Superinjection from Oriented Carbyne as the Result of Landau Quantization in Giant Pseudo-Magnetic Field

doi:10.4236/jmp.2013.47134

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Journal of Modern Physics, 2013, 4, 994-999

http://dx.doi.org/10.4236/jmp.2013.47134 Published Online July 2013 (http://www.scirp.org/journal/jmp)

Superinjection from Oriented Carbyne as the Result of

Landau Quantization in Giant Pseudo-Magnetic Field

Yuri Prazdnikov

Faculty of Physics, Moscow State University, Moscow, Russia

Email: [email protected]

Received April 25, 2013; revised May 26, 2013; accepted June 25, 2013

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

The qualitative explanation of the earlier published experimental data was obtained within new energetic model of ori-

ented carbyne. The conductivity spectrum and the superinjection effect feature Landau quantization in a giant pseudo-

magnetic field. The relativistic dispersion of carriers and non-dissipative character of their motion cause the effect of

superinjection where carriers go upwards on an energetic ladder. Raman-spectra and other data point out to the fact that

the plane of carriers’ motion is close to the carbyne-insulator interface. Quantum effects and on-surface conductivity

allow considering oriented carbyne as an analogue of topological insulator.

Keywords: Carbyne; Superinjection; Pseudo-Magnetic Field; Topological Insulator

1. Introduction

The arguments in favor of idea that the carbon era only

begins are given in [1]. Although sp1 carbon—carbyne

was discovered by Russian chemist A. M. Sladkov al-

ready more than half a century ago [2], it is still men-

tioned as a perspective material by Russian scientists

only. This characterizes well the majority of world scien-

tists’ respect to carbyne in general and its oriented form

in particular. Carbyne chains with the length of 44 atoms

were synthesized recently by authors [3] and this realized

as a small sensation. They see big future for carbyne’s

application in the molecular electronics. At the same time,

Russian publications about carbyne chains of hundreds

atoms length still remain unnoted. These articles present

experimental results that clearly favor the unique struc-

ture and properties of oriented carbyne. The main effects

are resistance quantization at room temperature [4] and

abnormal injection/emission capability [5,6]. Ideal re-

peatability of current-voltage characteristics (CVC),

quantization at room temperature and integration possi-

bility into the existing technology nowadays allow us to

consider oriented carbyne as one of the most promising

materials for nanoelectronics [7]. So what is the reason

of such sustainable skepticism by world's scientists? One

of the main reasons for skepticism is the lack of an accu-

rate theoretical model. This is due to the complexity of

modeling such nanosystems. The theory of topological

insulator [8,9] and the pseudo quantum Hall Effect in

two-dimensional systems have been developed not so far

[10]. Another skeptic’s important argument is that insta-

bility of pure carbon sp1 chains does not concern the ori-

ented form of carbyne. Individual carbon sp1 chains are

really not stable; they should be packed into the oriented

quasicrystal to be able to exist as a chain of hundreds

atoms. But even in this form carbyne can’t be obtained in

a large size crystal. This fact still has no correct explana-

tion and this is another skeptical argument.

Has long been noticed the key role of the surface

where oriented carbyne is growing up (at the thickness of

more than 1 micron oriented carbyne turns into an amor-

phous mixture of different phases of carbon). It has re-

cently become clear that the stability can be related to

presence of molecular hydrogen in interchain space [11].

The Author proposed new model of interchain dihydro-

gen bonds based on data about mass-spectra of the laser

ablation products.

Electrical conductivity of oriented carbyne is anisot-

ropic: chains are minimal quantum wires with ballistic

electron transport regime in longitudinal direction. There-

fore an electric field (unlike a magnetic one) inside car-

byne is two-dimensional. Conductivity across chains has

roughly an exponentially-stepped dependence on the

thickness of a carbyne film [4]. The spectrum of “magic”

thicknesses where the conductivity increases abruptly

had been discovered by authors, but its origin was not

clear.

Y. PRAZDNIKOV 995

2. Results and Discussion

Anisotropy of electrical conductivity appears mostly in

thin films. Also in contrast to the Raman spectra of thick

films (which are almost identical to the spectrum of dis-

ordered carbyne) the thinnest films have the spectrum of

another type (see Figure 1). There is no DG-peak, and

the C-peak looks like a plateau stretched for 400 cm−1.

This feature did not attract attention earlier because

there was no qualitative carbyne model. Now it is possi-

ble to suppose that the C-peak broadening to the right

occurs because of excitation of traversal oscillations in

an interchain bond’s plane. The strength of the bond cor-

responding to frequency of 400 cm−1 is weaker than the

strength of chemical bond С-Н what is adjusted with

supposed dihydrogen bond properties. The considerable

difference of Raman spectra from one to another allows

us to conclude that carbyne has a different form near the

substrate’s interface.

Typical plots for two different types of the samples of

the traversal resistance of a carbyne film of inverse

thickness [4] are shown in Figure 2. All data for Figure

Figure 1. Raman spectra of oriented carbyne films.

Figure 2. Quantization of transverse resistance on inverse

thickness. Semi-logarithmic coordinates. Squares—ﬁrst-type

samples, triangles—second-type samples.

2 were obtained at room temperature. The scheme of the

experiment with the samples of the first type is shown in

Figure 3. The scheme of the experiment with second

type samples is the same; the difference is in the scale of

the structure—it is an order of magnitude more. The car-

byne samples of the first type were grown on the 0.1 mi-

cron layer of SiO2 which lies on the doped silicon wafer;

the samples of the second type-on a quartz wafer 0.5 mm

thick. The distance between contacts is: for the first type

−0.6 microns, for the second type −0.5 mm.

In Figure 2 it is possible to see likeness to Hall resis-

tance quantization in two-dimensional systems in a tra-

versal magnetic field. We note here that we measured

classic resistance of the samples instead of Hall’s resis-

tance, which, as it is known, has different dependence.

Another difference of Figure 2 from the CVC of Hall’s

resistance is that it is plotted in half-logarithmic coordi-

nates and the steps’ height, accordingly, is exponentially

greater. This can be related to the fact of activation na-

ture of a traversal current [6]. Notice that the thinnest

films have two activation energies in different tempera-

ture ranges −0.19 eV and 0.23 eV.

The experiments [5,6] showed that current goes

through the dielectric substrate-carriers are injected

through a certain “effective barrier” which has a value on

the order of less than a real metal-insulator interface bar-

Figure 3. Samples and scheme of the experiment. (a) Top

view of the first-type microstructure of TiN electrode con-

tacts; (b) Cross section A—A of the structure and scheme of

measurement. Injection to SiO2 occurs at the point A; (c)

Typical metal island ﬁlm used in the experiments as the

third-type contact.

Y. PRAZDNIKOV

996

rier. This allows us to call this phenomenon as “superin-

jection”. Injection current exponentially depends on an

external transverse electric field. Such field dependence

for the thinnest carbyne film is shown in Figure 4. As

well as temperature dependence, this curve shows the

presence of two different values of the effective barrier,

which are calculated from the linear (in semi-logarithmic

coordinates, in Richardson–Dushman model, for more

details see [6]) approximation of current to zero. This

fact corresponds to the switching between neighbor steps

in Figure 2. This allows us to assume that resistance

quantization concerns only the first cross-layer, which

lies on the carbyne-insulator interface. In the latter case,

oriented carbyne is similar to topological insulator, in

which insulating materials conduct electricity on their

surface via special electronic states of the surface (the

difference is in one-dimensional conductivity of carbyne

inside the volume). Such substances were already syn-

thesized and even were found in nature [9] recently.

There are several unusual quantum effects such as for-

mation of massless charge carriers and spin quantum

Hall Effect in topological insulators. One of the most

interesting properties of topological insulators is that spin

oriented electrons cannot be scattered by impurities or

imperfections of the environment. For this reason, elec-

trons test very small or even zero resistance (like in su-

perconductors) from the environment. Such surface states

of topological insulators are “topologically protected”

and cannot be destroyed without breaking of quantum

mechanics laws (Dirac Prize 2012, Duncan Haldane,

Charles Kane, Shoucheng Zhang).

Superinjection from oriented carbyne is characterized

by height of an “effective” barrier through which the

Figure 4. The dependence of current from the central con-

tact (first-type sample) through SiO2 on the side contacts

potential. The carbyne ﬁlm thickness is 30 Å, the potential

of the central contact was kept constant at U1 = +10 V.

thermally-activated throw of carriers occurs; this throw is

characterized by Richardson–Dushman dependence of

current density on barrier height





:expjAT kT





. The height of this barrier



linearly depends on an external electric transverse field

and “magic” number n. We obtained the resistance spec-

trum at the fixed voltage 1 V at which CVC is exponen-

tial type. Therefore it corresponds to the spectrum of the

“effective” barrier height shown in Figure 5(a) in arbi-

trary units of energy 10 . Assumed these bar-

riers formed by sequential placed levels of one constant

energy spectrum we have calculated this energy spectrum.

It is shown in Figure 5(b) in arbitrary units where E = 0

corresponds to the level n = 0.



~logER

This spectrum is well approximated by the formula

72 502En



  which has the same form as the

spectrum for the relativistic Landau levels:

nD F

ee eBnc



. It should be noticed here that

the “n” in our figures shifted by 2 relative to the true

Landau spectrum and E0 appears as −72 in respect to E2.

As we mentioned above “effective” barrier height can

Figure 5. Energetic spectra of oriented carbyne in arbitrary

units E. (a) The spectrum of the “effective” barrier height;

(b) The energy spectrum of transverse states in oriented

carbyne and its approximation.

Y. PRAZDNIKOV 997

easily be switched by transversal electric field or tem-

perature or film thickness. Thus we could not find an

absolute value and used the relative “n”. Each level of

the Landau spectrum corresponds to the cyclotron orbit

of massless charge carriers—Dirac fermions. Theoreti-

cally their presence is possible in 2D dihydrogen trans-

verse chain layer. As we noted above, at least one such

layer exists at the carbyne-insulator interface, and this

can cause Dirac fermions appearance by analogy to to-

pological insulators.

The question about the origin of a quantizing magnetic

field oriented along the chains arises. A possibility of

formation so-called “pseudo-magnetic” field in graphene

by its deformation is discussed in [10]. Its value is so

large that it is able to cause Landau quantization at room

temperature. In the article [12] experimental evidence of

existence of such a field in graphene is obtained, and its

value is estimated to be hundreds of Tesla, what allow

authors to call it “giant pseudo-magnetic”. It is interest-

ing to note that oriented carbyne on pictures taken by an

atomic-force microscope has the unit cell a bit extended

in a traversal plane; this strain can induce a pseudo-

magnetic field.

The presence of a magnetic field can explain the pre-

viously noticed strong dependence of the injection/emis-

sion current on the environment. First of all, it is the in-

fluence of the substrate. In Figure 2 the difference in

spectra for samples on a thin dielectric layer and the solid

dielectric is visible. The quantization of the “magic”

thicknesses on n and its approximation by a cubic parab-

ola is presented in Figure 6 for two types of the samples.

As it could be seen from the approximations, the

magic thicknesses grow ≈40 times faster by n in the

samples of the first type than in the second:



23 2.5n



.6 1.9n

73d for samples of the first type, and

59 0d for the second ones.

Secondly, it is the influence of the interelectrode vac-

uum space width on the current of emission of electrons

into vacuum. This fact previously had no clear explana-

tion [6]. It is difficult to explain such strong influence by

a space charge field: the electron cloud density is con-

centrated near emission center (i.e., near the carbyne

surface). Figure 7 shows the set of CVC’s of current of

electron emission into vacuum from the samples of the

third type where oriented carbyne was grown on Cu is-

land film (50 nm) laying on a dielectric layer. These

samples have the same carbyne-in-wells type and are

characterized by the same CVC’s of injection/emission

current as the samples of the first two types, but the cur-

rent area is greater. Let’s note here the independence of

super—injection/emission on geometry and defects—an

island metal film which is used as a well-type contact in

the third type samples is characterized by the size and

Figure 6. The spectra of “magic” thicknesses and their ap-

proximations by cubic parabola. (a) First-type samples: d =

73 + 23 × (n − 2.5)3; (b) Second-type samples: d = 59 + 0.6 ×

(n + 1.9)3.

Figure 7. Electron emission from third-type samples. The

value of the interelectrode vacuum space is: (1) d = 0.4 mm;

(2) d = 0.08 mm; (3) d = 0.04 mm.

Y. PRAZDNIKOV

998

shape of the wells varying in wide ranges. It can be seen

(Figure 7) that narrowing of the interelectrode vacuum

space leads to a significant change in the CVC parame-

ters—in the height of the “effective” barrier φ and in

“field amplification coefficient” β. The calculated pa-

rameters are:

1: for 0.40 mm—φ = 0.4 eV, β = 20;

2: for 0.08 mm—φ =0.8 eV, β = 68;

3: for 0.04 mm—φ =1.6 eV, β = 153.

This effect can be related to a magnetic field. Mag-

netic properties of the metal anode can influence Landau

quantization in a magnetic field. But as the pseudo-field

is not classical, it is not absolutely clear how quantization

in a pseudo-magnetic field depends on the magnetic

properties of the environment. Perhaps the reason is that

the electrons’ motion on cyclotron orbits creates a clas-

sical magnetic field which is responsible for the effect of

the environment. The cyclotron orbits of larger radius

create more extended in normal direction magnetic fields.

Thus, while metal anode is getting closer, the orbits of

larger diameter are getting blocked firstly, as we can see

in Figure 7. At such a high sensitivity of superinjection

to the effect of the environment it is interesting to note

the independence of the “effective” barrier height on

dielectric type, contact material (Al, Cu and TiN are used)

and carbyne film thickness. The following dielectrics

were tested: SiO2, ZnO and organic dielectrics with a

bandgap of 2 - 3 eV. In all cases when the area of current

was equal (the same contact structure), almost identical

“effective” barriers were observed regardless of the car-

byne film thickness: 0.32 eV and 0.37 eV for holes and

for electrons accordingly. The calculation was made here

approximately on the basis of some evaluation of the

“effective” barrier’s cross-section in Richardson-Dush-

man model.

Extreme system sensitivity to a very minor variation of

some parameters with a strong resistance to the others is

the feature of quantum systems like topological insula-

tors. Summarizing the results we can construct the ener-

getic diagram of the relativistic Landau levels and of the

superinjection process as consequent activations on them

(see Figure 8).

The cyclotron orbits of electrons correspond to the

Landau levels n. Carriers are sequentially activated on

them and go to the orbit of bigger radius. The first barrier

(which can be seen at CVC as “an effective barrier”)

appears to be the highest. Dirac point ED in carbyne is

approximately 0.02 eV above Fermi level EF; the “effec-

tive” barrier height for holes injection is less than for

electrons for 0.04 eV. The essence of the traversal elec-

tric field effect is in orbits distortion and in change of

orbital velocity of carriers. Under the action of an exter-

nal “pulling of electrons” field the orbital velocity at the

carriers’ entry point to carbyne decreases in proportion to

Figure 8. The scheme of the superinjection process. (a) The

energetic diagram of superinjection as consequent thermal

activations on the relativistic Landau levels; (b) A top view

on injecting structure—metal contact surrounded by car-

byne. Carriers are sequentially activated on the cyclotron

orbits of bigger radius and finally injected downwards to a

dielectric layer. The bottom image shows the effect of an

external transversal electric field—circular orbits extend

into elliptic, and the orbital speed becomes variable.

the field intensity, correspondingly the effective barrier

reduces (solving exact Schrödinger equation for 2d-

Diracs particles in magnetic field is beyond the frames of

this article). A “retarding” field acts similarly: an orbital

velocity at the entry point increases and the effective

barrier occurs to be higher. For charge carriers to be

passed through the high barriers many consecutive acti-

vations are required, so final cyclotron orbit could have

quite big diameter. It may not even fit on the area of

carbyne—this may explain the observed hole injection

blocking while diameter of the metal well narrowing [5].

Meanwhile electron injection remains constant: less num-

ber of activations is required and the radius of the final

orbit becomes smaller. It is easy to note that classical

charge carriers cannot be sequentially activated: the pro-

bability of return downwards motion on an energy ladder

plenty times higher than the probability of upwards mo-

tion. It is only possible when carriers move without scat-

tering. While their upwards motion on an energy ladder,

charge carriers absorb phonons energy on the area of

cyclotron orbits, but the inverse process is impossible

because of the effect of “topological protection”.

The main oriented carbyne’s puzzle—the vertical sta-

bility of the chains—can be explained by the existence of

a giant pseudo-magnetic field as well. Conducting chains

align along the field lines due to the interaction of the

electrons moving along the chain with the pseudo-mag-

netic field (this can occur via the secondary classic mag-

netic field as we proposed above or we should assume

the pseudo-magnetic field extent in normal direction as

far as chains long). A slight deviation in their motion

along the field is forbidden by quantization of the trans-

verse motion energy because of the energy of the first

Landau level (~0.3 eV) several times more than the en-

ergy of thermal motion at 300 K. Thus, the oriented car-

byne looks like chains, which are “frozen” in the pseudo-

Y. PRAZDNIKOV

999

magnetic field by quantum laws.

3. Conclusions

We explained abnormal injection/emission properties of

oriented carbyne in terms of the modern theories of to-

pological insulator and the pseudo-magnetic field.

Within the new energetic model oriented carbyne is

similar to topological insulator. Its lateral charge trans-

port properties are determined by interface layer and

possess the unique propriety of “topological protection”.

It was synthesized much earlier than first known artificial

topological insulator.

Oriented carbyne is similar to graphene as well. The

transversal energetic spectrum is like massless Dirac par-

ticles’ spectrum in uniform giant pseudo-magnetic field.

The oriented carbyne interface layer acts as self-strained

graphene. It is the only such material known to date.

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