1. science
2. physics

Graphene - “most two-dimensional” system imaginable
A suspended sheet of pure graphene – a plane layer of C atoms bonded together in a
honeycomb lattice – is the “most two-dimensional” system imaginable.
A.J. Leggett
Such sheets have long been known to exist in
disguised forms – in graphite (many graphene
sheets stacked on top of one another), C
nanotubes (a graphene sheet rolled into a
cylinder) and fullerenes (buckyballs), which are
small areas of a graphene sheet sewn together
to form an approximately spherical surface.
Until 2004, it was generally believed
(a) that an extended graphene sheet
would not be stable against the effects of
thermal and other fluctuations, and
(b) that even if they were stable, it
would be impossible to isolate them so that
their properties could be systematically studied.
Modified from: http://www.ewels.info/img/science/graphite © Dr. Chris Ewels, Inst. of Materials
In 2004, André Geim et al. (University of Manchester, UK) demonstrated that both
these beliefs were false: they created single graphene sheets by peeling them off a
graphite substrate using scotch tape, and characterized them as indeed single-sheet
by simple optical microscopy on top of a SiO2 substrate. Now it is done mostly by
Raman spectroscopy.
Subsequently it was found that small graphene sheets do not need to rest on
substrates but can be freely suspended from a scaffolding; furthermore, bilayer and
multilayer sheets can be prepared and characterized.
As a result of these developments, the number of papers on graphene published in
the last few years exceeds 3000.
The Nobel Prize in Physics
2010
Andre Geim
Konstantin
Novoselov
Graphene is a very promising material both for applications and
fundamental research.
The trick: Finding the Graphene
• Using correct
substrate
• And correct light
frequency
• Interference effect
makes monolayers
show up in ordinary
optical microscope
Graphene
SiO
Blake et al (2007) arXiv:0705.0259
Si
Image sizes are 25x25 m. Top and bottom panels show the same flakes as in (a)
and (c), respectively, but illuminated through various narrow bandpass filters with a
bandwidth of ~10 nm.
What is graphene?
• “Imagine a piece of paper but a million times thinner.
•
•
•
•
This is how thick graphene is.
Imagine a material stronger than diamond. This is how
strong graphene is [in the plane].
Imagine a material more conducting than copper. This is
how conductive graphene is.
Imagine a machine that can test the same physics that
scientists test in, say, CERN, but small enough to stand
on top of your table. Graphene allows this to happen.
Having such a material in hand, one can easily think of
many useful things that can eventually come out. As
concerns new physics, no one doubts about it already...''
From a recently interview with Andre Geim.
Carbon is the materia prima for life and the basis of all organic chemistry. Because of the
flexibility of its bonding, carbon-based systems show an unlimited number of different
structures with an equally large variety of physical properties.
Graphene is a
honeycomb lattice
of carbon atoms.
Carbon nanotubes
are rolled-up
cylinders of
graphene
Graphite can be
viewed as a stack
of graphene
layers.
Fullerenes C60 are
molecules
consisting of
wrapped graphene
by the introduction
of pentagons on
the hexagonal
lattice.
From Castro Neto et al, 2009
Science of graphene
Experimental evidence of an unusual
quantum Hall effect was reported in
September 2005 by two different
groups, the Manchester group led by
Andre Geim and a ColumbiaPrinceton collaboration led by Philip
Kim and Horst Stormer [1,2]. In 2004
Geim’s group proved the possibility
of an electric field effect in graphene,
i.e. the possibility to control the
carrier density in the graphene sheet
by simple application of a gate
voltage [3].
[1] K. S. Novoselov, A. K. Geim, S. V. Morosov, D. Jiang,
M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A.
Firsov, Nature 438, 197 (2005).
[2] Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature
438, 201 (2005).
[3] K. S. Novoselov, A. K. Geim, S. V. Morosov, D. Jiang, Y.
Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov,
Science 306, 666 (2004).
Classical and quantum mechanics of 2DEG
Classical motion:
Lorentz force:
Perpendicular to the velocity!
Newtonian equation of motion:
m*v2/rc = evB; v=eBrc/m*; =v/2rc; c=2=eB/m*
Cyclotron orbit
Cyclotron frequency,
Cyclotron radius,
In classical mechanics, any size of the orbit is allowed.
Magnetotransport in 2DEG
Bohr-Sommerfeld quantization rule
The number of wavelength along
the trajectory must be integer.
Only discrete values of the
trajectory radius are allowed
Energy spectrum:
ωcτ ≥ 1
Landau levels
Wave functions are smeared around
classical orbits with
rn = lB (n+1)1/2;
lB= (ħ/cm)1/2
lB is called the magnetic length. It is radius
of classical electron orbit for n = 0.
  v/r; r v/; mv2/2= ħc(n+1/2); vn0 = (ħc/m)1/2; lB= rn0 = (ħ/cm)1/2
Magnetotransport in 2DEG
Science of graphene
‘Quantum electrodynamics (resulting from the merger of quantum mechanics and
relativity theory) has provided a clear understanding of phenomena ranging from
particle physics to cosmology and from astrophysics to quantum chemistry. The ideas
underlying quantum electrodynamics also influence the theory of condensed matter,
but quantum relativistic effects are usually minute in the known experimental systems
that can be described accurately by the non-relativistic Schrödinger equation. Here
we report an experimental study of a condensed-matter system (graphene, a single
atomic layer of carbon) in which electron transport is essentially governed by Dirac’s
(relativistic) equation. The charge carriers in graphene mimic relativistic particles with
zero rest mass and have an effective ‘speed of light’ c* < 106 m/s. Our study reveals a
variety of unusual phenomena that are characteristic of two-dimensional Dirac
fermions. In particular we have observed the following: first, graphene’s conductivity
never falls below a minimum value corresponding to the quantum unit of
conductance, even when concentrations of charge carriers tend to zero; second, the
integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer
filling factors; and third, the cyclotron mass mc of massless carriers in graphene is
described by E = mcc*2. This two-dimensional system is not only interesting in itself
but also allows access to the subtle and rich physics of quantum electrodynamics in a
bench-top experiment.’
[1] K. S. Novoselov, A. K. Geim, S. V. Morosov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov,
Nature 438, 197 (2005).
Properties of carbon
 Constituent of graphene
 6th element of the periodic table
 Built from 6 protons, A neutrons, and 6 electrons
 A = 6 and 7 yield the stable isotopes 12C and 13C
 A = 8 characterises the radioactive isotope 14C.
 12C (99% of all carbon atoms) has nuclear spin I = 0
 13C (1% of all carbon atoms) has nuclear spin I = 1/2
 14C (10-12 of all carbon atoms, -decays into nitrogen 14N, half-life of 5 700 years,
used for historical dating (radiocarbon), allows to date biological activity up to an
age 80 000 years.
 Elementary building block of all organic molecules and, therefore, responsible for
life on Earth.
In the presence of other atoms, such as H, O,
or other C atoms, it is favourable to excite
one electron from the 2s to the third 2p
orbital, in order to form covalent bonds with
the other atoms. The gain in energy from the
covalent bond is larger than the 4 eV
invested in the electronic excitation.
Crystal structure of carbon materials: sp1 hybridisation
In the sp1 hybridisation, the |2s state mixes with one of the 2p orbitals. A state with equal
weight from both original states, is obtained by the symmetric and anti-symmetric
combinations:
Example: Acetylene molecule
(H–C≡C–H)
(a) Schematic view of the
sp1
hybridisation. The figure shows the
electronic density of the |2s and |2px
orbitals and that of the hybridised
ones. (b) Acetylene molecule (H–
C≡C–H). The propeller-like 2py and
2pz orbitals of the two C atoms
strengthen the covalent σ bond by
forming two π bonds (not shown).
Crystal structure of carbon materials: sp2 hybridisation
In the sp2 hybridisation, the |2s state mixes with two 2p orbitals. The three quantummechanical states are given by:
Example: Benzene molecule
(H–C≡C–H)
(a) Schematic view of the sp2 hybridisation. The orbitals form angles of 120o. (b) Benzene
molecule (C6H6). The 6 carbon atoms are situated at the corners of a hexagon and form
covalent bonds with the H atoms. In addition to the 6 covalent σ bonds between the C
atoms, there are three π bonds indicated by the doubled line. (c) The quantum-mechanical
ground state of the benzene ring is a superposition of the two configurations which differ by
the position of the π bonds. The π electrons are, thus, delocalised over the ring. (d)
Graphene may be viewed as a tiling of benzene hexagons, where the H atoms are replaced
by C atoms of neighbouring hexagons and where the π electrons are delocalised over the
whole structure.
Crystal structure of carbon materials: sp3 hybridisation
In the sp3 hybridisation, the |2s state mixes with three 2p orbitals. Four club-like orbitals
mark a tetrahedron. The orbitals form angles of 109.5o degrees.
Example: Methane (CH4)
and diamond
A chemical example of sp3 hybridisation is
methane (CH4), where the four hybridised
orbitals form covalent bonds with the 1s
hydrogen atoms. In condensed matter
physics, the 2p3 hybridisation is at the
origin of the formation of diamonds, when
liquid carbon condenses under high
pressure. The diamond lattice consists of
two interpenetrating face-center-cubic (fcc)
lattices, with a lattice spacing of 0.357 nm
Crystal structure of carbon materials
The electronic structure of an isolated C atom is (1s)2(2s)2(2p)2; in a solid-state
environment the 1s electrons remain more or less inert, but the 2s and 2p electrons
hybridize.
One possible result is four sp3 orbitals, which naturally tend to establish a
tetrahedral bonding pattern that soaks up all the valence electrons: this is
precisely what happens in the best known solid form of C, namely
diamond, which is a very good insulator (band gap about 5 eV).
An alternative possibility is to form three sp2 orbitals, leaving over a more or less free
p-orbitals that form delocalized π-bonds. In that case the natural tendency is for the
sp2 orbitals to arrange themselves in a plane at 120o angles, and the lattice thus
formed is the honeycomb lattice.
Exfoliated graphene
Exfoliation includes several cycles of scotch-tape peeling from graphite with final
gluing to the SiO2 substrate treated by a mix of hydrochloric acid and hydrogen
peroxide to accept better the graphene sheets from the scotch-tape.
AFM
TEM
The 300 nm thick SiO2 substrate, turns out to yield an optimal contrast such
that one may, by optical means, identify mono-layer graphene sheets with a
high probability. AFM imaging and TEM are definite techniques for identifying
graphene.
Epitaxial graphene
Epitaxial growth technique consists of exposing hexagonal SiC crystal to
temperatures of about 1300o C in order to evaporate the less tightly bound Si
atoms from the surface. The remaining carbon atoms on the surface form a
graphine layers (graphitisation).
AFM
(a) Schematic view on epitaxial graphene. (b) AFM image of epitaxial
graphene on C-terminated SiC substrate. The steps those of the SiC
substrate. The 5-10 graphene layers lie on the substrate similar to a carpet
which has folds visible as white lines on the image.
Crystal structure of graphene
(a) Honeycomb lattice. The vectors 1, 2, and 3 connect nn carbon atoms, separated by a
distance a = 0.142 nm. The vectors a1 and a2 are basis vectors of the triangular Bravais
lattice. (b) Reciprocal lattice of the triangular lattice. Its primitive lattice vectors are a∗1 and
a∗2. The shaded region represents the first Brillouin zone (BZ), with its centre  and the two
inequivalent corners K (black squares) and K′ (white squares). The thick part of the border
of the first BZ represents those points which are counted in the definition such that no
points are doubly counted. The first BZ, defined in a strict manner, is, thus, the shaded
region plus the thick part of the border. For completeness, the three inequivalent
crystallographic points M, M′, and M′′ (white triangles) are also shown .
Crystal lattice structure
The modulus of the basis
vectors yields the lattice
spacing, ã = √3a = 0.24
nm, and the area of the
unit cell is Auc = √3ã2/2 =
0.051 nm2. The density of
carbon atoms and valence
electrones is, therefore, nC
= n = 2/Auc = 39 nm−2 =
3.9 × 1015 cm−2.
Lattice structure of graphene, made out of
two interpenetrating triangular lattices
a1 and a2 are the lattice unit vectors, and
i are the nearest-neighbor vectors.
Corresponding Brillouin zone.
Sketch of derivation (1)
Wallace, Phys. Rev. 71, 622 (1947)
Energy dispersion of π electrons in graphene
The picture and derivations adapted from Castro Neto et al., Rev. Mod. Phys. 81, 109 (2009)
Sketch of derivation (2)
Bloch wave function
Hopping parameter t ≃ −3eV
Conic (Dirac) points
Let us put
and expand the Hamiltonian in small
hopping parameter t ≃ −3eV
Coefficient
can be dropped
Similarly
It is suggestive to express the Hamiltonian describing conic points in the form
- Pauli matrices
The Hamiltonian is, from a formal point of view, exactly that of an ultra-relativistic (or
mass-less) particle of spin 1/2 (such as the neutrino), with the velocity of light c
replaced by the Fermi velocity vF, which is a factor 300 smaller.
Density of states close to Dirac points
In regular 2DEG
density of state is
energy independent:
ρ2D() = gm∗/2πħ2
The divergencies at ±t, called
van-Hove singularities, are
due to the saddle points of
the energy dispersion at the
M points at the borders of the
first BZ.
Hopping parameter t ≃ −3eV
Schematic plot of the density of states for electrons in graphene in the absence of
nnn hopping. The dashed line indicates the density of states obtained in a
continuum limit. This needs to be contrasted to the conventional case of electrons in
2D metals, with an energy dispersion of  = ħ2q2/2m∗, in terms of the band mass m∗,
where one obtains a constant density of states, ρ2D() = gm∗/2πħ2.
Density of states close to Dirac points: second order corrections
The second-order terms include nnn hopping corrections and off-diagonal secondorder contributions from the expansion of the sum of the nn phase factors. The latter
yield the so-called trigonal warping, which consist of an anisotropy of the energy
dispersion around the Dirac points. (b) Comparison of the contours at energy  = 1
eV, 1.5 eV, and 2 eV around the K′ point. Black lines - full dispersion and the grey
ones - second order within the low energy (continuum) limit.
Experimental characterization
Schematic view of an ARPES
measurement. The analyser
detects the energy Ef of the
photoemitted electron as a
function of the angles ϑ and ,
which are related to the
momentum of the electronic
state.
The energy dispersion relation of solids may be determined by ARPES (angle
resolved photoemission spectroscopy).
Thus there arises the prospect, which excites a lot of people, of finding analogs to
many phenomena predicted to occur in quantum electrodynamics in a solid-state
context.
Comment
However, it should be remembered that the Dirac excitations near K are not the
antiparticles of those near K’; rather it is the two possible combinations of the
excitations near one Dirac point on the A and B sub-lattices, with energies
respectively, which are one another’s “antiparticles.”
Eigenfunctions in the vicinity of the K-point
Note that when q rotates once around the Dirac point, the phase of
changes by
, not by
, as is characteristic for “spin-1/2” particles.
Important parameters for conic spectrum
Density of states at K-point:
Since there are 2 Dirac points
How one can introduce effective mass?
Doping shifts the Fermi level leading to creating a Fermi line.
This definition provides the cyclotron effective mass.
Klein tunneling
Due to the chiral nature of their quasiparticles, quantum tunneling in these materials
becomes highly anisotropic, qualitatively different from the case of normal, nonrelativistic electrons.
Massless Dirac fermions in graphene allow a close realization of Klein’s gedanken
experiment - unimpeded penetration of relativistic particles through high and wide
potential barriers.
The paradox: When the barrier increases,
transmission becomes perfect!
Schematic diagrams of the spectrum
of quasiparticles in single-layer graphene.
The spectrum is linear at low Fermi energies (<1eV). The
red and green curves emphasize the origin of the linear
spectrum, which is the crossing between the energy
bands associated with crystal sublattices A and B.
The Fermi level (dotted lines) lies in the conduction
band outside the barrier and the valence band
inside it. The blue filling indicates occupied states.
Explanation: Absence of backscattering for
Adapted from Beenakker, 2007
Because the magnitude v
of the carrier velocity is
independent of the energy,
an electron moving along
the field lines cannot be
backscattered— since that
would require v = 0 at the
turning point.
An electron-like excitation continue under the barrier as a hole-like one
Momentum changes its sign, but the (group) velocity is conserved.
As a result – anisotropic scattering.
Result for high energies
Under resonance conditions
transparent (interference effects) .
:
the barrier becomes
More significantly, however, the barrier always remains perfectly transparent for
angles close to the normal incidence φ = 0.
The latter is the feature unique to massless Dirac fermions and is directly related
to the Klein paradox in QED.
Klein tunneling is the mechanism for electrical conduction through the interface
between p-doped and n-doped graphene.
n-p-n junction in graphene
a) cross-sectional view of the device.
b) electrostatic potential profile U(x) along
the cross-section of a). The combination of a
positive voltage on the back gate and a negative
voltage on the top gate produces a central pdoped region flanked by two n-doped regions.
c) Optical image of the device. The barely visible
graphene flake is outlined with a dashed line and
the dielectric layer of PMMA appears as a blue
shadow. (Huard et al., 2007)
Minimal conductance of graphene
What happens with the conductance of
graphene when the Fermi level reaches
the conic point?
Does it vanish or not?
The conductance reaches a
minimum corresponding to double
value comparing to the value at
the lowest quantum Hall plateau.
Conductivity versus
gate voltage
Minimal conductance of graphene
The band structure of graphene has two valleys, which are decoupled in the
case of a smooth edge. In a given valley the excitations have a two-component
envelope wave function
The two components of
refer to the two sublattices in the two-dimensional
honeycomb lattice of carbon atoms.
Dirac equation:
with
the velocity of the massless excitations of charge
and energy ,
the momentum operator, ,
the position, and
a Pauli matrix. We choose the zero of energy such that the Fermi level is at
.
Boundary conditions:
The transversal momenta are quantized as:
Tworzydlo et al., 2006
Level quantization and quantum Hall Effect in graphene
At a typical doping, electrons are degenerate at room temperature.
In the absence of magnetic field the tight binding Hamiltonian close to Dirac points is
In magnetic field one has to replace
to get:
We have to find eigenvalues of this Hamiltonian versus magnetic field B
Let us assume that
and choose the Landau gauge
It is also convenient to choose dimensionless variables
Measuring lengths in units of
, one gets
The Hamiltonian can be rewritten as
It is immediately seen that the energies are parameterized by the quantity
Trick: let us apply the Hamilton operator twice. We have
Note that the operator
“dimensionless Harmonic oscillator” with eigenvalues
Consequently,
Quantum numbers n correspond to Landau
levels, but they are not equidistant.
The number of states per the Landau level
corresponds to the number of flux quanta
through the cell,
is the Hamiltonian of a
Experimental check: gated structures
Manchester group
Room-temperature quantum Hall Effect in graphene
At B=45 T the Fermi level is
located between n=0 and 1
At T= 300 K, the plateaus are
seen at B < 20 T
What was not discussed in detail….
• Bilayer graphene
• Epitaxial graphene and graphene stacks
• Surface states in graphene and graphene stacks
• Graphene nanoribbons
• Flexural Phonons, Elasticity, and Crumpling
• Disorder in Graphene: Ripples, topological lattice defects, impurity states,
localized states near edges, cracks, and voids; vector potential and gauge
field disorder, coupling to magnetic impurities
• Many-Body Effects: Electron-phonon interactions, electron-electron
interactions, short-range interactions
• Mechanical properties
• Potential device applications: Single molecule gas detection, Graphene nanoribbons as ballistic and FET transistor devices and components for integrated
circuits; Transparent conducting electrodes, Graphene biodevices, Nano
Electro Mechanical Resonators and Oscillators, components of lasers, etc…
100 GHz transistor from Wafer-Scale Epitaxial Graphene
Cutoff frequency of 100 gigahertz for a gate length of 240 nanometers. The high-frequency
performance of these epitaxial graphene transistors exceeds that of state-of-the-art silicon transistors
of the same gate length.
(A) Image of devices fabricated on a 2-inch
graphene wafer and schematic cross-sectional
view of a top-gated graphene FET.
(B) The drain current, ID, of a graphene FET (gate
length LG = 240 nm) as a function of gate
voltage at drain bias of 1 V with the source
electrode grounded. The device transconductance, gm, is shown on the right axis.
(C) The drain current as a function of VD of a
graphene FET (LG = 240 nm) for various gate
voltages.
(D) Measured small-signal current gain |h21| as
a function of frequency f for a 240-nm-gate
(◇) and a 550-nm-gate (△) graphene FET at VD
= 2.5 V. Cutoff frequencies, fT, were 53 and 100
GHz for the 550-nm and 240-nm devices,
respectively.
Ph. Avouris group, IBM
Model device acting as a
resistor standard
T=300 mK
Accuracy ca. 3x10-9
a, AFM images of the sample: large flat terraces on the surface of the Si-face of a 4H-SiC(0001)
substrate with graphene after high-temperature annealing in an argon atmosphere.
b, Graphene patterned in the nominally 2-μm-wide Hall bar configuration on top of the terraced
substrate.
c, Layout of a 7 × 7 mm2 wafer with 20 patterned devices. Encircled are two devices with dimensions
L = 11.6 µm and W = 2 µm (wire bonded) and L = 160 µm and W = 35 µm. The contact configuration
for the smaller device is shown in the enlarged image. To visualize the Hall bar this optical micrograph
was taken after oxygen plasma treatment, which formed the graphene pattern, but before the
removal of resist.
Nature Nanotechnology 5, 186 - 189 (2010)
First graphene touch screen
The process includes adhesion of polymer supports, copper etching (rinsing) and dry transferprinting on a target substrate. A wet-chemical doping can be carried out using a set-up similar to that
used for etching.
Sustains strain up to 6%
Extremely promising for
transparent electrodes
Nature Nanotechnology (2010)
Example: Graphene Q-switched, tunable fiber laser
Group by Ferrari, UK: preprint 2010
Graphene is used as a non-linear (saturated
absorption) medium to create short optical
pulses.
The authors have succeeded to make 2 μs
pulses, tunable between 1522 and 1555 nm
with up to 40nJ energy.
This is a simple and low-cost light source for
metrology, environmental sensing and
biomedical diagnostics.
Studies of graphene is a very interesting and promising area, but a lot of things
remains to be done to create graphene electronics.
Giant Faraday rotation
Graphene turns the polarization by
several degrees in modest magnetic
fields.
This opens pathways to use
graphene in fast tunable ultrathin
infrared magneto-optical devices.
The polarization plane of the linearly polarized
incoming beam is rotated by the Faraday angle θ
after passing through graphene on a SiC substrate
in a perpendicular magnetic field.
Studies of graphene is a very interesting
and promising area, but a lot of things
remains to be done to create graphene
electronics.
Simultaneously, the polarization acquires a
certain ellipticity.
Crassee et al., Nature Physics 2010
2010
Novel crumpling method takes flat graphene from 2D to 3D
University of Illinois at Urbana-Champaign, 17/02/2015
Crumpled graphene surfaces can be used as higher surface area electrodes for battery and
supercapacitor applications. As a coating layer, 3D textured/crumpled nano-topographies could
allow omniphobic/anti-bacterial surfaces for advanced coating applications
http://phys.org/news/2015-02-crumpling-method-flat-graphene-2d.html
Progress
https://www.youtube.com/watch?v=OyRfCyuoaOw
Introduction
https://www.youtube.com/watch?v=SXmVnHgwOZs
Musical
https://www.youtube.com/watch?v=xp9OKouxd4s
Girls commenting
https://www.youtube.com/watch?v=C_mCv4yeLug
Animation
https://www.youtube.com/watch?v=XDJRlBSXsow
Manchester
https://www.youtube.com/watch?v=DzLiaJsric4
For kids
ppt
https://www.youtube.com/watch?v=Mcg9_ML2mXY
https://www.youtube.com/watch?v=pmtJ0yiPVtY
Home activity for Tue. 3 and Wed. 4 March
a) Read these lecture notes and the cited literature if necessary. Try to grasp main
concepts. I am happy to provide you several pdf files if you need deeper
understanding. Identify issues that you would like to discuss on Practical, Wed. 4
March.
b) Work with questions to graphene: Questions and other questions.
c) Address Question 2.1 in TH on p. (36). Can you discuss it on practical?
d) Please choose date for full presentation. Available dates: March 4, 11, 25; April
22, 29; May 6, 13. Please notify of your choice. Please send pdf files of
presentations to my E-mail: pavlo.mikheenko@fys.uio.no to put them on web.
49
MENA5010 presentations
Hans Jakob Sivertsen Mollatt – presented
Jon Arthur Borgersen February 25
Knut Sollien Tyse March 18
Ymir Kalmann Frodason March 18
Simen Nut Hansen Eliassen- March 25
Steinar Kummeneje Grinde - April 22
Bjørn Brevig Aarseth April 29
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