'' regime at low and high currents, and voltage steps which represent
a lock-in between the vortex motion and linear ``phasons'', and which are
quantitatively predicted by a simple formula. At sufficiently high anisotropy,
the fluxons on the steps propagate ballistically.Comment: 11pages, latex, no figure
Single-vortex-induced voltage steps in Josephson-junction arrays
We have numerically and analytically studied ac+dc driven Josephson-junction
arrays with a single vortex or with a single vortex-antivortex pair present. We
find single-vortex steps in the voltage versus current characteristics (I-V) of
the array. They correspond microscopically to a single vortex phase-locked to
move a fixed number of plaquettes per period of the ac driving current. In
underdamped arrays we find vortex motion period doubling on the steps. We
observe subharmonic steps in both underdamped and overdamped arrays. We
successfully compare these results with a phenomenological model of vortex
motion with a nonlinear viscosity. The I-V of an array with a vortex-antivortex
pair displays fractional voltage steps. A possible connection of these results
to present day experiments is also discussed.Comment: 10 pages double sided with figures included in the text. To appear in
Journal of Physics, Condensed Matte
Collective Transport in Arrays of Quantum Dots
(WORDS: QUANTUM DOTS, COLLECTIVE TRANSPORT, PHYSICAL EXAMPLE OF KPZ)
Collective charge transport is studied in one- and two-dimensional arrays of
small normal-metal dots separated by tunnel barriers. At temperatures well
below the charging energy of a dot, disorder leads to a threshold for
conduction which grows linearly with the size of the array. For short-ranged
interactions, one of the correlation length exponents near threshold is found
from a novel argument based on interface growth. The dynamical exponent for the
current above threshold is also predicted analytically, and the requirements
for its experimental observation are described.Comment: 12 pages, 3 postscript files included, REVTEX v2, (also available by
anonymous FTP from external.nj.nec.com, in directory /pub/alan/dotarrays [as
separate files]) [replacement: FIX OF WRONG VERSION, BAD SHAR] March 17,
1993, NEC
Quantum Effects in Small-Capacitance Single Josephson Junctions
We have measured the current-voltage (I-V) characteristics of
small-capacitance single Josephson junctions at low temperatures (T=0.02-0.6
K), where the strength of the coupling between the single junction and the
electromagnetic environment was controlled with one-dimensional arrays of dc
SQUIDs. The single-junction I-V curve is sensitive to the impedance of the
environment, which can be tuned IN SITU. We have observed Coulomb blockade of
Cooper-pair tunneling and even a region of negative differential resistance,
when the zero-bias resistance R_0' of the SQUID arrays is much higher than the
quantum resistance R_K = h/e^2 = 26 kohm. The negative differential resistance
is evidence of coherent single-Cooper-pair tunneling within the theory of
current-biased single Josephson junctions. Based on the theory, we have
calculated the I-V curves numerically in order to compare with the experimental
ones at R_0' >> R_K. The numerical calculation agrees with the experiments
qualitatively. We also discuss the R_0' dependence of the
single-Josephson-junction I-V curve in terms of the superconductor-insulator
transition driven by changing the coupling to the environment.Comment: 11 pages with 14 embedded figures, RevTeX4, final versio
Mesoscopic quantum transport: Resonant tunneling in the presence of strong Coulomb interaction
Coulomb blockade phenomena and quantum fluctuations are studied in mesoscopic
metallic tunnel junctions with high charging energies. If the resistance of the
barriers is large compared to the quantum resistance, transport can be
described by sequential tunneling. Here we study the influence of quantum
fluctuations. They are important when the resistance is small or the
temperature very low. A real-time approach is developed which allows the
diagrammatic classification of ``inelastic resonant tunneling'' processes where
different electrons tunnel coherently back and forth between the leads and the
metallic island. With the help of a nonperturbative resummation technique we
evaluate the spectral density which describes the charge excitations of the
system. From it physical quantities of interest like current and average charge
can be deduced. Our main conclusions are: An energy renormalization leads to a
logarithmic temperature dependence of the renormalized system parameters. A
finite lifetime broadening can change the classical picture drastically. It
gives rise to a strong flattening of the Coulomb oscillations for low
resistances, but in the Coulomb blockade regime inelastic electron cotunneling
persists. The temperature where these effects are important are accessible in
experiments.Comment: 24 pages + 23 figures (available by fax or conventional mail, upon
request) tfp-1994-1
Vortex reflection at boundaries of Josephson-junction arrays
We study the propagation properties of a single vortex in square
Josephson-junction arrays (JJA) with free boundaries and subject to an applied
dc current. We model the dynamics of the JJA by the resistively and
capacitively shunted junction (RCSJ) equations. For zero Stewart-McCumber
parameter we find that the vortex always escapes from the array when
it gets to the boundary. For and for low currents we find
that the vortex escapes, while for larger currents the vortex is reflected as
an antivortex at one edge and the antivortex as a vortex at the other, leading
to a stationary oscillatory state and to a non-zero time-averaged voltage. The
escape and the reflection of a vortex at the array edges are qualitatively
explained in terms of a coarse-grained model of a vortex interacting
logarithmically with its image. We also discuss the case when the free
boundaries are at degrees with respect to the direction of the vortex
motion. Finally, we discuss the effect of self-induced magnetic fields by
taking into account the full-range inductance matrix of the array, and find
qualitatively equivalent results.Comment: 14 pages RevTex, 9 Postscript figure
Charge Solitons in 1-D Arrays of Serially Coupled Josephson Junctions
We study a 1-D array of Josephson coupled superconducting grains with kinetic
inductance which dominates over the Josephson inductance. In this limit the
dynamics of excess Cooper pairs in the array is described in terms of charge
solitons, created by polarization of the grains. We analyze the dynamics of
these topological excitations, which are dual to the fluxons in a long
Josephson junction, using the continuum sine-Gordon model. We find that their
classical relativistic motion leads to saturation branches in the I-V
characteristic of the array. We then discuss the semi-classical quantization of
the charge soliton, and show that it is consistent with the large kinetic
inductance of the array. We study the dynamics of a quantum charge soliton in a
ring-shaped array biased by an external flux through its center. If the
dephasing length of the quantum charge soliton is larger than the circumference
of the array, quantum phenomena like persistent current and coherent current
oscillations are expected. As the characteristic width of the charge soliton is
of the order of 100 microns, it is a macroscopic quantum object. We discuss the
dephasing mechanisms which can suppress the quantum behaviour of the charge
soliton.Comment: 26 pages, LaTex, 7 Postscript figure
- …