Gross R., Sidorenko A., Tagirov L. Nanoscale Devices

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Aharonov-Bohm Oscillations in Single Bi

Nanowires

D. Gitsu

, T. Huber

, L. Konopko

1,3

, A. Nikolaeva

1,3

Institute of Electronic Engineering and Industrial Technologies ASM,

Kishinev MD-2028, Moldova

Department of Chemistry, Howard University, 525 College St. N.W.

Washington, DC 20059

International Laboratory of High Magnetic Fields and Low Temperatures,

Wroclaw, Poland

Abstract: We report on the study of the magnetoresistance (MR) of 55 nm di-

ameter single bismuth nanowire at a temperature of 1.5 K. For a wide

range of magnetic fields and different sample orientations the MR

exhibit field-periodic modulations. We have observed 3 periods of

MR oscillations; one of them is consistent with theoretical predictions

for the Aharonov-Bohm oscillations in disordered cylinders. Two

others may be connected with Dingle’s predictions for oscillations re-

sulting from quantization of the electron energy spectrum.

Key words: magnetoresistance, Aharonov-Bohm oscillations, bismuth

Introduction

The semimetal Bi has a highly anisotropic Fermi surface, low carrier

density, and long carrier mean free path. Since for Bi the charge carriers

have a small effective mass, quantum confinement effects in Bi are more

clearly manifested and can be observed in nanowires of larger diameter

than those of any other material. It was theoretically shown that when

charge

carriers pass through a cylindrical conductor aligned with a

349

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 349–353.

350 D. Gitsu, T. Huber, L. Konopko, A. Nikolaeva

magnetic field, they reveal their wavelike nature in the appearance of the

resistance oscillations as a function of the applied magnetic field.

A particular type of quantum-size effects in normal conductors with long

carrier mean free path is the solid state analogue of the Aharonov-Bohm

effect (AB) [1] which exists in cylindrical wires as MR oscillations with a

period ∆B that is proportional to Φ

/S, where Φ

=h/e is the flux quantum

and S is the cross-sectional area of the wire. The longitudinal

magnetoresistance (LMR) oscillations of the AB-type, which are

equidistant in magnetic field with period ∆B=Φ

/S and decrease in

amplitude with increasing field due to electrons undergoing continuous

grazing incidence reflections at the wire wall, have been observed at 4.2 K

in single nanowires grown by the Ulitovsky technique with diameter

0.2<d<0.8 µm [2-5] and in a Bi nanowire arrays 270 nm in diameter [6].

Another type of quantum effect is Dingle oscillations which results from

the quantization of the electron energy spectrum. As the magnetic field is

changed, the discrete energy levels cross the Fermi energy of the electron

gas and thereby cause oscillations of the resistance with a magnetic field

period ∆B=kΦ

/S, where k assumes a set of values between about 0.9 and

2.2 [7]. The oscillations of this type also were observed in single Bi

nanowires grown by the Ulitovsky technique [2-5].

For the disordered cylindrical samples with short mean free path

(compared to the circumference of the cylinder) the new type of AB

oscillations with period ∆B=Φ

/2S was predicted by Al’tshuler, Aronov and

Spivak who applied the mathematical techniques developed to describe

weak localization in doubly connected structures like loops and cylinders

without leads [8]. In 1981 these oscillations were observed by Sharvin and

Sharvin [9] for a Mg cylinder 1 µm in diameter and 1 cm long.

In this work, we present our results for the magnetoresistance

measurements on single Bi wires with diameter of 55 nm at 1.5 K in high

magnetic fields up to 14 T with different sample orientations. In the hole

range of the applied magnetic field we have observed three periods of

equidistant MR oscillations with one of them equal to ∆B=Φ

/2S.

Experiment and Discussion

The single nanowire samples with diameter 55 nm were prepared by the

high frequency liquid phase casting in a glass capillary using an improved

Ulitovsky technique [10] and represented cylindrical single crystals with

the

(1011) orientation along the wire axis. All measurements were

Aharonov-Bohm Oscillations in Single Bi Nanowires 351

performed at the High Magnetic Field Laboratory (Wroclaw, Poland) in a

superconducting solenoid generating magnetic fields up to 14 T at

temperatures between 1.5 K and 2.1 K.

0 2 4 6 8 10 12 14

θ=0

θ=90

θ=48

B, T

dR/dB, a.u.

θ=32

Fig. 1. Magnetic field derivative of the resistance, dR/dB, for a single Bi wire

(d=55 nm) with glass coating vs. magnetic field at T=1.5 K. θ is an angle between

the direction of the applied magnetic field and the wire axis, θ=0 corresponds to the

longitudinal MR and θ=90

to the transverse MR.

The sample was measured in a two-axis rotator in which the sample

holder was rotated by means of a worm drive and a twisted fiber connected

to a shaft of a step motor. Together with MR data we measured the first

derivative of the MR with respect to the applied magnetic field using

modulation

technique (a small AC magnetic field of amplitude ∆B=7.5x10

-5

and a frequency of 13.7 Hz was produced by a special superconducting

modulation coil). A 5210 lock-in amplifier was used for demodulation of

the MR signal.

Figure 1 shows the derivative dR/dB of a 55-nm Bi nanowire sample for

various orientations between the wire axis and the magnetic field. We have

observed oscillations in the derivative of the MR signal at various

orientations of the sample. The observed oscillations are a superposition of

three frequencies. The distinct character of the beats for longitudinal MR

oscillations

made it possible to determine their periods with sufficient

352 D. Gitsu, T. Huber, L. Konopko, A. Nikolaeva

accuracy. For

=0 (longitudinal MR) we found ∆

=∆

=0.74 T, and ∆

= 1.21

T. Then, as the angle θ is increased, the two periods ∆

and ∆

split up. The

period ∆

is in good agreement with ∆B=Φ

/2S obtained for the wire

diameter d=60 nm, which very close to the actual wire diameter. The

observed oscillations (∆

) have an oscillation period corresponding to half

the normal Aharonov-Bohm period. Moreover, the observed variation of

the oscillation period as a function of the angle between the magnetic field

and the wire axis (see Fig. 2) is in satisfactory agreement with the

theoretical dependence ∆

(θ)=∆

(θ=0)/cosθ. The same angle dependence

was obtained in [3-4] for a Bi wire with d=0.56 µm, however, with the

normal Aharonov-Bohm period (see inset of Fig. 2). The carrier mean free

path in our sample is estimated to be longer than 1 µm but a period

∆B=Φ

/2S was predicted [8] for disordered cylindrical samples with short

mean free path.

0 20406080

0,5

1,0

1,5

2,0

2,5

0204060

0,2

0,3

0,4

- ∆

∆

, T

θ, Deg

B||J

B⊥J

∆

, kOe

θ, Deg

H||J

Fig. 2. Dependence of the three oscillation periods ∆

, ∆

and ∆

obtained from the

MR data of a 55-nm Bi nanowire on the angle between the direction of the applied

magnetic field and the wire axis. The solid line shows the ∆

(

=0)/cosθ law. A

similar dependence for the oscillation period ∆

obtained for a Bi nanowire with

d=0.56 µm [10] is shown in the insert.

Aharonov-Bohm Oscillations in Single Bi Nanowires 353

Due to the Ulitovski technology the interface between the Bi-core and

the glass surrounding may contain considerable trapped charge which can

produce a narrow (~ 6 nm) space-charge region. The carriers of this region

have shorter mean free path because of surface roughness scattering.

Two other periods ∆

, ∆

observed in our experiments, to our opinion are

the Dingle oscillations from the Bi core.

Acknowledgments

This work was supported by the Civilian Research Development Fund

under Grant

CGP # MO-E1-2603-SI-04.

References

1. Aharonov Y, Bohm D (1959). Phys Rev 115:485

2. Brandt B, Gitsu DV, Nikolaeva AA, Ponomarev YaG (1977). Zh Exp

Teor Fiz 72:2332 [(1977) Sov Phys JETP 45:1226]

3. Brandt NB, Gitsu DV, Nikolaeva AA, Ponomarev YaG (1982). Lect

Notes Phys 152:415

4. Brandt NB, Bogachek EN, Gitsu DV, Gogadze GA, Kulik IO,

Nikolaeva AA, Ponomarev YaG (1982). Fiz Nizk Temp 8:718 [(1982)

Sov J Low Temp Phys 8:358]

5. Brandt NB. Gitsu DV, Dolma VA, Ponomarev YaG (1987). Zh Exp

Teor Fiz 92:913

6. Huber TE, Celestine K, Graf MJ (2003). Phys Rev B 67:245317

7. Dingle RB (1952). Proc Roy Soc London Ser A 212:47

8. Al’tshuler BL, Aronov AG, Spivak BZ (1981). Zh Exp Teor Fiz Pisma

33:101 [(1981) JETP Lett 33:94]

9. Sharvin DYu, Sharvin YuV (1981) JETP Lett 34:272

10. Brandt NB, Gitsu DV, Joscher AM, Kotrubenko BP, Nikolaeva AA

(1976). Prib Tekh Eksp 3:256

Some Applications of Nanocarbon Materials for

Novel Devices

Z. A. Mansurov

al-Farabi Kazakh National University, 96A, Tole be Str., 480012, Almaty,

Kazakhstan

Abstract: The results of the synthesis and study of nanocarbon materials,

namely the structure and morphology of carbon formation, the

sorption of gold by carbonized apricot stones, the mechano-chemical

encapsulation of quartz particles by metal-carbon films, the

production of carbon-graphite cathodes for chemical sources of

current, the development of multifunctional catalysts for oil

hydrofining, the carbonization of vegetative raw material, and the

development of carbon containing refractories are presented.

Key words: nanocarbon materials, sorbent, carbonization

Introduction

The last years are characterized by the intensive development of

investigations on the formation of carbon nanotubes. It was found that Fe,

Ni, Co, their oxides as well as the alloys of these elements are the most

effective catalysts for carbon formation. As a result of a catalytic reaction

carbon is formed and is deposited on dispersed metallic particles. These

deposits have specific forms and properties which allow us to consider

them as perspective ultra-dispersed systems used in different areas of

chemistry. Over the last years, some experimental materials point at

specific developments which indicate a successful application of metal-

carbon compositions as adsorbents, catalysts carriers and catalysts for a

number of chemical reactions [1].

355

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 355–368.

356 Z. A. Mansurov

At present, the laboratories of the Chemical Physics Department and

Combustion Problems Institute of al-Farabi Kazakh National University

carry out investigations on obtaining carbonized materials on the basis of

local clays and wastes of the mining industry: chromite and bauxite

sludges, agricultural wastes (walnut shells and grape stones) and using them

in different applied aspects. The obtained adsorption-catalytic systems find

practical applications in oil purification from sulphur containing

compounds, purification of water from organic compounds and heavy metal

ions, purification of air from SO

and in obtaining improved types of

refractories, such as carriers of catalysts of hydrocarbon transformation

reactions [2-4].

The Structure and Morphology of Carbon Formations

It is possible to obtain a more suitable surface with a larger number of

active centers than present in the initial samples by carbonization. Figure 1

shows electron microscopy micrographs of carbonized chromite slime and

clay treated with Co salt. It is seen that formation of carbonaceous deposits

results in not only chemical (formation of metal carbide and carry-over of

carbide to carbon fiber), but also physical processes – carry-over of

particles to carbon mass. Pyrolysis on the surface of the catalyst results in

the formation of carbon deposits or the so-called catalytic carbon, the

amount of which is 5-10 times larger than the initial one. A developed

specific surface is related to the morphology of carbon deposits in the form

of fibers, tubes and clusters with the diameter of 1500-3000 Å. It should be

noted that the growth of carbon fibers (tubes) in general is complicated and

sometimes has a branched character, i.e. one metal particle initiates the

growth of several carbon fibers in different directions, the so-called

"octopus" effect [2].

Simultaneous participation of carbon and metals in the formation of

carbon fibers makes it possible to develop new nanostructured composition

materials with complex of widely varying properties.

Some Applications of Nanocarbon Materials for Novel Devices 357

Fig. 1. Scanning electron microscopy micrograph of chromium sludge and Co-

catalyst carbonized at T = 1073 K.

Sorption of Gold by Carbonized Apricot Stones [5]

At the present level of development of metal manufacturing, during the

processing of the complex composition a large amount of the noble metals

is lost. That is why the questions connected to the extraction of noble

metals from industrial solutions by sorption on carbonic sorbents still

remains relevant. The necessity of cheap sorbents satisfying industrial

requirements regarding sorption capacity, thermostability, controllable size

and pore structure etc., leads to the development of new methods for

obtaining suitable sorbents.

Carbonization of apricot stones (CAS) was carried out by a method

described in [2]. Carbonized sorbents based on apricot stones have the

codes CAS-1, CAS-2, and CAS-3. The sorption of gold (III) was studied by

electrochemical methods using a P-5848 potentiostate by means of

recording current vs. time, J-t, curves at constant potential corresponding to

the extreme current of gold electroreduction (III).

Carbonized sorbents based on vegetative raw material concurrently

possess ion-exchanging and reducing properties. Stationary potentials of

358 Z. A. Mansurov

CAS were measured to reveal their reducing properties. The sorbents of the

CAS series have relatively low oxidative-reducing potential that depending

on the CAS mark change between 0.20 V and 0.25 V. This implies that the

CAS sorbents possess reducing properties, which are probably determined

by the presence on the surface of carbonized sorbents of reducing groups –

carboxylic, phenolic, hydroxyl, amine. The relative amount of these groups

depends on the conditions of carbonization. At carbonization, in the

beginning predominantly aromatic compounds are formed, which with

increasing carbonization temperature are condensed into polycyclic

aromatic compounds (PAH) and in fullerene-like compounds. Thus,

carbonized sorbents are not only have ion-exchanging but also oxidative-

reducing properties.

The measured stationary (real) potential of the muriatic medium [AuCl

]

is 0.76 V. The difference of potentials between the gold-oxidant and the

sorbent-reducing agent ranges form 0.51 to 0.56 V. A potential difference

of 0.24 V is required in practice for completely passing any oxidative-

reducing reaction. It follows from these data that there is a real opportunity

for the reduction of gold (III) to the metallic state. This opportunity is

proved by magnitudes of CAS sorbent potentials after sorption of gold (III)

on it.

The reducing of gold (III) to the metallic state was proven by optical

microscopy images (see Fig. 2).

Extraction of metallic gold occurs non-uniformly over the whole surface

of the CAS particles, and in separate areas where the growth of gold

crystals occurs. Hence, the process of metallic gold extraction and sorbent

reducing groups’ oxidation is electrochemical, i.e. there are cathodic and

anodic areas. Cathode areas are formed in the initial moment of sorption

where further the reducing of gold (III) occurs.

Fig. 2. Micrograph of a sorbent CAS-2 + Au(III).

Some Applications of Nanocarbon Materials for Novel Devices 359

As well-known in chemistry the method of initial areas was used for the

determination of the magnitude of gold sorption velocity. Kinetic curves of

gold sorption on sorbents CAS-1, CAS-2, and CAS-3 in a solution of 0.1n

HCl have been obtained by an electrochemical method. Sorbent CAS-2 was

found to have maximum velocity of gold sorption as it is seen from Fig. 3.

Complete sorption of gold (III) on this sorbent occurs after 8 minutes,

whereas the time of complete sorption of gold (III) on CAS-1 is 11 minutes,

and on CAS-3 even 16 minutes. That is, the velocity of gold (III) sorption

decreases in the sequence CAS-2 > CAS-1 > CAS-3. Based on this data our

further research was focusing on the sorbent CAS-2.

Complete sorption of gold (III) occurs after 8 minutes in the range of

studied concentrations of gold (III) (8.88-3.5 mg/L) independent of its

concentration. At the same time, the steepness of the J-t-curve of gold (III)

was found to decrease from solution and consequently its sorption extends

with increasing gold (III) concentration.

The increase of gold (III) sorption velocity occurs in the presence of

copper salt (II) and iron (III) what is connected to the catalytic effect of

gold (III) reducing. Complete sorption of gold (III) occurs after 5 minutes

in the case of the presence of copper (II) ions, and after 1.5 minutes in the

case of iron (III) ions, whereas it takes 8 minutes in absence of these

admixtures.

Fig. 3. Kinetic curves of gold (III) sorption on various sorbents in 0.1n HCl

solution. Sorbent mass – 0.2 g, particle diameter – 0.5 mm, gold concentration –

17.75 mg/L. Solution volume – 20 mL.

Gross R., Sidorenko A., Tagirov L. Nanoscale Devices - Fundamentals and Applications

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