Intermittent Josephson effect with feedback voltage and temperature oscillations in graphite-coated nanocapsules with superconducting TaC core

0.55 MB·English

by  Dianyu Geng

Intermittent Josephson effect with feedback voltage and temperature oscillations in
graphite-coated nanocapsules with superconducting TaC core
Dianyu Geng,1 Zhenhua Wang,1,∗ Da Li,1 Zhidong Zhang,1 and Xiaolin Wang2
1Shenyang National Laboratory for Materials Science,
Institute of Metal Research, and International Center for Materials Physics,
Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China
2Institute for Superconducting and Electronic Materials,
Faculty of Engineering, Australian Institute for Innovative Materials,
2
University of Wollongong, Wollongong, Australia
1
0
AnintermittentJosephsoneffectintheformofvoltageandtemperatureoscillationsinthevoltage
2
- current curves near 2 K is observed in pellets consisting of superconducting TaC nanocapsules

n coated with graphite. This phenomenon is attributed to non-equilibrium conditions, when Cooper
a pairsacrossajunction,whichstimulatetheemissionofphotonsandthefeedbacktemperaturechange
J ofthejunction. Itoccursinathree-dimensionalgranularframeworkcomposedofTaC/carbon/TaC

9 tunneling junctions with a Mott metal-insulator transition, below the critical temperature Tc of
1 non-idealtype-IIsuperconductor TaC.

] PACSnumbers: 75.20.-z,75.75.Lf,61.46.Hk
n
o
c
The Josephson tunneling effect in superconductors to that electron pairs intermittently tunneling through
-
r is one of the most important quantum effects [1–3]. the Josephson non-zero voltage junctions emit photons
p
Nanocapsules(orcore-shellnanostructures)havealready [2]. At low temperature, the superconductive currents
u
s revealed abundant new physics and potential applica- firsttakeplaceinthejunctions. emittingphotons,arising
t. tions [4, 5]. Superconducting nanocapsules consisting of temperature and resistance, and then the superconduc-
a
superconductors (of any type) as core and normal (i.e. tive currents decrease (or stop), decreasing the Cooper
m
non-superconducting)materialsasshellsareparticularly pairs and the temperature until the next cycle (the su-
-
interesting in terms of the fabrication of junctions. The percurrentstakeplaceagainattemperaturelowenough).
d
n behavior of tunneling supercurrents in Josephson junc- There is a feedback of the temperature change and the
o tions may be very unlike ordinary experience. For in- voltage - current function of the junctions. The combi-
c stance, Josephson predicted non-equilibrium properties nation effect of the superconductor TaC and the Mott
[
of coupled superconductors[2], such as the occurrence of metal-insulatortransitionofgraphitearelikelyresponsi-

4 dc supercurrents(i.e. the transferofCooperpairsacross ble for the oscillations.
v the barrier), provided the potential difference is such
The carbon-coated TaC nanocapsules studied in this
7
thatenergycanbeconservedbyabsorptionorstimulated
9 workhavebeenfabricatedviaanarcdischargeprocessin
emissionofaphoton(ormultiphoton). Intermittent-type
0 ethanolvapor andargonatmosphere. The details of this
4 chaos occurring in rf- and dc-current-driven Josephson method have been described elsewhere [11–13]. A piece
. junctions was also investigated [6–10].
9 of pure Ta metal and a graphite rod were used as anode
0 andcathode,respectively. Thephaseandstructureofthe
It is particularly important to detect the transforma-
1 TaC(C)nanocapsuleswereinvestigatedbyX-raydiffrac-
tion between Cooper pairs and electrons during non-
1
tion (XRD) using Cu-K (λ = 0.15405 nm) radiation.
: equilibrium processes in Josephson junctions. These in- α
v The particle size was analyzed by high-resolution trans-
spire us to fabricate Josephson junctions using carbon-
i
X coated TaC nanocapsules and to investigate their super- mission electron microscopy (TEM). The transport and
magneticpropertiesweremeasuredinaQuantumDesign
r conductivecharacteristicsrelatedtothejunctiontunnel-
a superconducting quantum interference device (SQUID)
ing effect. It is expected that a collective variant of the
magnetometer, with maximum temperature tolerance of
single-electrontunnelingand/orsupercurrenteffectsmay
less than5 mK below 5 K.The relativeerrorofthe tem-
take place in a three-dimensional framework of granular
perature and voltage data is less than 0.1%. For the
superconductors with tunneling junctions [11–13]. Al-
resistivity measurements, as-prepared TaC(C) nanocap-
though there have been many studies on intermittent-
suleswerepressedintopelletsunder1.2GPa. I-Vcurves
type Josephson effect [6–10], up to our knowledge, there
weremeasuredwith a Keithley 2400Source Meter and a
has been no report on intermittent Josephson effects
Keithley 2182 Nanovoltmeter. The temperature depen-
with feed-back temperature change on materials. In this
denceoftheresistivityandtheI-Vcurvesweremeasured
Letter, we report the structure and electric, magnetic,
using the SQUID in the sweep mode.
andsuperconductingpropertiesofTaC(C)nanocapsules.
Near 2 K, voltage and temperature oscillations are ob- The TEM image in Fig. 1 shows the core/shell struc-
servedinthecurrent-voltagecurves,whichareattributed tureoftheTaC(C)nanocapsules. Thecrystalplanespac-
2
0.002
FC H= 50 Oe
0.000
TC =10.2K
g) 0.04M (emu/g)
mu/-0.002
(e 0.02 MHC2 Hc2
M
-0.004
0.00
-1000 -500 0 500 1000
Hic
H (Oe)
-0.006 -0.02
ZFC Hc1
-0.04
-0.008
0 50 100 150 200
T (K)
FIG.1. TEMmorphologyandcore/shellstructureofTaC(C)
nanocapsules. TheleftinsetshowsacrystalgrainofTaC(C),
and the right inset contains the XRDpattern. FIG. 2. Zero-field-cooled (ZFC) and field-cooled (FC) mag-
netization of TaC(C) nanocapsules as a function of tempera-
ture,measuredinamagneticfieldof50Oe. Theinsetshowsa
hysteresisloopat2K,whichistypicalforanon-idealtype-II
ingsofthecoresforsomeofthenanocapsulesinFig. 1are
superconductor.
onlyinonedirection,andtheyusuallyconsistofonlyone
TaC grain coated with a carbon shell. The left inset of
Fig. 1showsasinglenanocapsulewhichcontainsasingle
grainofTaC as coreand carbonas shell. The character- TaC(C) is a non-idealtype-II superconductorwith Tc =
isticspacingofthestrong-reflection(111)planeofTaCis 10.2 K [14–17], and there is in the magnetic fields from
0.258 nm. The size of the nanocapsules ranges between 0 Oe to 1000 Oe, and then to -1000 Oe to 1000 Oe. On
10 and 20 nm. The XRD pattern shown in the right theinitialmagnetizationcurve,attheinitialcriticalfield
inset of Fig. 1 indicates that the phases in the nanocap- Hic = 250 Oe, the negative magnetization begins to in-
sulesareindeedTaCandC.Thethicknessofthespacing crease. On the loop, at H = 100 Oe, the magnetization
in the carbon shell is 0.34 nm, which indicates that the begins to shift. Hc1 = 100 Oe is the lower critical field,
shell is graphite with (002) orientation. The TaC grains and Hc2≈920 Oe is the upper critical field, showing that
are separated by the graphite, which acts as a conduc- thesuperconductivityoftheTaC(C)nanocapsulesistyp-
tance barrierbetweentwoTaC grains. The electronsare ical of a non-ideal type-II superconductor, for which the
trapped inside isolated TaC grains. The grain connec- magnetization process is irreversible. For ideal type-II
tions in the system of nanocapsules may be considered superconductors, the remanent magnetization at Hc2 is
as zero-dimensional,althoughthe grainsizes in three di- zero,andthemagneticfluxlatticeissymmetric[17]. For
mensions are in nanometers. The tunneling framework the TaC(C) nanocapsule conductor in the first quadrant
consists of superconductor-insulator-superconductor(... forH=920Oe,MHc2isnotzero,butapproximately0.01
TaC/(C)/TaC...)tunnelingjunctions,whichvaryamong emu/g. (H is from 1000 Oe to 920 Oe.) The magnetic
themselves because of the different thicknesses of the hysteresis loop changes with the magnetic field, and the
graphite shells and the different sizes of the TaC core. magnetic flux lattice is not symmetrical in the TaC(C)
nanocapsules. For the upper criticalfield, the higher the
The temperature dependence of the zero-field-cooled magnetic-field range, the higher the MHc2 is. It trends
(ZFC) and field-cooled (FC) magnetization of TaC(C) toward a limiting value which is smaller than the rema-
nanocapsules, measured in a magnetic field of 50 Oe, nentmagnetization. Thispropertyisusefulforobtaining
which is lower than the first critical field, is presented a high critical current density in superconductors [18].
in Fig. 2. The ZFC curve shows a clear superconductive Graphite is a semiconductor with zero activation en-
transitiontemperatureT of10.2Kfromparamagnetism ergy at zero temperature [19] and a Mott insulator with
c
to diamagnetism, at the point where the TaC cores be- a metal-insulator transition [20, 21]. Figure 3 presents
come superconducting. The FC curve initially exhibits the temperature dependence of the resistivity (ρ) mea-
Pauliparamagnetismandindicates strongmagneticvor- sured at zero field at a current of 100 nA by means
tex pinning features. The insetin Fig. 2 shows the mag- of the four-probe dc method. The ρ-T curve shows a
netichysteresisloopat2K,whichisasymmetricbecause metal-insulator transition, which can be ascribed to the
3
time(S)

12 1800 1500 1200 900 600 300 0
2.8K
1.2ln ( c m ) 1.4x10-7 cm 3K
400 5K 400
10 0.8 -7 7K
1.2x10 9K
0.4 11K 90 mV
m8 1.0x10-7 300 2K 300
c6 -000..04.4 0.5 T-10/.46 81.0.9x91902-8 2.T0(0K0)0 2.0008 V (mV)200 T-2 200 TmK
4
100 100
2 100 nA 164 mV 36 mK T=T-2
S 0 0
0
0 10 20 30 40 50 0 50 100 150 200 250 300
T(K) I ( A)
FIG. 3. Temperature dependence of the resistivity (ρ) of a FIG. 4. Current (I) versus Voltage (V) and temperature
pellet of TaC(C) nanocapsules measured at a current of 100 fluctuations (△ T= T-2). V-I curves of a pellet of TaC(C)
nA.Therightinset presentsamagnification of atthelowest nanocapsules successively measured at 11, 9, 7, 5, 3, and 2
temperatures (point S). In the left inset, is plotted on a K.Thelowest curvepresentsthetemperaturefluctuations△
logarithmic scale against T−1/4. T(= T-2) of V-I curve measured at 2 K. The top scale of
time(s) corresponds to thetime for every curve. The voltage
oscillation, 90mV=Vs=Σii==n1Vsi,asdescribedbelowinthe
text,resultsfromthesupercurrentatthatmoment;combined
graphite shells of the TaC nanocapsules. Above 2.8 K, voltage from the Ohmic part and the single-electron tunnel-
the resistivity is semiconductor-like, and below 2.8 K, it ing part is 164 mV. The maximum temperature difference is
is metallic and precipitous decreased. At 2 K the resis- 36 mK for theI-△T curve.
tivityofthenanocapsuleshasreachedzero,whichmeans
that the TaC nanocrystals are in the superconducting
state. The right inset shows a magnification of the be- curved,indicating thatthe conductionmechanismstarts
havior of ρ near 2 K. The left inset of Fig. 3 shows a deviating from Ohm’s law.
plot of ρ on a logarithmic scale against T−1/4. It il- In Fig. 3, on the ρ-T curve, from 10 K to 3 K, the
lustrates that the resistivity is that of a Mott insulator, higher the temperature, the higher ρ is, which corre-
whichissimilartowhathasbeenreportedforNbC(C)-C sponds to what is shown in Fig. 4 that the lower the
[11], carbon-coated Sn nanoparticles [12], and Mo car- temperature, the higher the voltage is. Very interest-
bide nanoparticles embedded in a carbon matrix [13]. ingly,at 2 K,the voltageexhibits oscillatorybehavioras
Thisexplainstheelectrical-conductionmechanismofthe a function of current, which can not arise from Ohmic
TaC(C)nanocapsulecomposite,whichcontainsanintrin- current and single-electron tunneling.
sic frameworkof nanocrystalline TaC and graphite. The During measurement in the sweep mode at 2 K, the
main process in the resistivity is a Mott metal-insulator temperature of the sample was observed to oscillate de-
transition [20, 21]. spitethetemperaturecontrol,becausewhenH=0there
Figure4showsV-Icurvesthatweresubsequentlymea- are still some remaining magnetic fluxes inside. To indi-
suredat11,9,7,5,3,and2Kbymeansofthetwo-probe cate how the temperature oscillates with the current, an
dc method(foil: length3.34mm; width, 1.88mm; thick- I-∆T(∆T=T-2K)curveispresentedatthebottomof
ness, 0.06 mm) in the current range from 300 µA to 0 Fig. 4. In the oscillations, the voltage and temperature
µA, with decreasing steps of 2.5 µA. During the mea- increase over a short time (< 0.05 s) and then decrease
surementprocessthetimefrom300µAto0µAwas1800 slowly (> 120 s). The oscillations in temperature and
s. The top scale of time(s) corresponds to the time for voltage are synchronous.
every curve measurement. At 11 K, which is above T , From Figs.2 and 3, we know that at 2 K, the TaC
c
the V-I curve follows Ohmic behavior, with V/I = R = nanograins are superconductors. The Cooper pairs tun-
constant. BelowT ,single-electrontunnelingtakesplace nelingatnon-zerovoltagethroughtheTaC/C/TaCjunc-
c
with conductance close to 4e2/h. Comparing the curves tions give rise to the emission of photons, which results
at9 K,7K,5 K,and3K,the voltageincreaseswith de- inanincreaseinthetemperature. Infact,thevoltageex-
creasing temperature, and the curves gradually become hibits oscillatory behavior accompanied by temperature
4
0.25
V) 0.20
m
V( 0.15 0.16 mV s
0.10
I=50 nA H=0
0.04
68 mK
K)0.02
T(
0.00
-0.02
-0.04
0 600 1200 1800 2400 3000 3600
time (S)
FIG.5. Voltage(V)versustime(t)andtemperaturefluctua- FIG.6. (a)ACooper pairtunnelsthroughtheith Josephson
tions ( T =∆T-2) curves of a pellet of TaC(C) nanocapsules junction, emitting a photon, ~ω =2eV , as it crosses the
i si
successively measured at 2 K, with H=0 and I=50 nA. The interfacebetweenthetwoTaC(C)nanocapsules. Eisthefree
V-t and ∆T-t curves oscillate like a music score, and the big energy in the TaC nanocapsules. (b) TEM morphology of
oscillation amplitudeis0.16mV.Thechangingrangefor∆T oneJosephsonjunctionintheTaC(C)nanocapsules,andthe
is68mK.Vand∆Talsoexhibitasfunctionsoftimeandthe thickness of graphite layers between the two TaC grains is 1
characteristic quantumindeterminacy. nm.
rent,andthesingle-electrontunnelingcurrent. Thetotal
change(∆T=T-2). Figure5representsthatthevoltage
current measured in the I-V curves is
(V) and ∆T versus time (t) curves, which were succes-
sively measured at 2 K, with a current I = 50 nA at the n
absence of a magnetic field (H = 0). The measurement Ii =I.
method is shown as Fig. 4. The V-t and ∆T-t curves i=1
X
oscillate like a music score, and the big oscillation am-
In the systemfor the equivalent model, the ith tunnel-
plitude is 0.16 mV. The resistance, V/I, does not follow
ing junction may be written as follows [2]:
Ohmic and single tunneling electron behavior and the
voltage jumps with T, which indeed exhibits a quantum ~ω =2eV ,
i si
effect.
In Fig. 2, Tc is observed to be 10.2 K, and in Fig. where ωi is the frequency of the emitted photon when
3, the maximum resistance temperature is 2.8 K. In su- a Cooper pair is tunneling through the ith TaC/C/TaC
perconductors,the free energy,which correspondsto the tunneling junction; V is the non-zero potential differ-
si
condensation energy, equals E ∝ (Tc-T)2 [22]. For the ence between the two sides of the ith junction (see Fig.
supercurrent through TaC/C/TaC tunneling junctions, 6). Then:
thetemperaturedifferenceneedstobeatleastoverT -T
c
≈10.2K-2.8K=7.4Ktoovercomethebarriersbetween n ~ n
V = V = ω (i=1,2,3,...,n), (1)
TaC and graphite. s si 2e i
!
i=1 i=1
The supercurrent, the electric Ohmic current, the X X
single-electron tunneling current, and their correspond- whereV isthevoltagebarrierthatmustbesurmounted
s
ing voltages coexist. To explain the oscillations, all forCooperpairstocrossthejunctionsandemitphotons.
TaC nanocapsules are assumed to be isolated from each There are involved the special rules for the interfering
other. TheTaC(C)nanocapsulesarepressedintoaspec- amplitudesfortheCooperpairsandelectronsthatoccur
imen, which forms a three-dimensional granular frame- in the processes. The amplitude for the Bose particles
work composed of TaC/C/TaC tunneling junctions. We is the sum of the two interfering amplitudes, and for the
assumethenumberoftunneljunctionsinthepellettobe Fermi ones it is minus.
equal to n and use the equivalent lumped circuit model When measuredthe I-V curves some Cooper pairs are
[23, 24] for the experiments. interference. ForthestateswithBoseparticles,theprob-
For the ith tunneling junction, the total current I is abilityintheBosecaseislargerthanthatoftheparticles
i
composed of the supercurrent, the electric Ohmic cur- actedindependently [22,25]. When the tunneling effects
5
takeplace,the probabilityamplitudes ofCooperpairsin a function of the time. The mechanism is that the su-
graphite abruptly increase and give rise to the emission percurrentsgothroughtheJosephsonjunctionsandemit
ofphotons and consequently,the temperature jumps up; photonswiththefeedbackresistance,temperaturechange
increasingtheresistanceofgraphite. Thenthesupercur- of the TaC(C) junctions.
rentstops andthe number ofCopper pairs is quickly de- The authors acknowledge the support of the National
creased, which are transformed to single electrons. Sub- NaturalScienceFoundationofChinaundergrantnumber
sequently, the temperature begins to drop down. With 51102244andtheNationalBasicResearchProgram(No.
decreasingthe temperatureofthe system,the numberof 2012CB933103),the Ministry of Science and Technology
Cooper pairs is gradually increased, and the resistance ofChina. ThisworkisalsopartlysupportedbytheAus-
of graphite decreases until the next cycle. The proba- tralian Research Council through a Discovery project.
bility amplitudes of Copper pairs also are a function of
the time (See Fig. 5) and exhibited quantum indetermi-
nacy. In fact, there is a competitive mechanism between
the junction barrierand the free energy of the supercon-
∗ [email protected]
ducting carriers in the TaC nanograins. A phase tran-
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