Marulanda J.M. (ed.) Electronic Properties of Carbon Nanotubes

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Multiple Andreev Reﬂections and Enhanced

Quantum Interferences with Reentrant Behavior

in NbN/Network-like Carbon Nanotubes/NbN

SNS Junctions

Yuan-Liang Zhong

, Hayato Nakano

, Tatsushi Akazaki

and Hideaki Takayanagi

Department of Physics, Chung Yuan Christian University

2,3

NTT Basic Research Laboratories, NTT Corporation

Department of Applied Physics, Tokyo University of Science

Taiwan

2,3,4

Japan

1. Introduction

The superconducting proximity effect has been studied in superconductor (S)/normal

conductor (N) junctions or SNS junctions for a few decades. If a clean contact is brought

into an SN junction, some cooper pairs will penetrate into the normal conductor from the

superconductor to form an incident electron and a retroreﬂected hole in it. This process is

called Andreev refection (AR). If both electrodes are superconducting, two SN junctions

with very-low-barrier tunnel junctions, a series of ARs can be observed in the differential

resistance at submultiples of gap voltage, 2Δ/ne, where n=1,2,.. (Octavio et. al.,1983) and

Δ is superconducting energy gap. These subharmonic gap structures (SGS) occurring

at the maximum slopes of differential resistance are due to multiple Andreev reﬂection

(MAR) (Bezuglyi et. al.,2000). If the ARs can be bounded at the two SN boundaries to

conﬁne the electron-hole motion spatially in the normal region, this Andreev bound states

are localized states carrying ﬁnite supercurrent. The AR process has been studied in

ballistic and diffusive SNS junctions using metal, the two-dimensional electron gas (2DEG)

of semiconductor heterostuctures (Hoss et. al.,2000; Nitta et al.,1994; Octavio et. al.,1983),

carbon nanotubes(Bezuglyi et. al.,2000) and graphene (Dirks et al.,2011) as normal conductor.

Carbon nanotubes (CNTs) with a diameter of only a few nm as normal conductors are

one of the best candidates for studying quasi one-dimensional (1D) proximity effect and

AR. Though some experiments and theories have demonstrated 1D Tomonaga-Luttinger

liquid behavior in single-wall carbon nantube (SWNT) or even multi-wall CNT (MWNT)

(Bockrath et al.,1999), some experiments have shown AR (Morpurgo et al.,1999), MAR

(Jarillo-Herrero et al.,2006; Buitelaar et al.,2003; Jorgensen et al.,2006), Andreev bound states

(Pillet et al.,2010) and supercurrent in CNTs (Jarillo-Herrero et al.,2006; Kasumov et al.,1999),

2 Will-be-set-by-IN-TECH

and even superconducting quantum interference device made with CNTs

(Cleuziou et al.,2006).

The superconducting proximity effect in the network-like structure with quasi-1D CNT will

be discussed in the chapter. The enhanced quantum interferences can be given rise to

as Aharonov-Bohm(AB)-type oscillations due to the loops as AB ring in the network-like

structure by applied magnetic ﬁeld. We have studied the MAR and enhanced quantum

interferences, and the reentrant behavior of conductance in this random network CNT.

The updated superconducting proximity effect theory for reentrant behavior has shown

that the proximity correction to the conductance

G

(V, T, B) disappears at low energies

and reaches a maximum value around temperature T or bias voltage V corresponding

to the Thouless energy (correlation energy), E

constant (Volkov&Takayanagi,1997;

Golubov,Wilhelm&Zaikin,1997; Nakano&Takayanagi,2000) (see Fig. 12). This reentrant

behavior in

G

occurs near eV

∼

, k

∼

,orB

∼

,whereB

is a correlation

magnetic ﬁeld. The reentrant behavior has also been predicted for magnetoconductance

oscillations, but has not been completely observed in experiment yet. In what follows, we

also present the MAR in magnetic ﬁeld and then demonstrate the reentrant behavior of the

conductance and magnetoconductance ﬂuctuations.

Fig. 1. Raman spectra of carbon nanotubes taken with 785-nm excitation from a sample

consisting CNTs on SiO

/Si substrate. The Raman spectra peaks of carbon nanotubes, RBM

modes at

∼200 cm

−1

, the high-energy graphitelike mode at ∼1600 cm

−1

and the

defect-induced D mode at

∼1300 cm

−1

, were observed. Inset: Carbon nanotubes on SiO

/Si

wafer substrate.

2. Fabrication of carbon nanotubes bridging superconducting electrodes

2.1 Fabrication of carbon nanotubes

CNTs were synthesized on a silicon wafer with 100-nm-thick thermal oxide by the chemical

vapor deposition method using Co catalyst. A Co ﬁlm is about 0.1-0.3 nm thick by

560

Electronic Properties of Carbon Nanotubes

Multiple Andreev Reﬂections and Enhanced Quantum Interferences with Reentrant Behavior

in NbN/Network-like Carbon Nanotubes/NbN

SNS Junctions 3

Fig. 2. Schematics of NbN/Network-like Carbon Nanotubes/NbN SNS Junctions (middle).

The patterns of NbN electrodes (top) and an AFM image of the CNTs device (bottom) are

made on SiO

substrate. The circle marks indicate the crossed junction of carbon nanotubes

(bottom)

electron-beam deposition. The diameter of the Co nanoparticles control the diameter of the

CNTs. For the synthesis procedure, argon gas fed into the furnace was heated to reach the

growth temperature of 900-1000

◦

C and then replaced by pure methane at a ﬂow rate 300

/min with the pressure of 500 Torr for 5-10 min. This growth condition is optimized

for SWNT growth and we observed very few MWNTs in TEM and AFM images. Inset of

Fig. 1 shows the carbon nanotubes on the SiO

substrate. The CNTs belong to the SWNTs

of individual nanotubes or bundles, which were measured from the height of each nanotube

in an AFM (the CNTs with the diameter of 1-3 nm) and was conﬁrmed by Raman spectra

measurement. Raman spectroscopy technique was used to measure the characteristic of

carbon nanotubes to show in Fig. 1. The diameter-selective Raman scattering is particularly

important for the Raman band at about 200 cm

−1

, which is associated with the radical

breathing mode (RBM) of the carbon nanotube (Rao et al.,1997), to indicate the characteristic

of SWNTs and sharp high energy graphite-like mode (G band) are also supported this results.

The CNTs were freely synthesized to form random network structures, as shown in the inset

of Fig. 1.

2.2 Fabrication of superconducting electrodes

The CNTs are growth between the electrodes with Co catalyst patterns using lithography

technique. The CNTs were directly connected to NbN electrodes as shown in Fig. 2.

Between the electrodes were designed to be 1.5 μm length on the photomask. The number

of CNTs between the NbN electrodes was roughly estimated to be about 1000-2000. These

network-like CNTs have the characteristic of quasi-diffusive transport, which is due to the

network structure including defects, bundles and crossed junctions that marked in the bottom

561

Multiple Andreev Reflections and Enhanced Quantum Interferences

with Reentrant Behavior in NbN/Network-like Carbon Nanotubes/NbN SNS Junctions

4 Will-be-set-by-IN-TECH

ﬁgure of Fig. 2. A excellent superconducting properties for NbN electrodes with 100-nm

thickness and 1-μm wide have typically high superconducting critical temperature T

∼15

K and high superconducting critical magnetic ﬁeld H

 20 T. Optimum ohmic contact in

junctions was made by annealing. The samples in vacuum were annealed with an infrared

heater at 700

◦

Cfor∼15 min and contact resistance was reduced nearly 1∼ 2ordersof

magnitude. After the annealing, the T

of NbN electrodes is close to 11 K. The samples were

measured using the lock-in technique and four-probe method in a helium cryostat.

Fig. 3. The schematic process of Cooper pairs into normal conductor given rise by

superconducting proximity effect

eV > 2 /3 ǻ

eV > ǻeV > 2 ǻ

SNS

(a) (b)

(c)

Fig. 4. Schematic process of (a) normal transport, (b) AR, and (c) MAR. There are different

electron transparent probability T shown on ﬁgure for different transport processes

3. Superconducting proximity effect and Andreev r eﬂection

The Cooper pairs into normal conductor diffusion process is given rise by superconducting

proximity effect shown in Fig 3. In the junction of SN-thermal bath, Cooper pairs into

normal diffusive conductor move within a distance called thermal coherent length, ξ

√

¯hD/2πk

T, before breaking, and then keep coherence in the phase of two electron called

coherent electron pairs. Cooper pairs leak into normal-conductor side from superconductor as

562

Electronic Properties of Carbon Nanotubes

Multiple Andreev Reﬂections and Enhanced Quantum Interferences with Reentrant Behavior

in NbN/Network-like Carbon Nanotubes/NbN

SNS Junctions 5

generating correlated electron-hole pairs at SN interference called Andreev reﬂection . Figure

4 shows a processes of AR. For electron voltage higher than superconducting energy gap



(see Fig. 4(a)), electron merely transport in normal process. For electron voltage lower than 

(see Fig. 4(b)(c)), Cooper pairs leak at SN junction to create Andreev reﬂection (Fig. 4(b)) and

even MAR (Fig. 4(c)).

Fig. 5. Differential resistance as a function of applied voltage at different constant

temperature between 2 and 11 K. The resistances are offset from each other for clarity. MAR

occurs at 3 and 6 meV (solid line arrows) and AR occurs at zero-bias voltage above around 9

The MAR was observed by measuring differential resistance as a function of applied voltage.

Figure 5 shows SGS due to the MAR (Bezuglyi et. al.,2000; Hoss et. al.,2000; Nitta et al.,1994)

and the submultiples of the gap voltage,

±2Δ/e and ±Δ/e(solid line arrows). The MAR

become smeared gradually at temperature above

∼ 7KandthenadipoftheARisobserved

at more high temperature but below T

,11K.Inaddition,theMARandARwereobserved

in different constant magnetic ﬁeld between 0 and 4.3 T at temperature 1.75 K (Fig. 6).

The SGS and AR dip become smeared above

∼450 mT and ∼1.5 T, respectively. Pervious

experiments on 2D SNS junctions based on clean semiconductor heterostructures have also

observed the MAR and AR smeared in the magnetic ﬁeld (Nitta et al.,1994), but only below

afewμT. The suppression of MAR and AR in a magnetic ﬁeld can be easily understood

by a physical process shown in Fig. 7. The AR takes place at the SN interfaces, and

quasi-particles trajectories are deﬂected and the angle of incidence is increased. Because the

parallel momentum becomes larger than the perpendicular momentum, the AR probability

is suppressed (Mortensen et al.,1999). Though the smearing mechanism is the same as

other dimensions, owing to 1D CNTs with small diameters, the quasiparticles are not easily

deﬂected and their parallel moment not easily enhanced during motion as schematic process.

Therefore, the applied magnetic ﬁeld for seaming AR is larger than other dimensions over

two orders of magnitude.

563

Multiple Andreev Reflections and Enhanced Quantum Interferences

with Reentrant Behavior in NbN/Network-like Carbon Nanotubes/NbN SNS Junctions

6 Will-be-set-by-IN-TECH

Fig. 6. Differential resistance as a function of applied voltage in constant magnetic ﬁeld

below 4.3 T. MAR processes occur at 3 and 6 meV (solid line arrows) and reentrant behavior

occur at close zero zero bias (dash line arrows). The MAR is smeared by applying magnetic

ﬁeld over

∼250 mT. Above 0.4 T, the curves of peak are changed to dip at around zero bias

voltage. ARs disappear at over 2 T.

Fig. 7. Schematic process of the AR in 2DEG (2D system) and CNT (1D system) at NS

junction with an incident electron (e) and a retroreﬂected hole (h) in an applied magetic ﬁeld

below mT. The electron and hole can not be easily deﬂected in CNT compared with 2DEG in

applied magnetic ﬁeld and are still conﬁned in CNT

4. Magnetoconductance ﬂuctuations and enhanced quantum interference

A single electronic wave that is split into two propagating waves over different paths as shown

in Fig. 8. The quantum interference of electron will be modulated by an applied magnetic

ﬁeld passed through in the ring. The oscillations in conductance due to this AR effect can be

observed in the conductor ring of ballistic transport by measuring magnetoconductance. In

the metallic wire within mesoscopic scale of diffusive transport, a single electron that scatters

around the closed path and interference with itself by impurities scattering to cause AB effect

in some loops. Some oscillations by loops in wire will be formed ﬂuctuations in conductance

called universal conductance ﬂuctuations (UCF). Some loops in network-like CNT as the

interference loops are shown in Fig. 9.

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Electronic Properties of Carbon Nanotubes