Journal of Modern Physics, 2013, 4, 994-999 Published Online July 2013 (
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
Received April 25, 2013; revised May 26, 2013; accepted June 25, 2013
Copyright © 2013 Yuri Prazdnikov. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
opyright © 2013 SciRes. JMP
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 cm1.
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 cm1 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. Squaresrst-type
samples, trianglessecond-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 AA of the structure and scheme of
measurement. Injection to SiO2 occurs at the point A; (c)
Typical metal island lm used in the experiments as the
third-type contact.
Copyright © 2013 SciRes. JMP
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 lm 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.
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.
Copyright © 2013 SciRes. JMP
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.
Copyright © 2013 SciRes. JMP
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-
Copyright © 2013 SciRes. JMP
Copyright © 2013 SciRes. JMP
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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