Graphene - most two-dimensional system imaginable

Transcription

1 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: Dr. Chris Ewels, Inst. of Materials

2 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 SiO 2 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 last years is enormous. The Nobel Prize in Physics 2010 Andre Geim Konstantin Novoselov : publications Graphene is a very promising material both for applications and fundamental research.

3 Progress Introduction Musical Girls commenting Animation Manchester For kids ppt

4 Model of Graphene Structure Photo credit: CORE-Materials, "Model of Graphene Structure," via Flickr. CC BY-SA 2.0

5 My optical image

6 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.

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8 Superconductivity in Ca-doped graphene 2015 J. Chapman 1, Y.Su 1, C. A. Howard 2, D. Kundys 1, A. Grigorenko 1, F. Guinea 1, A. K. Geim 1, I.V. Grigorieva 1, R. R. Nair 1 1 School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK 2 Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK

9 2016

10 Lithium doping turns graphene into a superconductor 2015

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12 Feb 26, 2016 Graphene slides friction-free over gold

13 Bill Gates funds creation of thin, light, impenetrable graphene condoms By Sebastian Anthony on November 21, 2013 at 10:55 am Graphene is incredibly thin and strong but you might not know that it also happens to be the most thermally conductive solid material in the world (only superfluid helium has better conductivity). Furthermore, graphene seems to be impermeable to everything but water. All of these factors combine to make graphene the perfect material for condoms that are incredibly safe, and yet so thin, light, and thermally conductive that it s almost like you re not wearing a condom at all. GRAPHENE SEX REVOLUTION 04.FEBRUARY.2016 The Gates have already given out $1 million in research grants to condom developers who are working to create a new, high-tech condom of the future. The next generation of condoms will be designed to be super-sensitive and super-durable, and they may even enhance pleasure. A graphene condom so thin that it would feel like wearing nothing at all.

14 The trick: Finding the Graphene Using correct substrate And correct light frequency Interference effect makes monolayers show up in ordinary optical microscope Graphene Blake et al (2007) arxiv: SiO 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.

15 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 t 1. Describe graphene and its crystal lattice. What is its difference from other forms of carbon? What kind of hybridisation is realised in graphene? Describe other types of carbon hybridisation; give examples of compounds where it takes place. Graphite can be viewed as a stack of graphene layers. Fullerenes C 60 are molecules consisting of wrapped graphene by the introduction of pentagons on the hexagonal lattice. From Castro Neto et al, 2009

16 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 Columbia- Princeton 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]. 2. Does graphene show quantum Hall effect (QHE)? Is it usual quantum Hall effect? If not, what is the difference? Is graphene a 2DEG? What is its density of states as function of energy? Is any difference in QHE for the single layer and double-layer graphene? [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).

17 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* < 10 6 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 m c of massless carriers in graphene is described by E = m c c* 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).

18 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 12 C and 13 C A = 8 characterises the radioactive isotope 14 C. 12 C (99% of all carbon atoms) has nuclear spin I = 0 13 C (1% of all carbon atoms) has nuclear spin I = 1/2 14 C (10-12 of all carbon atoms, -decays into nitrogen 14 N, half-life of years, used for historical dating (radiocarbon), allows to date biological activity up to an age 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.

19 Crystal structure of carbon materials: sp 1 hybridisation In the sp 1 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 sp 1 hybridisation. The figure shows the electronic density of the 2s and 2p x orbitals and that of the hybridised ones. (b) Acetylene molecule (H C C H). The propeller-like 2p y and 2p z orbitals of the two C atoms strengthen the covalent σ bond by forming two π bonds (not shown).

20 Crystal structure of carbon materials: sp 2 hybridisation In the sp 2 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 sp 2 hybridisation. The orbitals form angles of 120 o. (b) Benzene molecule (C 6 H 6 ). 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.

21 Crystal structure of carbon materials: sp 3 hybridisation In the sp 3 hybridisation, the 2s state mixes with three 2p orbitals. Four club-like orbitals mark a tetrahedron. The orbitals form angles of o degrees. Example: Methane (CH 4 ) and diamond A chemical example of sp 3 hybridisation is methane (CH4), where the four hybridised orbitals form covalent bonds with the 1s hydrogen atoms. In condensed matter physics, the 2p 3 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 nm

22 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 sp 3 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 sp 2 orbitals, leaving over a more or less free p-orbitals that form delocalized π-bonds. In that case the natural tendency is for the sp 2 orbitals to arrange themselves in a plane at 120 o angles, and the lattice thus formed is the honeycomb lattice.

23 Exfoliated graphene Exfoliation includes several cycles of scotch-tape peeling from graphite with final gluing to the SiO 2 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 SiO 2 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. 5. What are main techniques of graphene fabrication? Is exfoliated graphene different from epitaxial graphene? What substrates are used to visualise graphene optically? What are the definite techniques for identifying graphene?

24 Epitaxial graphene Epitaxial growth technique consists of exposing hexagonal SiC crystal to temperatures of about 1300 o C in order to evaporate the less tightly bound Si atoms from the surface. The remaining carbon atoms on the surface form a graphene 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.

25 Classical and quantum mechanics of 2DEG Classical motion: Lorentz force: Perpendicular to the velocity! Newtonian equation of motion: m*v 2 /r c = evb; v=ebr c /m*; =v/2 r c ; c =2 =eb/m* Cyclotron orbit Cyclotron frequency, Cyclotron radius, In classical mechanics, any size of the orbit is allowed. Magnetotransport in 2DEG

26 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: ω c τ 1 Landau levels Wave functions are smeared around classical orbits with r n = l B (n+1) 1/2 ; l B = (ħ/ c m) 1/2 l B is called the magnetic length. It is radius of classical electron orbit for n = 0. v/r; r v/ ; mv 2 /2= ħ c (n+1/2); v n 0 = (ħ c /m) 1/2 ; l B = r n 0 = (ħ/ c m) 1/2 Magnetotransport in 2DEG

27 Landau quantization and it s consequences

28 Origin of low xx in Quantum Hall effect Equipotential lines E E 0 = -ne 2 /m* For classical transport, For quantum transport, j n = m 2 mv F πħ 2 2 = k F 2 ħ 2 2πħ 2 = k 2 F 2π 1 B = j e ħk F 2 ρ xy = ħk 2 F j e 2π 2 ek = h 1 F e 2 j

29 Crystal structure of graphene (a) Honeycomb lattice. The vectors 1, 2, and 3 connect nn carbon atoms, separated by a distance a = nm. The vectors a 1 and a 2 are basis vectors of the triangular (oblique) 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. 3. Describe reciprocal lattice of graphene. How are inequivalent points in honeycomb lattice reflected in the structure of the first Brillouin zone?.

30 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 A uc = 3ã 2 /2 = nm 2. The density of carbon atoms and valence electrones is, therefore, n C = n = 2/A uc = 39 nm 2 = cm 2. Lattice structure of graphene, made out of two interpenetrating triangular lattices a 1 and a 2 are the lattice unit vectors, and i are the nearest-neighbor vectors. Corresponding Brillouin zone. 4. What is the area of unit-cell in graphene. What are the and bonds? How to calculate density of valence electrons in graphene? What is its value?

31 Sketch of derivation (1) Wallace, Phys. Rev. 71, 622 (1947) 6. Formulate Tight-Binding Model for electrons in graphene. What is the complication in graphene in comparison with Tight-Binding Model for simple honeycomb lattice? Introduce the energy overlap integral.

32 Energy dispersion of π electrons in graphene 7. Describe energy dispersion of π electrons in graphene. How can it be obtained in Tight-Binding Model? The picture and derivations adapted from Castro Neto et al., Rev. Mod. Phys. 81, 109 (2009)

33 Sketch of derivation (2) Bloch wave function Hopping parameter t 3eV

34 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 v F, which is a factor 300 smaller.

35 Density of states close to Dirac points In regular 2DEG density of state is energy independent: ρ 2D ( ) = gm /2πħ 2 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 8. What is energy dispersion in graphene close to conic (Dirac) points? How is energy linked with wave vector there? Is Fermi velocity included in the link between energy and wave vector? What is trigonal warping? 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 = ħ 2 q 2 /2m, in terms of the band mass m, where one obtains a constant density of states, ρ 2D ( ) = gm /2πħ 2.

36 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.

37 Experimental characterization Schematic view of an ARPES measurement. The analyser detects the energy E f 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). 9. What technique do you know that is suitable to map the energy dispersion of electrons? What is result of its application to graphene?

38 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.

39 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. 10. What is the rest mass of charge carriers in graphene? How to introduce its cyclotron effective mass? Does it depend on charge carriers density and how?

40 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.

41 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. 11. Is it possible in tunnelling that transmission becomes better when the barrier height increases? Does it anything to do with graphene? What is the Klein tunnelling? How can electron go from conduction to valence band without backscattering?

42 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 : 12. Describe anisotropic and resonant scattering in graphene. What is the property of a barrier at angles close to the normal incidence? Describe the experimental realization of n-p-n junction in graphene. 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.

43 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 p- doped 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) 12. Describe anisotropic and resonant scattering in graphene. What is the property of a barrier at angles close to the normal incidence? Describe the experimental realization of n-p-n junction in graphene.

44 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. 13. What happens with the conductance of graphene when its Fermi level reaches the conic point? Does it go to zero? If not, at what value it stops? Conductivity versus gate voltage

45 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

46 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

47 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

48 Trick: let us apply the Hamilton operator twice. We have Note that the operator is the Hamiltonian of a 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, 14. What is specific about the level quantization and quantum Hall Effect in graphene? Are Landau levels equidistant? What is the number of states per Landau level? Does it linked with the number of magnetic flux quanta through the cell?

49 Experimental check: gated structures 15. How to tune density of electrons in graphene? What is graphene s typical mobility of electrons? How is it dependent on temperature? What is the mean free path of electrons at room temperature? Can one see quantum Hall effect at room temperature? Manchester group

50 Room-temperature quantum Hall Effect in graphene Bilayer graphene shows fractional quantum Hall effect tuned by an electric field. 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 2. Does graphene show quantum Hall effect (QHE)? Is it usual quantum Hall effect? If not, what is the difference? Is graphene a 2DEG? What is its density of states as function of energy? Is any difference in QHE for the single layer and double-layer graphene?

51 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

52 100 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, I D, of a graphene FET (gate length L G = 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 V D of a graphene FET (L G = 240 nm) for various gate voltages. 16. What applications of graphene do you know? What is their importance? (D) Measured small-signal current gain h 21 as a function of frequency f for a 240-nm-gate ( ) and a 550-nm-gate ( ) graphene FET at V D = 2.5 V. Cutoff frequencies, f T, were 53 and 100 GHz for the 550-nm and 240-nm devices, respectively. Ph. Avouris group, IBM

53 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 mm 2 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, (2010)

54 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)

55 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.

56 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

57 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

58 Tapping into graphene-oxide's antibacterial properties to fight infections Graphene oxide has antibacterial and antifungal properties and is effective against four important human pathogens. Coating medical instruments and devices in the carbon-based material could help to reduce infections, especially after an operation, as well as reducing antibiotic use and antibiotic resistance. 200 nm sheets of graphene oxide in a water solution killed around 90% of S. aureus and E. faecalis, and around 50% of E. coli in less than two hours. "Graphene-oxide sheets can cut bacterial membranes acting as a nano-knife, wrap the bacteria as a blanket stopping their growth, or oxidise bacterial cellular components," Around 25,000 people in Europe die every year from resistant bacterial infections. Without new antibacterial agents, routine medical procedures and operations could soon become impossible. Palmieri says that while bacteria rapidly evolve resistance to antibiotics, the "antibacterial mechanism of graphene oxide, based on both mechanical injury and chemical oxidation" makes it hard for resistance to develop.

59 36.7K Ever since its discovery ten years ago, scientists and engineers have expressed great expectations for the wonder material graphene. Just a single atom thick, these carbon sheets are not only the world s thinnest material, but they are also the strongest. It therefore may not come as a complete surprise that scientists are now considering its use in body armor. After conducting miniature ballistic tests, graphene was found to perform twice as well as the material traditionally used in bulletproof vests, raising the possibility that it could be used as protection for police officers or members of the armed forces. Graphene consists of a sheet of single carbon atoms arranged in a honeycomb structure. Alongside being incredibly strong, graphene also conducts heat and electricity remarkably well, resists rust and has excellent optical and mechanical properties. Graphene also achieves this impressive range of characteristics while being incredibly lightweight, which is why scientists began to wonder whether it would make a good addition to body armor. Unfortunately, testing it out is not as simple as firing bullets through it and seeing what happens, because atomthick material would be obliterated by such an impact. Examining its vigor therefore required a different tactic, so scientists from the University of Massachusetts-Amherst created a miniaturized ballistics test. As described in the journal Science, the researchers used lasers to superheat gold filaments, which behaved like gunpowder and fired tiny silica spheres, or microbullets, at sheets of graphene ranging from 10 to 100 nanometers in thickness. By comparing the kinetic energy of the spheres before and after they penetrated the sheets, they found that graphene dissipates this energy by warping into a cone shape at the site of impact, and then cracking outward. While these cracks represent a weakness, the material still performed twice as well as Kevlar, the lightweight fiber used in body armor. Furthermore, it absorbed between 8 and 10 times the impacts that steel is able to withstand. In the future, scientists might be able to overcome the cracking problem by combining it with other materials to generate a composite, the researchers said. Interestingly, another paper came out this week in Nature which revealed a previously unknown property of graphene: it is permeable to protons. This raises the possibility that it could be used to improve fuel-cell technology, or even to harvest hydrogen from the atmosphere. Hydrogen fuel cells create electrical energy through a reaction between hydrogen and oxygen. They rely on semipermeable membranes that allow the passage of protons but block other particles. Existing materials, however, let some hydrogen fuel leak through, which reduces efficiency of the system. But graphene seems to be impermeable to everything but protons, suggesting it could be an ideal solution to the problem. Furthermore, this newly identified property could mean that one day, graphene could be used as a sieve to extract hydrogen from air, meaning we could pump fuel from the atmosphere and generate electricity from it. While that prospect is exciting, it is purely speculation at this stage. [Via Science, New Scientist, BBC News, Science Alert, E&T, Nature and Nature]

60 Screening of dendritic flux avalanches A conductive layer deposited on or applied to superconductor can be used to protect a particular area from the invasion of avalanches. P. Mikheenko, J. I. Vestgaarden, S. Chaudhuri, I. J. Maasilta, Y. M. Galperin, T. H. Johansen, Metal frame as local protection of superconducting films from thermomagnetic avalanches, AIP Advances 6, (2016).

61 Dendritic instability in YBa 2 Cu 3 O 7 films triggered by transient magnetic fields M. Baziljevich, E. Baruch-El, T. H. Johansen, and Y. Yeshurun APPLIED PHYSICS LETTERS 105, (2014) a) - d) Flux patterns in the YBCO film at temperatures 13, 20, 30, and 40 K, respectively A height profile plot obtained by AFM measurement of the 150- nm thick YBCO film in an area where the original slit extended its length by the avalanche activity., September 2016, Lviv, Ukraine

62 Laser annealing of graphene ink Optimizing the optical and electrical properties of graphene ink thin films by laser-annealing, S. K. Del, R. Bornemann, A. Bablich, H. Schäfer-Eberwein, J. Li, T. Kowald, M.l Östling, P. H. Bolívar and M. C.Lemme, 2D Materials 2, (2015). Transparency of the graphene film. Highly flat and uniform graphene films are obtained by a laser annealing technique., September 2016, Lviv, Ukraine

63 Graphene footprint of dendritic avalanches in YBa 2 Cu 3 O x films I Optical image of the surface of an YBa 2 Cu 3 O x - based multi-layer with imprints of dendritic flux instabilities extending from 1 to 3 and from 2 to 3. Arrow shows direction of the transport current in the sample. SEM images of footprints in graphene., September 2016, Lviv, Ukraine

64 EDX and AFM study of YBa 2 Cu 3 O x film covered by graphene Carbon map (a) and corresponding SEM image of the surface of YBCO/STO/LCMO multilayer (b) with imprint branches of dendritic flux instability. AFM image of the surface of YBCO/STO/LCMO multilayer with an imprint of dendritic flux instability on the left together with thickness profile (bottom panel) along the horizontal line seen in the top panel., September 2016, Lviv, Ukraine

65 MOI study of NbN film covered by graphene Magneto-optical image of dendritic flux avalanche penetrating a conductive frame in NbN superconducting film. The image was obtained at 3.7 K by applying a magnetic field of 6.8 mt perpendicular to the film. b) The graphene cover on top of the same film., September 2016, Lviv, Ukraine

66 Origin of changes in graphene cover Cavitation is the formation of vapour cavities in a liquid i.e. small liquid-free zones ("bubbles" or "voids"). When subjected to higher pressure, the voids implode and can generate an intense shock wave. Cavitation is a significant cause of wear in some engineering contexts. Collapsing voids that implode near to a metal surface cause cyclic stress through repeated implosion. Graphene flakes are partially removed from the cover due to cavitation., September 2016, Lviv, Ukraine

67 Magneto-optical imaging of brain tissue Diamagnetic levitating frog a) b) a) Optical image of a slice of brain. b) Magneto-optical image of the same slice as in a). During the experiment, sample was pressed by the indicator film, spreading it to a bigger then in a) area. Black color in the image corresponds to diamagnetic response., September 2016, Lviv, Ukraine

68 Search for spin-polarised behaviour in bio-nano-pd I ( A) 2,5 2,0 1,5 1,0 0,5 0,0-0,5-1,0-1,5-2,0-2,5-0,03-0,02-0,01 0,00 0,01 0,02 0,03 V (V) IV curve of the dry sample of nano-bio-pd powder with remnants of bacterial shells. Arrows show direction of the record. The sample with planar area of 5x5 mm 2 and thickness of few microns demonstrates stable, reversible and linear IV characteristic with resistance of about 11 K. There are no any features on the IV curve that would suggest spin-polarized or quantum behaviour. The high resistance indicates that contribution of graphene nanoflakes in electron transport is not dominant and Pd nanoparticles remain weakly connected to each other., September 2016, Lviv, Ukraine

69 Transport measurements of muscles tissue I ( A) ,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0 V (V) Current (arb. units) Ohm-like behaviour Superconductor Semiconductor Voltage (arb. units) IV curves of the muscles tissue recorded in the process of the drying of the sample. Small black arrows show direction of the record. Large red arrow indicates increase of resistance in the process of measurement., September 2016, Lviv, Ukraine

70 Four-electrodes transport measurements Optical image of a slice of brain exposed to water solution of graphene flakes and connected to the wires. The electrical current was passed between leads 1 and 4 and potential was measured between 2 and 3. The red arrow marks narrow constriction between the leads 1 and 2. A dark spot close to the sample contains remnants of graphene leaked from the slice. White area is an insulating polytetrafluoroethylene (PTFE) tape, September 2016, Lviv, Ukraine

71 Transport measurements of brain tissue I ( A) I (ma) ,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 V (V) 0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 V (V) Current-voltage characteristic of the brain tissue measured in the four-probe configuration. Small black arrows show direction of the record. Current-voltage characteristic of the brain slice shown in three-probe configuration with current leads 2 and 4, and potential leads 2 and 3., September 2016, Lviv, Ukraine

72 Superconductivity in brain?, September 2016, Lviv, Ukraine

73 Quantum behaviour in brain R (k ) R q = h/e ,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 V (V) Current-voltage characteristic of the brain slice re-plotted as voltage dependence of the resistance., September 2016, Lviv, Ukraine

74 Possibility of superconductivity in brain R (k ) R qs = h/4e R qsl = h/8e 2 0 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 V (V) Temperature dependence of the resistance of five YBCO bridges. The dashed line is the quantum of resistance R q =h/4e 2 = 6.45 k. P. Mikheenko et al., Phys. Rev. B 72, (2005). A low-current part of the voltage dependence of the resistance around the group of points marked in previous slide by the magenta arrow., September 2016, Lviv, Ukraine

75 Evolution of I-V curves in brain: extended range I (ma) V (V) a) R (k ) R q = h/e 2 b) V (V) I-V (a) and R-V (b) representations of the transport measurements for the slice of brain in an extended voltage interval., September 2016, Lviv, Ukraine

76 Evolution of I-V curves in brain tissue I (ma) a) R (k ) R q = h/e 2 b) V (V) V (V) Evolved IV (a) and RV (b) curves of the brain sample acquiring a semiconducting behaviour., September 2016, Lviv, Ukraine

77 Link between energy gap and critical temperature Possibility of Synthesizing an Organic Superconductor W. A. Little Phys. Rev. 134, A1416 Published 15 June I (ma) T c =1644 K V 2 = 3.53 k B T c W. A. Little, 1964 T c =2200 K 0.58 V T c =1906 K Yu.M.Ivanchenko, P.N.Mikheenko, V.F.Khirnyi, Kinetics of the destruction of superconductivity by the current in the thin films. Zhurnal eksperimentalnoi i teoreticheskoi fiziki, v.80, N 1, p (1981). U (V), September 2016, Lviv, Ukraine

78 Link between energy gap and critical temperature = 3.53 k B T c I ( A) V T c =1940 K 0.42 V 2 T c =1380 K W. A. Little, 1964 T c =2200 K U (V), September 2016, Lviv, Ukraine

79 Comment on room temperature superconductivity Superconductivity has high potential for quantum processing of information with decoherence time for its isolated islands as large as 10 3 seconds and the time for one quantum operation of 10-9 seconds *. Superconductivity was not seriously considered to be involved in brain activity since it usually takes place at very low temperatures. The recent progress in research and perhaps graphene-assisted transport measurements demonstrated here may change this paradigm. Obtained results would be in agreement with a statement that if room-temperature superconductivity exists, life in its evolution had sufficient time to find it and use for its purposes, namely in longtime memory and quantum processing of information. This, in its turn, may have resulted in consciousness in higher-level living organisms. * S. Hameroff, Philos. Trans. R. Soc. Lond. Ser A, Math. Phys. Sci. 356, 1869 (1998)., September 2016, Lviv, Ukraine

80 Conclusions Transport and magneto-optical measurements of various biological samples were performed. The transport measurements were carried out after exposing samples to water solution of graphene nanoplatelets. The intriguing features of the quantum of resistance and superconductor-like current-voltage characteristics have been observed in electrical transport of brain tissue. The results may indicate existence of room temperature superconductivity in brain tissue, which could have implications for understanding of quantum transport and processing of information in living organisms., September 2016, Lviv, Ukraine