Temperature dependence measurements of the supercurrent-phase relationship in niobium
nanobridges
A. G. P. Troeman,
1
S. H. W. van der Ploeg,
2
E. Il’Ichev,
2
H.-G. Meyer,
2
A. A. Golubov,
1
M. Yu. Kupriyanov,
3
and
H. Hilgenkamp
1
1
Faculty of Science and Technology and Mesa
+
Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede,
The Netherlands
2
Department of Cryoelectronics, Institute for Photonic Technology, D-07702 Jena, Germany
3
Nuclear Physics Institute, Moscow State University, 119992 Moscow, Russia
Received 16 August 2007; published 14 January 2008
The current-phase relationship has been measured as a function of temperature for niobium nanobridges with
different widths. A deformation from Josephson-like sinusoidal characteristics at high temperatures to sawtooth
shaped curves at intermediate and multivalued relationships at low temperatures was observed. Based on this,
possible hysteresis in the current-voltage characteristics of niobium nanobridge superconducting quantum
interference devices can be attributed to phase slippage.
DOI: 10.1103/PhysRevB.77.024509 PACS numbers: 74.78.Na, 74.45.c, 74.50.r, 85.25.Cp
I. INTRODUCTION
One of the fundamental characteristics of superconducting
structures is the relationship between the supercurrent
through and the phase difference across the structure. The
prediction
1
and first experimental verification
2
of periodical
current-phase relationships CPRs in superconductor-
insulator-superconductor tunnel junctions triggered the onset
of research on Josephson devices. Much of the classical stud-
ies on this subject focused on structures where two supercon-
ducting layers are separated by a barrier with a thickness of
the order of the superconducting coherence length . With
the advances in nanotechnology, the development of super-
conducting structures with lateral dimensions of the order of
also became possible. Examples of such systems are super-
conducting nanobridges, which, when of sufficiently small
dimensions, are known to exhibit a periodical CPR.
3,4
Based
on this similarity to classical Josephson tunnel junctions, the
development of superconducting quantum interference de-
vices SQUIDs incorporating two of such nanobridges has
been a topic of ongoing research, e.g., for the detection of the
magnetization reversal of small magnetic clusters
5–7
and in
scanning SQUID microscopes.
8–11
The application of super-
conducting nanobridges as single photon detectors, for in-
stance, as described in Ref. 12, has been a topic of interest in
recent years. In addition, hot electron bolometers based on
superconducting nanobridges are explored as detectors in as-
trophysical observations at terahertz frequencies.
13
Recent
fundamental interest in superconducting nanobridges has fur-
thermore been motivated by the possible application of such
structures in flux qubits.
14,15
Even though applications based on the Josephson-like
characteristics of superconducting nanobridges have been in-
vestigated extensively, up until now, the exact nature of the
CPRs in these structures has mainly been studied theoreti-
cally. It is predicted to be dependent on the dimensions of the
structure. According to the Kulik-Omelyanchuk model,
16
a
gradual temperature T dependent deformation of the CPR
from sinusoidal at high T to sawtoothlike at lower T is ex-
pected in the clean limit. Strongly nonsinusoidal CPRs at
low T are also predicted in the diffusive regime for nano-
wires with lengths L
0
l
1/2
where
0
is the BCS coher-
ence length and l the electronic mean free path and small
transverse sizes W L. These models were qualitatively veri-
fied for the CPR in clean ballistic niobium point contacts.
17
Recent quantitative agreement between experiment and
theory was reported for aluminum atomic contacts.
18
Likharev and Yakobson first considered the effect of an in-
creasing weak link length on the CPR for structures in which
the temperature is close to the critical temperatures of both
the electrodes T
c
and the nanobridge T
c
.
19
Their model
describes a similar deformation of the CPR, from sinusoidal
to sawtoothlike, as a function of increasing bridge length.
Furthermore, at a critical length L 3.5
0
T, with
0
T the
Ginzburg-Landau GL coherence length, the nature of the
CPR becomes multivalued. In this limit, superconductivity is
suppressed above the critical current by phase slippage of the
superconducting order parameter in the structure. Dur-
ing a phase slip, the order parameter fluctuates to zero, al-
lowing the relative phase to relax by 2 and resulting in a
voltage pulse. In the GL regime, this model was extended to
two dimensions in Ref. 20. For wide a 3.5T and long
L 4.4T nanobridges, the coherent motion of vortices
across the structure is expected to determine the CPR.
For fixed values of the bridge length and T
c
= T
c
, the de-
scribed deformation of the CPR and crossover as a function
of decreasing temperature were discussed quantitatively by
Kupriyanov et al.
21
within a model valid at arbitrary tem-
peratures. In terms of the GL approach, this can be explained
by the fact that T increases as a function of temperature,
which, for fixed L, is physically similar to a decrease of the
effective bridge length. Based on the models discussed
above, the predicted transition of the CPR in a superconduct-
ing nanobridge L
0
l
1/2
is qualitatively depicted in Fig.
1. The dotted line corresponds to the sharp drop in phase
related to the phase slip mechanism.
Previously, the described crossover was studied only in-
directly in experiment by measuring the power dependence
of Shapiro steps in the current-voltage IV curves of
microwave-irradiated Sn microbridges.
22
This study con-
PHYSICAL REVIEW B 77, 024509 2008
1098-0121/2008/772/0245095 ©2008 The American Physical Society 024509-1