Looking for critical behavior in graphene

May 18, 2010 By Miranda Marquit, Phys.org feature

Graphene sheet. Image credit: Lawrence Berkeley National Laboratory
(PhysOrg.com) -- "One of the hopes people have for graphene is in electronic devices. It is seen as a possible replacement for silicon, due to its unique properties," Herb Fertig tells PhysOrg.com. Graphene conducts well, and it is easy to cool, making it ideal for use in electronic devices continually shrinking in size. However, scientists have yet to understand some of the properties of graphene, including how to control the flow of electrons. "In silicon," Fertig continues, "there is an energy gap that can be exploited to manipulate the flow of electrons. Graphene is a good conductor, but it is less clear how to control the electrons."

In an effort to better understand some of the properties of graphene, Fertig, a professor at Indiana University, worked with Jianhui Wang, a student at Indiana University, and Professor Ganpathy Murthy at the University of Kentucky, to develop an analytical calculation that could shed some light on the way that graphene behaves. Their work appears in : “Critical Behavior in Graphene with Coulomb Interactions.”

“During in most systems there is a point known as criticality, in which you have a strange state, where there are different length scales at the same time. This applies in any system at a critical point,” Fertig says. In graphene, though, calculations show that this state should be present without any need to adjust parameters to a special point. It should just naturally be present due to interactions. So far, it has been difficult to detect this effect. Most models of graphene behavior, Fertig says, ignore interactions between electrons. “It’s a big mystery because estimates show that electron interactions might be important in graphene, and that the potential energy should be big, but you don’t see the effects.”

Fertig and his colleagues hope that being able to measure critical behavior in graphene could help researchers solve some of the mysteries about graphene. “Our calculation shows that if you find the right thing to look at, you can see this special critical state where graphene is acting as if it is at a phase transition,” he explains. The calculations carried out by Fertig, Wang and Murthy suggest that careful measurements of the electron density around impurities in graphene could lead to the observation of this critical behavior.

“You can’t avoid impurities in graphene,” Fertig explains. “They always get in there. react to such impurities. If you look at the charge distribution around one, it should reflect the critical behavior. This should be possible using scanning microscopy.”

Scanning microscopy has been used to look at nanostructures, and have even seen impurities. However, these efforts have not been at sufficiently high resolution. Fertig points out, though, that there are some microscopes that use high enough resolution; they just haven’t been used to study impurity states in graphene. “To my knowledge,” he says, “there is no fundamental reason why this can’t be done. It’s about making the connections and putting the pieces together.”

Fertig thinks that if scientists could actually observe critical behavior in graphene, it might answer some questions about the material. “If we could see some evidence of interactions in graphene, and better understand why they have been difficult to detect so far, it could open new possibilities for controlling the electronic properties of graphene.” This could mean that efforts to replace silicon with graphene might be one step closer.

“This is just one avenue of possibility,” Fertig warns, “and it would be a long way off. But if we could understand why interactions in graphene don’t work like we think they should, it might be helpful in developing applications for in the future.”

Explore further: A huge step toward mass production of graphene

More information: Jianhui Wang, H.A. Fertig, and Ganpathy Murthy, “Critical Behavior in Graphene with Coulomb Interactions,” Physical Review Letters (2010). Available online: link.aps.org/doi/10.1103/PhysRevLett.104.186401


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2.1 / 5 (7) May 18, 2010
..during phase transitions in most systems there is a point known as criticality, in which you have a strange state, where there are different length scales at the same time. This applies in any system at a critical point..
This is not so strange state if we consider, even common fog or boiling watter contains phases with different length scales at the same time - droplets and bubbles. The electrons simply condense on the surface of graphene sheets. One of evidences of this behavior of such transition is so called balistic transport: the electrons are spreading in two dual ways. They're usually moving slowly, but at less or more rare moments some electrons are spreading a much faster. One example of quantum criticality point from common life is crunching and crackling of fresh snow. The increased speed of electrons manifests at tiny distances only, we could call it a brief superconductivity.

Why these electrons are behaving in so strange way at graphene and not in bulk graphite?
1 / 5 (1) May 18, 2010
So "different length scales" in graphene is referring to the bond length between C's?
2.6 / 5 (5) May 18, 2010
Inside of materials a balance between attractive and repulsive forces of electrons and atom lattice exist. We can say, electrons are covering atoms like poorly adhering layer of watter. For example alkali metals or bulk graphite crystal behaves like pile of wet meshes full of water, which is kept between layers by its surface tension.

When we separate individual graphene sheet from graphite crystal, then the things suddenly change: a single sheet has a double surface with compare to bulk crystal. At the surface of single graphene sheet a relative excess of electrons exist and these electrons have nowhere to move against another electrons.

We can compare this situation to the separation of single wire mesh layer from pile of wet sieves full of water. Many water can be held between layers, but when we separate a single layer from bulk, then the single mesh exhibits relative abundance of water, which would usually fall off in the form of water droplets.
3 / 5 (6) May 18, 2010
So "different length scales" in graphene is referring to the bond length between C's?
Nope, it's referring to droplets of electrons, condensing at surface of graphene sheets. The electrons are strongly adhering to carbon layer, but they're repel mutually at the same moment. Because then cannot leave the graphene layer so easily, they collapse around atom nuclei. As the result, electrons are compressed heavily, whenever the graphene sheet gets separated from crystal as the animation bellow illustrates.


As the result, the graphene sheet is covered by highly compressed layer of electron fluid in similar way, like the wire mesh pulled out of watter. Due the strong surface tension of electron fluid the pressure inside of layer is much higher, then at the bulk phase. And the electrons start to condense into another phase in similar way, like compressed water vapor.
3 / 5 (6) May 18, 2010
As the result, part of electrons in graphene sheet spread their charge in collective way like wagons in compacted train. The charge spreads along surface of graphene in waves, the speed of which is comparable to speed of light. Such motion is typical for spreading of current inside of superconductors.

Whereas the remaining part of losely coupled electrons is still spreading like individual automobiles at the street. They collide mutually and they're spreading in noncoherent, rather turbulent and slow way.

As the result, the separated sheet of graphene has a significantly higher electric and heat conductivity in comparison to bulk graphite, but still too low with compare to real superconductors. But at small distances the electrons are still able to jump from place to place in high speed - so we can say, at the nanometer scale this material behaves like dynamic mixture or 2D foam of many superconductor and conductor islands.
May 18, 2010
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2 / 5 (4) May 18, 2010
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May 18, 2010
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May 18, 2010
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