the real physical conduction mechanism in monolayer
TRANSCRIPT
The real physical conduction mechanism in monolayer Graphene and
superconductivity in intercalated Bilayer Graphene
- Research paper -
Aco Z. Muradjan - independent researcher
10.03.2016
"Give me a place to stand on, and I will move the Earth." - Archimedes
Abstract
In following research paper, the new possible solution for the real physical conduction mechanism, at first,
in monolayer Graphene, is proposed. A general model how electrons travel and transport energy through
these conductors will be based on benzene molecule, which molecule with six carbon atoms in the ring like
structure exist. After that, the structure of benzene molecule with the Graphene will be related, the
fascinating two-dimensional material which flat network of interconnected benzene rings in hexagonal
honeycomb lattice are arranged, from single to many atomic layers. The new bond structure, for this
unusual bond structure in Graphene, is proposed. Also a new mechanism for the unclear mechanism as;
how electrons always travels with same speed in Graphene, independent of applied voltage, will be
presented.
Second, the new mechanism presented here, has also great potential and capability for solving the essential
conducting mechanism in similar unusual phenomenon, known as superconductivity. This mechanism can
be especially efficient in the superconducting materials as intercalated Bilayer Graphene, where charge-
density waves and bipolar supercurrent, were for the first time observed.
For the both of this mechanisms the most important thing is the “stand on” point, round which atoms or
molecules can frilly rotate.
Introduction
To identify or recognize the real physical conduction mechanism in specific materials, especially in
graphene and similar like compounds, and above all in superconducting materials, remains one of the holy
grails in physics.
It is well known, that electrical current, as response to an electric field is usually explained by flow of free
electrons through materials, However, when different conduction mechanisms in compounds was
discovered, as in conducting polymers, semiconductors and superconducting materials, it became clear that
traditional electron’s mechanism and theories are not satisfactory to explain how current through
materials is carried.
So the new discoveries as pseudo gaps, charge density waves, electrons and charge orders, stripes, massless
electrons and many others, as elements of conducting mechanism and superconductivity, became a part of
many research efforts and in proper way explained. However, some of them need better explanation and
integration in the new conducting mechanism and associated theories.
Discoveries, which are with topic correlated
1825 - For the first time the benzene molecule is isolated and identified (Michael Faraday)
1865 – Proposition for benzene structure as ring of six carbon atoms with cyclic structure (Friedrich
August Kekule)
1911 – Discovery of superconductivity (Heike Kamerlingh Onnes)
1929 – Cyclic nature of benzene confirmed (Kathleen Lonsdale)
1965 – Graphite-Potassium (C8K), the first superconducting graphite intercalation compound reported
(Hannay, N. B. et al.)
1986 - Discovery of high temperature superconductivity in cuprates as ceramic materials (Georg Bednorz
and Alex Muller)
2003 – For the first time Graphene is measurable produced and isolated (Andre Geim and Konstantin
Novoselov)
2006- Discovery of high-temperature superconductivity in iron-based compounds (Kamihara, Yoichi;
Hiramatsu, Hidenori; Hirano, Masahiro; Kawamura, Ryuto; Yanagi, Hiroshi; Kamiya, Toshio and
Hosono, Hideo)
Note: 2001 – Proposal for the new covalent three electrons bond connection, with real space distribution
between all six Carbon atoms in Benzene ring (bond order 1,5), instead alternating double bond with four
electrons (bond order 2) and single bonds with two electrons (bond order1) Universal Periodic System -
preposition from Aco Z. Muradjan
From Benzene to Graphene
Because the structure of benzene as cyclic ring is very significant for resolving the unique conduction
mechanism in some specific compounds, as mono layer or Bilayer graphene, at first will be in details
explained the preposition for space alignments of the atoms and electrons in Benzene ring.
Benzene (C6H6) is one of the most intriguing molecules. The structure of benzene was for many years a
problem for chemists, as problem of real nature of bonds in molecule. The real structure of this molecule is
enigma until present days.
Known facts for Benzene C6H6 molecule
Benzene is a perfectly regular hexagon.
Benzene is aromatic organic hydrocarbon and is very stable molecule
Benzene is also a planar molecule (all the atoms lie in one plane)
All bond angles = 120 degrees
All C-C bonds are exactly the same with same length dCC= 140 .10-12 [m] or 140 [pm]
All C-H bonds are equivalent dCH = 110 [pm]
All angles in C atom are tetrahedral 109o28’
Carbon atom has four valent electrons while Hydrogen has one valent electron
In the molecule, there are 30 electrons (24 from Carbon atoms and 6 from Hydrogen atoms)
As effort to satisfy this mixture of facts, or most of them, in a unified way, especially how a cyclic ring
molecule with molecular formula (C6H6) could be built of carbons atoms which make four bonds, Kekule in
1865, for the first time, propose the bonds structure in Benzene ring with three double bonds and three
single bonds. This arrangement is also known as conjugated double bonds. Some of today used structural
diagrams for Benzene are shown below:
Despite many criticisms, this model was widely accepted. This model is still in use today, with several new
added concepts and rules as rapid vibration between single and double bonds, resonance, resonance
hybrid, delocalization of the electrons, Huckel’s rule and so on.
Besides achievement of these new concepts, it must be noticed that structural formulas of chemical
compounds, especially for Benzene molecule, are convenient representation and do not necessarily describe
reality or real physical structure.
Explanations for most of the facts for Benzene are still doubtful and open for discussion. As example, all
the bonds in Benzene ring are the same – confirmed by using x-ray diffraction d = 140 [pm] and lay
between single bond length 154 [pm] and double bond length 134 [pm]. Until today, there is no acceptable
explanation. Also the two fundamental concepts in organic chemistry as aromaticity (Huckel cyclic planar
arrangement) and chirality (Mobius half twist conjugated system), applied on benzene molecule, are still
far from satisfactory explanation.
The real physical structure of Benzene is still a challenge for chemists and physicists.
New proposition for real structure of Benzene C6H6 molecule
The most challenging problem in the direction of understanding the real structure of Benzene molecule,
with all known facts, is to define location of all electrons in space round Carbon and Hydrogen atoms in
cyclic ring, using chemical covalent bonding as starting position.
According present knowledge, covalent bonding happens when atoms are hold together, sharing pairs of
electrons. There are three forms of covalent bonding - single, double and triple.
Single bonding is the condition of sharing one pair or two electrons by atoms. Double bonding is the
condition when atoms share two pairs or four electrons and triple is when atoms share three pairs or six
electrons. This bonding of valent Carbon’s electrons is shown on the below example with dots or dashes.
As starting point, for the new preposition for Benzene structure, the Hydrogen molecule (H2) is present as
the simplest single bonding molecule.
Each Hydrogen atom has one proton and one electron. Therefore, in Hydrogen molecule, each Hydrogen
nucleus attracts both electrons and repels other proton. The reason for covalent bonding is the electrostatic
attraction between positive nucleus and negative electrons and repulsion between protons and between
electrons.
This is still the only explanation. Until today, there are no other known forces involved in this covalent
bonding connection. The theory of exchanging the electrons between atoms, like valley ball players with
ball, has no any real basis.
The bonding dispositions of positive nucleuses and negative electrons, when bond lengths are in static or
dynamic equilibrium, are present on the picture below.
Therefore, when the single bond between atoms presented with dashes in structural formula, the places for
shared electrons are not between nucleuses but at their sides. Same situation is for double and triple
bonding structural formulas.
For example, electron disposition for carbon – carbon covalent bond connections, which are with different
bond order, presented on next pictures, in most simplified form.
Electrons between Carbon atoms repulse each other’s while Carbon atoms and electrons between them
attract each others, so all differently charged atoms and electrons in balanced dynamic condition coexist.
Having this on mind, to satisfy all basic facts for bonding structure in Benzene molecule, the next
preposition was invented and proposed on internet in 2001; Universal Periodic System (AM), which
preposition was presented with space electron distribution.
Beside the three known covalent bond connection - single double and triple, the fourth covalent bonding
type exist. This is the bond connection with three electrons or single and a half bond connection.
This preposition, beside appear very strange, is more reliable than the existing two protons with one
electron (H2+) bond connection.
In 1921 J.J. Thomson suggest similar preposition with three-electron bond connection, as solution for
electronic bonding structure in benzene molecule, image below.
This preposition was similar to Thiele’s partial valence preposition but this proposal became unpopular
and forgotten since electrons as point particles were treated. In addition, it was hard to imagine at such
time and same as today, that group of three electrons might have the proper bonding space distribution.
Besides many different quantum mechanical interpretations for electron existence, electrons, without any
uncertainties, are real particles, with very well defined physical and mechanical properties.
In some cases when electron loses their kinetic energy, with numerous multiple collisions, the velocity
decrease and they became slow electrons. For illustration, conducting DC or AC electrons in metals are
examples for such slow electrons motion. In such cases, they act as point particles with very well defined
space distribution, same as protons, because they have similar field strength.
Today, the quantum mechanics with the formulation of the Schrödinger wave equation gives more formal
description of energetic properties of electrons and very little about real electron’s space distribution.
The field distributions between positive and negative particles in new proposed three electrons bonding
structure are also balanced, same as in double bond connection. This type of bond connection is very stable
in cyclic molecules, which molecules are with proper angles between atoms and reveal similar saturated
character as they are all with single bond connection.
Cyclic molecules with theirs specific strong circular structure, serves as backbone for the electrons, with
proper space balanced distribution, in circular ring to be positioned.
Applied on Benzene ring, this three electrons covalent bonding will look like next image:
Benzene C6H6
Similar structure has Borazine, isoelectronic and isostructural with benzene, where Carbon’s neighbors,
Boron and Nitrogen, replace Carbon atoms. Borazine has aromatic smell too.
In addition, s- triazine, aromatic molecule with Carbon and Nitrogen ring atoms.
Carbon atoms in Benzene molecule have local tetrahedral symmetry and usually have tetrahedral
orientations of his four electrons. The analysis of positive and negative fields in Benzene molecule will show
that moving of any electrons from his position in molecule is almost impossible without external energy
disturbance. They give the impression of being like frozen electrons. All atoms and electrons exist round
their mutual dynamic balanced position. The repulsion-attraction distances between all thirty electrons
from Carbon and Hydrogen atoms, in benzene molecule, are perfectly balanced. The electrons in this
three electrons bond structure are real electrons, which exist above and under benzene planar ring with six
electrons each, left or right from carbon nucleus.
The existence of unhybridized orthogonal overlapped orbital’s, or delocalized system which form
continuous loop of parallel orbitals, over and under ring, is hard to believe that signify reality because
there is no enough electrons for doing such cyclic systems.
Twelve electrons (from thirty) needed for sigma bond between Carbon and Hydrogen atoms, twelve
electrons needed for sigma bond between six carbon atoms. The rest six electrons are not enough for
double parallel cyclic clouds under and over benzene ring.
With the new proposed structural formula, all basic facts for structure of Benzene molecule will be or are
satisfied.
Present in 3d space, the location of all valent-bonding electrons in region round Carbon and Hydrogen
atoms in cyclic ring, with its space tetrahedral structure disposition, as next images will look like.
Conduction mechanism in Graphene and other similar compounds
Now the question that arises from proposal in this paper in next appearance can be formulated:
How these new tree electrons covalent boding structure in Benzene molecule, presented here, can help this
unusual conduction mechanism in graphene and others similar compounds, as real process to be
recognized?
The prospective promising answer to this question is as follow:
The essential concept for understanding this unique type of conduction mechanism in Graphene, and similar
conduction compounds is connected with well known conformation mechanism in compounds correlated with
the tetrahedral space structure disposition of valent electrons, which in honeycomb lattice structures, or in
open and closed chains structures can be found.
Conformation mechanism is different geometric arrangement of atoms in space that result from rotation
about single bond. The most basic example for this mechanism is conformation of Ethane CH3-CH3.
Because the carbons atoms are connect by single bonds, the bond is able to rotate freely, allowing various
conformations to exist. Atoms and bonds remain unchanged on the molecule; the only difference is the
position and angles in which certain parts of molecule are in this confirmation process rotated. There are
two main positions in molecule, staggered and eclipsed projection. Conformations differ in the energy. The
staggered conformation has a lower energy (12,5 kJ/mol) than the eclipsed conformation.
Benzene molecule and conformation mechanism
In benzene molecule, such rotation is possible round every single bond connection between Hydrogen and
Carbon atoms and in a single and half bond connections between Carbon atoms.
First the single bond connection exist between all six Carbon and Hydrogen atoms so all three other
tetrahedral valent electrons from Carbon atoms can rotate round this H–C bond connection inside the
ring.
If the benzene molecule in a magnetic field will be placed than the upper and the lower π electrons are
enforced to circulate inside the ring in a “ring current”.
Second, it’s the single bond (sigma electron) in three electrons bond connection between Carbon atoms in
benzene ring. Such rotation is possible because benzene ring serve as anchor for all possible rotations for
such or similar cyclic molecules. The rotation like this is responsible for well-known electrophylic aromatic
substitution mechanism in benzene molecule. Nonaromatic molecules, which contain carbon - carbon
double bonds, prefer electrophylic addition reactions, while aromatic molecules support electrophylic
aromatic substitution.
This Electrophylic aromatic substitution mechanism in benzene molecule here in details will be presented
because this will show that such special rotation mechanism is possible also in bigger molecules, as
graphene or in open or closed polymers chain structures, as Polyacetylene and others conjugated
conducting polymers.
This mechanism is responsible for energy or electrons transport through cyclic rings or chains.
Notes for Electrophylic aromatic substitution image are present below it:
Sigma electron lies in C1-C4 plane, which is the cross section of whole benzene ring. For better observation
σ (sigma) electrons are little bit twisted (rotated) from C1-C4 cross section line.
In this example, rotation is round C1 sigma electron, but all Hydrogen atoms in benzene molecule, can be
with this same mechanism also easily substituted.
Rotation start after electrophyle attack upper or lower electron and the ring has no more aromatic
structure, which ring is not during this rotation progression destroyed.
After finishing the rotation cycle, the benzene ring will get aromatic structure again, only difference is that
the three tetrahedral valent electrons from Carbon atom C1 are for 120o rotated and that Hydrogen atom
is with electrophyle substituted.
In bigger molecules, which contain benzene rings, there are no Hydrogen atoms only Carbon atoms with
electrons between them. The electrophylic aromatic substitution mechanism in such molecules has different
significance which implication will be present in graphene, a single-atom-thick sheet of graphite.
GRAPHENE
Graphene is a single flat atomic layer made of tightly packed interconnected benzene rings bonded together
in a repeating hexagonal honeycomb lattices structure. This two dimensional material has many
extraordinary characteristic with very unique electronic properties.
Some of them are:
Very high graphene’s carrier mobility with relativistic effects detected at velocity much slower than
speed of the light.
The carriers responsible for charge conducting in graphene act as if they are massless, with velocity
around 1. 106 m/s2, and they behave like photons in free space.
Graphene as good conductor respond very quickly to an applied voltage but energy transport
through graphene sheet do not depends on applied potential.
The energy spectrum of Graphene is symmetric between positively and negatively charged carriers.
Beside graphene has small or even zero energy gaps between conduction and valence bands
graphene’s unique band structure forces charge carriers always to travel with same speed no
matter what is happening with material.
Charge carriers in Graphene can travel ballistic in zig-zag direction, for many microns, without
colliding with any impurities.
The flow control of the electrons current through graphene, with on–off switch, is not with
satisfactory certainty realized yet.
From all of facts shown above is evident that these radically different behaviours of electrons in graphene
are strongly connected with graphene’s honeycomb lattice structure, or with other words, with unique
properties of benzene molecule as basic building blocks.
The new structure of benzene, which is with three-electron bond connection between all six Carbon atoms
here presented, differs from hypothetical Kekule structure with alternating double and single bonds.
This bond disposition is connected with aromaticity, a well known property of benzene like cyclic rings.
Therefore, if in bigger flat molecules as Coronene and Graphene this new benzene structure will be
applied, the bond disposition of valent electrons will be redistributed over molecule or graphene sheet in
different ways. For Graphene mono layer sheet as big no aromatic molecule, every benzene ring, without
exception, has only four connection bonds with three electrons, and two bond connections with two
electrons, or total sixteen bonding electrons in every benzene ring.
Coronene aromaticity:
The graphene most basic primitive cell has only four benzene rings, same as the carbon basic structure of
Pyrene (C16H10).
But Coronene (C24H12) is the smallest graphene look like sheet. Presented with the new three- electron bond
connection Coronene has three basic dispositions of cyclic aromatic rings in molecule. Aromaticity
primarily depends on number of electrons in carbon – carbon bond connection and their orientation in
cyclic ring. In every bond aromatic bond connection three electrons must exist. With this new statement or
rule, which follows new three electron bond connection, is evident that there are no enough electrons for
total Coronene aromaticity.
Similar limitations and rules for graphene are also relevant.
Coronene different cyclic bond orientation or three-electron bond dispositions, with different
aromaticity, on next picture are presented.
Graphene aromaticity:
Graphene has no aromatic system as globally delocalized π system or locally aromatic systems, but has
different chemical bonding structure and different disposition of three electron bonding connections. Such
electron bond disposition is very important for some of extraordinary graphene’s properties.
On next images two of the most possible sigma electrons bond dispositions are presented:
Beside these two most common bond dispositions, the global hexagonal circular aromaticity can be created
also in grapheme. This will happen if the strong perpendicular magnetic field on graphene sheet will be
applied, whose centre is same as the applied magnetic field centre. The valleys of sigma bonds between
aromatic circular rings are also with hexagonal circular shape. In such case different graphene properties
or effects can be expected or observed. In a static magnetic field an electrons pass through graphene sheet
in a different circular trajectory, known as cyclotron orbits. This is because the carbon atoms, from
different hexagonal circular rings, with different circular ring radiuses coexist and because of that, with
different velocity will be forced to go around.
Conduction mechanism in graphene:
When a power or external energy potential is get to drive a current through a piece of material, as a single-
atom-thick sheet of graphene, then is a correlated electron’s actions achieved. An interrelated electrons’
behavior, as the action of every electron, causes a cascade that affects all of its neighbors.
The start rotation of the first Carbon atom in Graphene, almost immediately, cause rotation of the chains
of Carbon atoms (like million gears in chain) through honeycomb rings or trough crystal lattice, and
transfer charge or energy (electrons with high potential energy level) in linear or zig-zag direction.
The electrons move through material in tiny ribbons of graphene, coherently and without collisions, or like
charge density waves, without loss of energy.
Linear or zig-zag electron’s direction in grapheme
The first key factor for such type of conductance is chain of molecules and second is sigma (connection with
two electrons) bond connection, which connection allows free rotation of tetrahedral located valent
electrons. This mechanism was previously as conformation mechanism presented. The red lines on above
images present such sigma bond connections. Energy transport or charge transport through chain of
carbon atoms is with hip-hop electron mechanism from Carbon atom to Carbon atom generated.
Graphene has these two key factors on room temperature.
On the other hand, here, very strange behavior occurs. As response to electronics’ negative electric field,
electron’s rotation from one Carbon atom in one direction will produce the electrons from next Carbon
atom in the chain, to rotate in opposite direction.
Now the new important question is; how charge or energy is throughout monolayer sheet of graphene
transferred or transported, which with two different sub lattice’s rotation directions exist?
The energy transport or charge transport, with hip hop electron mechanism, from Carbon atom
to Carbon atom, besides the electrons rotate in different directions, only in one direction, through
the chain, will be transmitted. This mechanism is presented on picture below.
So in Graphene sheet, depends of electron’s rotation direction, two sub lattices structures exist. First is (K)
lattice sub structure, with clockwise - or up rotation, and second (K’) lattice sub structure, with anti
clockwise – or down rotation direction.
The rotation velocities of valent electrons define the velocity of charge or energy transport through chain,
which velocity does not depend of its energy. This unusual and strange anomalous behaviour can be found
only in compounds with chain of atoms and also with sigma bond connection, which allows free rotation
of valent electrons, always tetrahedral located in space. Such behaviour can be observed in solid, as
graphene - two dimensional materials or in some special bulk three dimensional materials.
This energy or charge transport through chain is similar to water transport, hand by hand, in bucket
brigade, to put out the fire. Peoples do not move from their place (they can rotate round their places left or
right) but buckets with water are moving through the line. Every man in line accepts the bucket form man
before them, transfers through hands and gave the bucket to the next man in line. Bucket with water pass
from person to person, in sequence, in such way that the line balances itself or is self-organizing. Peoples
are Carbon atoms, bucket - electrons and water - energy (photons, phonons or solitons).
This mechanism is very well presented on next two images of graphene sheet. On these images, the (K)
lattice’s sub structures with up rotation and K’ lattice’s sub structures with down rotation, are very well
presented and can be easily observed. Also are presented the valleys of sigma bonds between (K) and (K’)
Carbon atoms, round which the Carbon’s tetrahedral valent electrons rotate.
Left image is original while right image is zoomed small section of the original image. Graphene is one of
the easiest materials for making images with “scanning tunnelling microscope”, or with “atomic force
microscope” where the actual atoms position can be very well observed or determined. This original image
is from image-gallery from the Institut fur Physik, the University of Augsburg, Germany, made with AFM in
2004. The image size is 2x2 nm2.
Image credit: http://www.physik.uni-augsburg.de/exp6/imagegallery/afmimages/afm-image-graphite.jpg
Or: http://www.sciencebrainwaves.com/wp-content/uploads/2010/03/afm-image-graphite1.jpg
From all of what is present above is evident that the structure of graphene’s honeycomb lattice is very
important for most of graphene’s extraordinary properties, and serves as base, for such properties to be
achieved.
Such lattice structure and electrons bond dispositions enable the basic mechanism for great graphene
conductivity to appear. This is the conformation mechanism. This process or mechanism need very small
amount of potential (energy) for activation.
For example, the total rotational energy barrier for ethane about C – C bond, from staggered to eclipsed
conformation, is less than 2.8 kcal/mol, or 0.12 eV. For graphene sheet, this rotational energy barrier must
be even smaller.
When this rotation process starts, there is no easy way to stop such rotation, except defects in material.
With this process or mechanism, charge carriers in graphene can travel ballistic for many microns. Also is
evident that the energy transport through graphene sheet, in wide range of applied potential, depends only
on rotation velocity of tetrahedral valent electrons. Because of that, electrons propagate similar to waves,
with sinusoidal pattern, or like ripples on water. This fluctuating order last very short time and because of
that, the electrons look like they are massless. The only limit for the rotation velocity of tetrahedral valent
electrons is number of added impurities (electrons) and type of substrate, on which the graphene
monolayer is set down.
Superconductivity in intercalated Bilayer Graphene - C6CaC6
The superconductivity, beside great interest and many research efforts, has not been still, in monolayer
graphene achieved.
But, the graphene intercalated compounds (GICs), as superconducting compounds, have recently received
much attention because of theirs very interesting physical properties, especially because of high –
superconducting critical temperature Tc (11,5 K) with Ca, as intercalated compound.
Besides great research hard work there are still big dilemmas about precise mechanism of
superconductivity in intercalated compound CaC6. Besides several other proposals, the general picture of
conventional phonon - driven superconductivity, which as general concept is accepted, need more evidence.
This because new observable facts are in intercalated Bilayer Graphene discovered, as charge density
waves and bipolar supercurrent.
Why such behavior was only in Bilayer graphene noticed, while in monolayer graphene was not this
behavior, until now observed?
The answer lies in different electron numbers in every bond connection and different electrons bond
disposition in graphene’s basic building block – benzene ring.
In mono layer Graphene, in every so told simple benzene ring, as basic building blocks, electrons are
located in such way that always there are four bond connections with three bonding electrons, while rest
two bond connections are with two electrons, or total it must be sixteen electrons in every ring.
But in Bilayer Graphene, where between two graphene sheet s, atoms or ions from different compounds
are intercalated, the number of electrons and electron’s bond disposition, in simple benzene rings, differ
from that in mono layer graphene.
In every benzene ring , where below ring Calcium (Ca) atoms are located, it must be five bond connections
with three electrons and only one bond connection with two electrons, or total there are seventeen (17)
electrons. This is the region where superconducting current is flowing in two separated stripes.
In rest benzene rings, outside stripes, which are without Ca atoms, there are benzene rings with three bond
connections, which are with three electrons and three bond connections with two electrons, or total there
are fifteen (15) electrons in every such benzene ring. This is the region with no conductivity.
There are also region of benzene rings, between conducting bands, where sigma bond connection with two
electrons exist, and where benzene rings have four bond connections with three electrons and two bond
connection with two electrons, or total sixteen (16) electrons.
Round this sigma bond’s connection, electrons will line up coherently, in two bands, when the critical
superconducting temperature is get. All of these different electron dispositions are present on next image.
Arrangement of valent electrons in Bilayer Graphene
Such different rearrangement of valent electrons in Bilayer graphene is consequence of compound’s
properties, which are as sandwich, between two graphene sheets intercalated. When sandwich compounds
are formed with intercalated atoms or ions, as in Ferrocene or other Metallocenes, minimum five bonding
electrons, from upper ring and five bonding electrons from down ring must be involved. In sandwich
compounds, intercalated compounds always in +2 oxidation states are present, because the bond
connection is always between +2 positive intercalated ion and upper and down negative electron rings.
Ferrocene or other similar Metallocenes
So, when Calcium atoms are intercalated between graphene sheets they are always +2 oxidation states. To
make bond connection with existing up and down grapheme sheets, Calcium (Ca) atoms (ions) need five
bonding electrons from both benzene rings round Calcium atom (up and down benzene rings). However,
both benzene rings, before injection of Calcium atoms, as is said before, have only four ring electrons each.
Therefore, to make bond connection, Calcium atoms attract, or borrow electrons from regions round them,
to realize the proper sandwich five-bond connections.
Similar sandwich complexes with five electrons, Calcium (II) coordinate with Cyclopentadienyl ligands.
In such case, in intercalated Bilayer graphene with Calcium atoms exist regions rich with electrons (17 el)
and regions poor with electrons (15 el). Therefore, in every rich benzene ring, above Calcium, there is an
extra electron taken from nearest benzene ring, where one electron is missing.
This new properties can be very well visualized one next image where supercurrent exists in two parallel
stripes, which are with two bands each separated with regions without superconductivity.
The existence of this sigma bond will enable the chains of the atoms to be interconnected through upper
graphene sheet and revolve free round these sigma bond connections; image above with – blue curly
arrows.
Prospective free rotation is possible also round sigma electron in three electron bond connections, in
benzene rings, where Calcium atoms are located. Because of unequal layout of five-three bonding
connections in benzene rings with calcium atom, there are little bit movement of Calcium atoms below
surface, from benzene ring’s centre toward three successive–three bonding connection.
Round these bond connections which are located in two parallel conducting bands, in superconducting
state, tetrahedral valent electrons are aligned coherently and in a phase, in such way that produce field,
which with (STM), or other instruments, can be observed.
This unusual behavior created in intercalated Bilayer Graphene, look like waves on graphene surface. On
image below, Yellow regions, with red zig-zag line, present a disposition of single (sigma) bond connection
between atoms where electron from Carbon atoms can freely rotate.
Charge conducting waves in intercalated Bilayer Graphene
These doubled conducting stripes are from region with no conductivity separated. In every stripe, there are
electrons with right or up rotation, and electrons with left or down rotation. Because of that, every second
electron, in zig-zag line, can be as ripples on graphene surface visualized, with scanning tunneling
microscope (STM).
Researches from London Centre for nanotechnology (LCN) have discovered, for the first time, this
electronic stripes called ‘charge density waves’, on the surface of intercalated graphene sheets with the
calcium (CaC6), using an instrument known as scanning tunneling microscope (STM) and spectroscopy
(STS) at atomic scale. The report for this discovery was publishing in Nature Communications, 29th
November 2011. They find that distance between stripes has 1.125 nm.
This mechanism is very well presented on image below, which is as result from their research work, and
made by: K.C. Rahnejat, C.A. Howard, N.E. Shuttleworth, S.R. Schofield, K. Iwaya, C.F. Hirjibehedin, Ch. Renner, G.
Aeppli, M. Ellerby. Charge density waves in the graphene sheets of the superconductor CaC6.Nature
Communications, 2011; 2: 558 DOI: 10.1038/ncomms1574.
Image: Charge density waves on the surface of the intercalated graphene sheets (CaC6)
Credit: http://spie.org/Images/Graphics/Newsroom/Imported-2012/004112/004112_10_fig1.jpg
So from all of that, what is sad before, is evident that there is no need always charge transfer from
intercalated compounds, for Bilayer graphene sheet to attain superconductivity. It is evident that doped or
intercalated compounds, in this case, only serve as instrument to rearrange the electrons in graphene
sheets. In some different superconducting compounds, they serve as strong support, which enable Carbon
or others atoms without resistance to go around.
Similar results, as superconductivity in Bilayer graphene, is get when the intercalated compound Calcium
is interchanged with similar metallic compound, with +2 oxidation state, as Ytterbium.
Conclusion:
Graphene with its extraordinary physical and mechanical properties is very important material. Because
of that especially is important to understand very well all the basic principles and phenomenon closely
connected with conductivity in monolayer graphene or superconductivity in Bilayer graphene.
Additionally is very significant to be recognized the essential mechanism for modifying and controlling the
graphene’s electronic parameters and properties.
Furthermore very important is next question: Is the mechanism for graphene conductivity and
superconductivity, presented here, valid as base, to find successful theory for compounds with similar
phenomenon’s, like high-temperature superconductivity materials, as cuprates, iron based and other
ceramic superconductors?
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