Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions
The moderately damped regime in a Josephson junction (JJ) is quite common in devices characterized by low critical currents and therefore by low Josephson energies. Measurements of switching current distribution (SCD) are a direct way of discriminating the phase dynamics also in the nontrivial cas...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1182482017-05-30T03:04:38Z Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions Massarotti, D. Longobardi, L. Galletti, L. Stornaiuolo, D. Rotoli, G. Tafuri, F. К 75-летию со дня рождения И. К. Янсона The moderately damped regime in a Josephson junction (JJ) is quite common in devices characterized by low critical currents and therefore by low Josephson energies. Measurements of switching current distribution (SCD) are a direct way of discriminating the phase dynamics also in the nontrivial case of moderate damping, which is going to be more and more common with advances in nanopatterning superconductors and in materials science finalized to build hybrid systems. We report on measurements of SCDs, both in thermal and quantum regime, on moderately damped YBaCuO grain boundary biepitaxial JJs. A direct transition from phase diffusion regime to macroscopic quantum tunnelling occurs at about 130 mK. The crossover to the quantum regime is tuned by the magnetic field and phase dynamics is described by a fully consistent set of junction parameters derived through numerical simulations. 2013 Article Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions / D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo, G. Rotoli, F. Tafuri // Физика низких температур. — 2013. — Т. 39, № 3. — С. 378–383. — Бібліогр.: 37 назв. — англ. 0132-6414 PACS: 74.72.–h, 85.25.Cp, 74.50.+r http://dspace.nbuv.gov.ua/handle/123456789/118248 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
К 75-летию со дня рождения И. К. Янсона К 75-летию со дня рождения И. К. Янсона |
| spellingShingle |
К 75-летию со дня рождения И. К. Янсона К 75-летию со дня рождения И. К. Янсона Massarotti, D. Longobardi, L. Galletti, L. Stornaiuolo, D. Rotoli, G. Tafuri, F. Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions Физика низких температур |
| description |
The moderately damped regime in a Josephson junction (JJ) is quite common in devices characterized by low
critical currents and therefore by low Josephson energies. Measurements of switching current distribution (SCD)
are a direct way of discriminating the phase dynamics also in the nontrivial case of moderate damping, which is
going to be more and more common with advances in nanopatterning superconductors and in materials science
finalized to build hybrid systems. We report on measurements of SCDs, both in thermal and quantum regime, on
moderately damped YBaCuO grain boundary biepitaxial JJs. A direct transition from phase diffusion regime to
macroscopic quantum tunnelling occurs at about 130 mK. The crossover to the quantum regime is tuned by the
magnetic field and phase dynamics is described by a fully consistent set of junction parameters derived through
numerical simulations. |
| format |
Article |
| author |
Massarotti, D. Longobardi, L. Galletti, L. Stornaiuolo, D. Rotoli, G. Tafuri, F. |
| author_facet |
Massarotti, D. Longobardi, L. Galletti, L. Stornaiuolo, D. Rotoli, G. Tafuri, F. |
| author_sort |
Massarotti, D. |
| title |
Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions |
| title_short |
Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions |
| title_full |
Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions |
| title_fullStr |
Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions |
| title_full_unstemmed |
Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions |
| title_sort |
macroscopic quantum tunneling and retrapping processes in moderately damped ybacuo josephson junctions |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2013 |
| topic_facet |
К 75-летию со дня рождения И. К. Янсона |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118248 |
| citation_txt |
Macroscopic quantum tunneling and retrapping
processes in moderately damped YBaCuO
Josephson junctions / D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo,
G. Rotoli, F. Tafuri // Физика низких температур. — 2013. — Т. 39, № 3. — С. 378–383. — Бібліогр.: 37 назв. — англ. |
| series |
Физика низких температур |
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2025-07-08T13:37:31Z |
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| fulltext |
© D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo, G. Rotoli, and F. Tafuri, 2013
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3, pp. 378–383
Macroscopic quantum tunneling and retrapping
processes in moderately damped YBaCuO
Josephson junctions
D. Massarotti1,2, L. Longobardi3,2, L. Galletti1,2, D. Stornaiuolo2,
G. Rotoli3, and F. Tafuri3,2,1
1Dip. Scienze Fisiche, Universitá di Napoli Federico II, Monte S. Angelo via Cinthia, Napoli 80126, Italy
E-mail: dmassarotti@na.infn.it
2CNR-SPIN, UOS Napoli, Monte S. Angelo via Cinthia, Napoli 80126, Italy
3Dip. Ingegneria dell'Informazione, Seconda Universitá di Napoli, via Roma 29, Aversa (CE) 81031, Italy
Received November 1, 2012
The moderately damped regime in a Josephson junction (JJ) is quite common in devices characterized by low
critical currents and therefore by low Josephson energies. Measurements of switching current distribution (SCD)
are a direct way of discriminating the phase dynamics also in the nontrivial case of moderate damping, which is
going to be more and more common with advances in nanopatterning superconductors and in materials science
finalized to build hybrid systems. We report on measurements of SCDs, both in thermal and quantum regime, on
moderately damped YBaCuO grain boundary biepitaxial JJs. A direct transition from phase diffusion regime to
macroscopic quantum tunnelling occurs at about 130 mK. The crossover to the quantum regime is tuned by the
magnetic field and phase dynamics is described by a fully consistent set of junction parameters derived through
numerical simulations.
PACS: 74.72.–h Cuprate superconductors;
85.25.Cp Josephson devices;
74.50.+r Tunneling phenomena; Josephson effects.
Keywords: phase dynamics, MQT, moderately damped regime, phase diffusion.
1. Introduction
In the last few years, studies on phase dynamics and
macroscopic quantum phenomena have been extended to
junctions composed of materials other than the traditional
low critical temperature superconductors (LTS) [1–3] and
to novel types of structures with unconventional barriers
composed for instance of graphene sheets [4] or of grain
boundaries [1]. Issues on macroscopic quantum phenome-
na on wire and nanostructures have been renewed by the
advances in nanopatterning and in achieving high quality
nanowires [5,6]. Progress in engineering new materials
into junctions and in understanding and controlling the
physics of interfaces may offer novel solutions for junc-
tions of superior quality and complementary functionali-
ties, and therefore may lead in the long run to improve also
specific qubit performances [7]. Measurements of switch-
ing current distribution (SCD) have turned to be more and
more standard tools to investigate phase dynamics in un-
conventional and hybrid systems and nanostructures. High
critical temperature superconductors (HTS) are an example
of unconventional systems, because of the d-wave order
parameter symmetry and of the presence of low-energy
quasiparticles. In HTS Josephson junctions (JJs) low-
energy quasiparticles are expected to induce higher levels
of dissipation [8–10] when compared to LTS systems. A
comparative study in systems so different and complemen-
tary is of great interest. HTS systems are characterized in
suitable conditions by intermediate levels of dissipation,
that make these junctions fall in the moderately damped
regime (MDR). In LTS systems, MDR is more frequently
the natural consequence of a reduction of the critical cur-
rent cI . Low cI are induced or by size reduction typically
in the submicron regime [11–15] or by very low critical
current density cJ [16–18]. Lower critical currents result
in lower Josephson energies. These devices are charac-
Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 379
terized by intermediate levels of dissipation and by phase
diffusion (PD) phenomena [11,13–16, 18–21]. The low
critical current cI limit seems to be characteristic also of
all futuristic nanohybrids devices incorporating nanowires
or unconventional barriers [18,22–24], and MDR is intrin-
sically more common than it could be expected. In this
work we report on measurements of SCDs on moderately
damped 2 3 7YBa Cu O x− grain boundary (GB) biepitaxial
JJs down to the quantum regime [25]. The capability to
engineer junctions on different substrates offers the oppor-
tunity to disentangle the role of the shell circuit in the
phase dynamics and thus a tuning of the capacitive effects
in HTS GB biepitaxial JJs. Experimental data are support-
ed by Monte Carlo simulations of the phase dynamics, in a
wide range of temperatures and dissipation levels. This
allows to address relevant issues on how to quantify dissi-
pation in the MDR and a partial reconstruction of a phase
diagram as guideline for a wide range of moderately
damped systems.
2. Resistively and capacitively shunted junction model
and phase dynamics
The dynamics of a current-biased JJ is governed by the
phase difference ϕ of the order parameter across the junc-
tion. In the framework of the resistively and capacitively
shunted junction (RCSJ) model [26], the phase dynamics is
equivalent to the motion of a particle in a washboard po-
tential 0= (cos / )J cU E I I− ϕ + (see Fig. 1):
2 22
0 0
2
1 = 0
2 2
UC
R tt
φ φ∂ ϕ ∂ϕ ∂⎛ ⎞ ⎛ ⎞+ +⎜ ⎟ ⎜ ⎟π π ∂ ∂ϕ⎝ ⎠ ⎝ ⎠∂
, (1)
0φ is the flux quantum, 0cI represents the junction critical
current in absence of thermal fluctuations and the term
involving the capacitance C represents the mass of the par-
ticle respectively. 0 0= / 2J cE I φ π is the Josephson energy
and the tilt of the washboard potential is given by the bias
current I.
The strength of the friction can be expressed through
the junction quality factor = pQ RCω , where pω =
02 /ceI C= is the plasma frequency. When the bias cur-
rent is ramped from = 0I to 0< ,cI I the junction is in the
zero voltage state in absence of thermal and quantum fluc-
tuations and the particle is confined to one of the potential
wells, where it oscillates at the plasma frequency. When
ramping the bias current I, the tilt of the energy potential
increases and the height 3/2
0( ) = (4 2/3) (1 / )J cU I E I IΔ −
of the energy barrier between consecutive wells decreases.
Due to effects of thermal fluctuations and quantum tunnel-
ing the junction may switch to the finite voltage state for
values of 0< cI I . The relative weight of these two escape
processes depends on the temperature of the system. For
>>B pk T ω the escape process is dominated by thermal
activation (TA) with a rate [27]:
( ) ( )( ) = exp
2
p
T T
B
I U II a
k T
ω ⎛ ⎞ΔΓ −⎜ ⎟π ⎝ ⎠
. (2)
At low enough temperature the escape is dominated by
macroscopic quantum tunneling (MQT) with a rate [28]:
( ) ( ) 0.87( ) = exp 1
2
p
q q
p
I U II a
Q
⎡ ⎤ω ⎛ ⎞ΔΓ − +⎢ ⎥⎜ ⎟π ω ⎝ ⎠⎢ ⎥⎣ ⎦
. (3)
Once the phase particle gets over a hill by fluctuations,
it keeps running, provided that the damping is below some
critical value. The escape from this metastable state corre-
sponds to the appearance of a finite voltage across the
junction and the particle runs down the washboard poten-
tial with a damping 1.Q− The transition to the running state
(see Fig. 1(a)) only occurs if the kinetic energy gained by
the phase particle running down the tilted washboard po-
tential is not all dissipated, but enough energy remains to
carry the phase over the next hill. This occurs if the junc-
tion is in the underdamped regime ( >> 1Q ) [29]. In the
experiments of Ref. 29, a detailed experimental protocol
has been established to prove the quantum behavior of the
phase ϕ across a JJ and its crossover to the thermal re-
gime, used in most of later experiments. The relevant pa-
rameters of the junction and the dissipation level have been
determined in situ in the thermal regime from measure-
ments of resonant activation in the presence of micro-
waves. Such method still represents the most powerful way
to characterize the dissipation level in the underdamped re-
gime. In the moderately damped regime (1 < < 5Q ), fol-
lowing an event of escape the particle may travel down the
potential for a few wells and then be retrapped in one of
Fig. 1. (Color online) Phase dynamics in the tilted periodic poten-
tial U: thermal (TA) (green dashed line) and quantum (MQT) (red
dashed line) escapes are shown in the ideal case of very low dis-
sipation ( >> 1Q ) (a). In the MDR (1 < < 5Q ) the MQT rate is
significantly affected by dissipation (see Eq. 3) and retrapping
processes in subsequent potential wells become relevant, giving
rise to the PD regime (b).
D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo, G. Rotoli, and F. Tafuri
380 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
the following minima of the potential (Fig. 1(b)) [11,20].
The analytical expression for the retrapping rate is given by:
21/2 2
0 0
( ) = exp ,
2 2
J JR R
R p
c B B c
E E QI I I I
I
I k T k T I
⎡ ⎤⎛ ⎞⎛ ⎞− −⎢ ⎥Γ ω − ⎜ ⎟⎜ ⎟π ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦
(4)
where 0= 4 /R cI I Qπ is the retrapping current in absence
of thermal fluctuations [30]. At low bias the process of es-
cape and retrapping may occur multiple times generating
diffusion of the phase until an increase of the tilt of the
potential, due to a change in the bias current, raises the ve-
locity of the particle and the transition to the running state
occurs. This is known as PD regime [11,13–16,18–21].
The experimental observation of such regimes in a JJ is
based on the measurement of the SCDs and the study of
the behavior of its first and second momenta (the mean I
and the width )σ as function of temperature. The resulting
distribution of the switching probability P(I) is used to
compute the escape rate out of the zero-voltage state as
a function of the bias current I [31]:
( )
1( ) = ln
( )
i I
i I I
P I
dII
I dt P I
≥
≥ +Δ
⎛ ⎞
⎜ ⎟
Γ ⎜ ⎟Δ ⎜ ⎟
⎝ ⎠
∑
∑
, (5)
where /dI dt is the current ramp rate and IΔ is the chan-
nel width of the analog-to-digital converter. In an under-
damped junction ( > 10Q ) [29], below a crossover temper-
ature crT the escape process is due to MQT, marked by a
temperature independent σ , while above crT the process
of escape is due to TA with a distinctive increase of σ
with temperature as 2/3T . In moderately damped junctions
[11,13–16,18–21] a transition from TA to PD regime oc-
curs at a crossover temperature *
cr> .T T *T corresponds
to a distinctive change in the sign of the temperature deriv-
ative of σ, with / > 0d dTσ for *<T T and / < 0d dTσ for
*>T T .
3. Phase dynamics of YBaCuO grain boundary
biepitaxial Josephson junctions
The search of macroscopic quantum effects has become
feasible in HTS systems once high-quality JJs with signi-
ficant hysteresis in the current-voltage (IV) characteristics
were available. MQT and energy level quantization were
first observed in 2 3 7YBa Cu O x− GB biepitaxial JJ [1]. A
specific feature of these structures is the use of a [110]-ori-
ented 2CeO buffer layer, deposited on [110] 3SrTiO (STO)
substrates. YBCO grows along the [001] direction on the
2CeO seed layer, while it grows along the [103] / [013]
direction on STO substrates. In the experiment of Ref. 1,
the measurements of SCDs as a function of temperature
substantially follow what commonly measured on LTS JJs,
with a saturation of the measured σ below 50 mK, which
corresponds to the crossover temperature crT from the ther-
mal to the MQT regime.
The capacitance C plays a role of primary importance in
setting phase dynamics, as evident from Eq. (1) [26]. In re-
cent studies on PD [19,32], the possibility to vary C on a
broader scale was relevant to tune the transition tempera-
ture *.T Such studies have the goal to “avoid” the PD re-
gime by extending the TA regime to higher temperatures; a
solid method to characterize the dissipation level in MDR
is missing. In HTS JJs a complete understanding of the
capacitive effects is still lacking. In STO based biepitaxial
devices, the JJ is embedded in a shell LC circuit, which
originates from a large kinetic inductance, due to the cur-
rent flow in the c -axis direction, and from a capacitive
element in parallel to the junction, due to the large stray
capacitance of the STO substrate [33]. In this work we
have engineered junctions on 0.3 0.7 0.65 0.35 3(La Sr )(Al Ta )O
(LSAT) rather than STO substrates. The new design fully
responds to the task of reducing stray capacitances. The
resulting device is a relevant term of comparison to search
the origin of the capacitive effect in GB JJs, and is more
representative of the intrinsic nature of the GB [25,34].
Specific capacitances are on average one order of magni-
tude lower than those measured on STO-based devices
[1,34]. To study the escape rates of YBaCuO GB JJs we
have thermally anchored the sample to the mixing chamber
of a 3He/4He Oxford dilution refrigerator and performed
measurements of the junction switching current probability.
A full description of the apparatus is discussed in detail
elsewhere [16]. Filtering is guaranteed by a room tempera-
ture electromagnetic interference filter stage followed by
low pass RC filters with a cut-off frequency of 1.6 MHz
anchored at 1.5 K, and by a combination of copper pow-
der and twisted pair filters thermally anchored at the mix-
ing chamber of the dilution refrigerator. The bias current
of the junction is ramped at a constant sweep rate
/ = 20 мA/sdI dt and at least 410 switching events have
been recorded using a standard technique. We report data
for two different samples with interface orientations of 50°
for sample A and 75° for sample B respectively. These
angles determine robust overlap of the d-wave lobes on
both sides of the junctions [10,34,35].
SCDs collected over a wide range of temperatures on
sample A are reported in Fig. 2(a) and 2(b) for two differ-
ent values of the magnetic field ( = 0H and = 12 GH
respectively). The temperature dependence of the width σ
of the SCD curves measured on sample A and B is shown
in Fig. 3(a). Our data are characterized by two distinct re-
gimes. In Fig. 2(a), when increasing the temperature above
140 mK the switching current hystograms shrink rather
than broaden, which corresponds to the negative tempera-
ture derivative of σ in Fig. 3(a). This behavior is consistent
with a diffusive motion due to multiple escape and re-
trapping processes in the potential wells. The σ dependence
Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3 381
has been fitted through Monte Carlo simulations [20,25]
with a damping factor = 1.3Q (light grey line in Fig. 3(a)).
The dissipative essence of the quality factor Q strongly
depends on the value of the effective frequency dependent
resistance ( )R ω and of shunting capacitance C, which are
in turn determined by several interplaying effects, such as
circuit impedance, subgap resistance and stray capacitance
[11]. Since these parameters are not easily accessible, a
reliable way able to estimate the quality factor Q in the
MDR is of great interest. Below 140 mK, hystograms over-
lap and σ saturates, which is a typical signature of a quan-
tum activation regime. In analogy to what commonly done
to prove MQT in underdamped junctions [29], we use the
magnetic field to tune in situ the junction parameters and
the quantum crossover temperature crT to unambiguously
prove MQT as source of the saturation of σ below cr .T In
the inset of Fig. 3(a) we report the temperature dependence
of σ measured for sample A at the two different magnetic
fields of 0 G and 12 G respectively. = 12 GH lowers
0cI reducing at the same time the crossover temperature
cr .T Relevant device parameters are summarized in Table 1.
Table 1. Device parameters
Sample Angle, ° 0, AcI μ 2, A/cmcJ C, fF Q cr ,T mK
A 50 1.79 25 10⋅ 74 1.28 144
B 75 1.20 25 10⋅ 64 1.30 135
Taking advantage of the design flexibility of state-of-
the-art YBaCuO GB biepitaxial JJs [1,34], we have sub-
Fig. 2. Switching current hystograms as function of temperature
measured on sample A for = 0H (a) and = 12 GH (b), respec-
tively. Above the crossover temperature crT ( cr 140T mK in
(a) and cr 120T mK in (b)), the hystograms shrink rather than
broaden and become more symmetric. These are signatures of
effectiveness of retrapping processes.
Fig. 3. (Color online) Thermal behavior of σ of the SCDs meas-
ured on sample B. The light grey solid line (1) is the result of
Monte Carlo simulations in the diffusive regime with a quality
factor = 1.3Q , while the blue dashed line (2) indicates the satu-
ration of σ below cr.T The inset shows temperature dependent
data for sample A at = 0H and = 12 G.H The black dashed
lines (3,4) indicate the average values of σ in MQT regime and
the value of cr ,T which are both reduced by the magnetic field
(a). Experimental escape rates Γ of sample A are shown as func-
tion of the switching current. In the inset, thermal behavior of the
skewness γ is reported for = 0H and = 12 GH . In the PD
regime, retrapping processes cause a progressive bending of Γ
and symmetrization of switching hystograms signalled by the
thermal dependence of γ (b).
16
14
12
10
8
�
,
n
A
�
,
n
A
H = 0
H = 12 G
100
T, mK
T, mK
T, mK
8
7
6
5
4
3
(a)
(b)
18 100 500 1000
30 mK
153 mK
269 mK
353 mK
510 mK
E
sc
ap
e
ra
te
,
s–
1
10
7
10
6
10
5
10
4
10
3
10
2
1.10 1.15 1.20 1.25
H = 12 G
H = 0
S
k
ew
n
es
s
–0.1
–0.2
–0.3
–0.4
–0.5
100
Switching current, A�
1
2
3
4
D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo, G. Rotoli, and F. Tafuri
382 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 3
stantially engineered devices with *
cr<T T [25]. For tem-
peratures T well below cr ,T MQT contributions to escape
rates are larger than those coming from both thermal es-
cape and multiple retrapping processes differently from the
case cr> .T T In the PD regime the level of dissipation is
such that, after an escape event, the phase can be retrapped
in a subsequent valley and therefore does not simply roll
down the washboard potential. Retrapping processes affect
the symmetry of the SCDs. The parameter which is com-
monly used to measure the symmetry of a generic distribu-
tion is the skewness γ [16,20]. This is defined as the ratio
3
3 /m σ where 3m is the third central moment of the dis-
tribution. = 0γ corresponds to a symmetric distribution
while an asymmetric distribution with a tail on the left
(right) side has < 0γ ( > 0)γ . Phase diffusion also ap-
pears in the escape rates Γ , shown in Fig. 3(b), as a func-
tion of the switching current I. The escape rates are calcu-
lated from the switching distributions using Eq. 5. Below
cr ,T the escape rates approximately fall on a straight line
according to MQT escape rate (Eq. 3), while above crT
retrapping processes cause a bending in Γ versus I curves
[14,16]. In the PD regime the switching distributions be-
come more symmetric as signalled by the dependence of γ
on the temperature (see inset of Fig. 3(b)).
Monte Carlo simulations have been performed for dif-
ferent values of the quality factor Q ranging from 1 to 5.
Only TA and PD processes have been calculated in the
graphs reported in the inset of Fig. 4. For each of these
curves, *T approximately indicates the transition tempera-
ture from TA to the diffusive regime. Q tunes *T and
modifies the slope of the σ (T) fall-off at higher tempera-
tures. Such numerical simulations also allow us to fully
reconstruct the ( , /B JQ k T E ) diagram reported in Fig. 4
[13,25]. The transition curve between the PD regime and
the running state following TA has been determined nu-
merically by varying the quality factor Q as function of
the ratio between the thermal energy and the Josephson
energy. In Fig. 4 Q and the ratio /B Jk T E are derived for
all experiments pointing to PD both on LTS and HTS JJs
[13–16,25] and compared with numerical outcomes. The
proximity of experimental data to the simulations suggests
the validity of such approach and the 'universal' nature of
the transition curve. A phase diagram valid in a large range
of dissipation conditions emerges as a functional guide to
classify the switching behavior and to settle the fundamen-
tal junction parameters and energies in the MDR. It is
therefore a reference for phase dynamics of novel types of
junction and system for which the nature of the current-
induced transition from the superconducting to the normal
state has not been completely clarified.
4. Conclusions
In summary, we have observed MQT in the moderately
damped regime in GB YBaCuO JJs and a direct transition
from the quantum activation regime to the phase diffusive
regime. The diffusive regime appears to be of higher im-
portance with the advent of JJs of very reduced size which
are becoming to be highly utilized in superconducting hy-
brid nanoscale devices [5,6,36,37]. This experiments con-
tributes to settle an unexplored region of the phase diagram
which is a valid guideline in order to define the relation
between the fundamental junction parameters and energies
in moderately damped systems.
Acknowledgments
This work is supported by MIUR PRIN 2009 under the
project “SuFET based on nanowires and HTS”. We also
acknowledge partial support by a Marie Curie International
Reintegration Grant No. 248933 hybMQC within the 7th
European Community Framework Programme and by
“FIRB-Futuro in Ricerca 2012” — Project HybridNanoDev
(Grant No. RBFR1236VV).
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