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Graphene and Electrons vs Ohm’s Law

Current is motion of charged particles such as electrons, which flow from the negative to the positive pole. In other words, by measuring the voltage in different parts of the conventional conductor, we can always say exactly in which direction the electrons move as well as-the positively charged holes do. But graphene is not like that.

In monatomic carbon layer that is folded of flat and regular hexagons most unusual properties are manifested.

Graphene shows incredible mechanical strength and superior thermal conductivity, and the electrons can flow "contrary to" Ohm's law in it, as if the resistance of the material were negative. This behavior of electrons sooner resembles a viscous liquid rather than electric current.

These unusual properties of "graphene electricity" are predicted in a new paper, which was recently published by  Nature Physics journal. We talked with Gregory Falkovich who is

one of the co-authors and an employee at the Moscow Institute for Information Transmission Problems.

You write about the "negative resistance" in graphene - is it possible to explain this unusual wording?

- In this formula, we are missing an important word - we are talking about a "nonlocal negative resistance". And then everything can be explained. Imagine that you have a strip of graphene, the upper and lower boundaries of which are connected to contacts feeding current. Let's call them points 1 and 2. Now we take two other points, aside from the 1 and 2 - let it be the point 3 and 4 –and we measure the voltage between them. In other words, current flows through the first two points, and at the two others we measure voltage. And then we see how they are related to each other.

Typically, we expect that if the voltage is positive than the current is positive, the holes flow from the lesser potential to the greater, and the electrons do the contrary. This is the case in conventional conductors, in accordance with Ohm's law. Thus it will be with graphene and some other materials, if 1 and 2 coincide with 3 and 4. But when 3 and 4 are arranged alternatively, the sign of the voltage on them may be opposite. Thus, as if current flows in the reverse direction.

Why does this happen?

- The motion of electrons in a normal conductor obeys Ohm's law. They practically do not interact with each other: they are flying under the influence of electromagnetic field, slam into atoms, changing the trajectory, again affected by the field ... That is, the main "limitation" of their movement are the atoms of the crystal lattice of the conductor.

In graphene, apparently, there is a special mode in which the electrons flow very differently. They begin to interact with each other - so much that collisions between them have much greater effect on their movement than collisions with atoms do. Their movement is close to that in viscous fluid: the electrons involve neighboring electrons into motion.

This can be represented by the example of the vessel with a pair of holes on the sides. If we inject water through one of them, and it flow it from the other one, then there reverse twists in such a liquid. The same is true for graphene. Apart from the formulas, the mechanism is quite simple, and for me, as for fluid dynamics specialist, is very interesting that the principles of the oldest branch of physics were applicable in this new field.

What are the features of graphene that make  electrons flow like a viscous fluid?

- This is primarily due to the very high quality of the crystal lattice, which is retained even at quite normal temperatures. The electrons flow as if they drive over   open and flat roads. They are dense streams, so that they begin to "rub" against each other - this is a viscous flow regime. This behavior is not only possible in graphene, but also in other materials having good lattice without defects.

In ordinary conductors lattice is not as streamlined, and electrons constantly collide with the atoms like moving over very bumpy road. These are metallic conductors, and that Ohm's law. But electrons in graphene behave like massless relativistic particles. This gives rise to the most extraordinary effects.

By varying the number of electrons and holes in graphene, we can achieve different modes to display different properties. Attempts to find the modes have been taken for a long time in which sticky "e-liquid" flows in graphene. And this is just the essence of our idea: it can be done by registering the current extra points and observing whether it is subject to Ohm's law.

It should be noted that in parallel to this article there are at once two publications, including the work of the Manchester group of Andrei Geim, who were able to observe the effects that are very similar to those that we have described in theory - that is, the negative resistance. We all worked independently, and although the data may be due to other causes, it is possible that this is based on our mechanism.

Studies of these viscous currents in graphene may have some prospects for further use? In science - and perhaps, in the new technologies?

- Well, of course! From the point of view of science it is interesting just as the application of hydrodynamics to the new field of physics. After all, in the end, it's part of the mechanics, it is one of the oldest areas of science, on which our physical intuition relies largely. We operate forces, motion, currents and  it is more difficult to imagine relativistic behavior. But if we can use usual mechanical, hydrodynamic models and views for this purpose, it will greatly facilitate the study. This means that many well-studied phenomena can be recreated on the micro level.

For example, if we better understand the passage of the viscous "e-liquid" in graphene, we will be able to locally affect it. After all, to create current at a certain point, we need to create electric field in it. But if we deal with the movement of electrons as with viscous flow, we are able to do so due to "friction" between the two apart from the field. This opens yet unknown but great prospects for a new stage of development of electronics.

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