Nano ideas

Yesterday I had another paper accepted. Woo!

Once again it was with Applied Physics Letters, and once again they were prompt and easy to deal with. I have three other papers in the system at the moment, and in the time they’ve all been there, I’ve submitted two papers to APL and they were both accepted before getting any result from the other journals. Good stuff APL.

That being said, it’s not that APL pushes things through without adequate review. The referee’s reports of everything I’ve sent to APL has always been fair and well thought through. The comments from yesterday’s referee were particularly pertinent and reflected a thorough understanding of the theory, results, and implications. Good stuff APL!

Anyway, here is the result:

Imagine you have a sheet of graphene, and somehow you figure out how to stretch it (this is more difficult than it seems). The bonds will distort like this:

The way the bonds in graphene are distorted if graphene is stretched along different directions (F).

I’ve assumed that the bond lengths will be unchanged but will rotate. This was an interesting thing to derive actually. It’s really classical, has nothing to do with quantum physics, but I didn’t really know how to go about it. I’m sure it’s been done a million times before by different people, but it was much more interesting to derive it myself. What’s interesting about it, is that as you stretch something, it’s width decreases, but it’s length increases, and so the bond rotations aren’t always exactly what you think they’ll be, or even in the direction you think they’ll be in (like in the 45 degree case).

Anyway, so I figured out what happens when you shine light on this. What I found was that light polarised in one direction will be absorbed more than the other depending on the stretching direction. The discrepancy is about 10% for stretching angles (rotation of the bonds in the above figure) of only about 2 degrees. This is a large deviation for such a small amount of stretching.

Variation of the optical conductivity for light polarised along two orthogonal directions as a function of the angle you stretch it along.

Even more interesting is this result:

The Hall conductivity of stretched graphene as a function of the incident light intensity.

What this means, is that when you shine light on stretched graphene which is polarised in one direction, it will re-emit light (and be conductive) in the orthogonal direction. At a particular energy the sign of this effect reverses. This is pretty cool.

Well that’s it.

I just watched a very interesting talk on youtube called

David Gross: The Coming Revolutions in Theoretical Physics

Prof. Gross is a nobel prize winning quantum field theorist. The talk is brilliant. He obviously understands where Physics is at, which makes his explanations as simple as they can get at this stage (which still isn’t particularly simple). But it’s very entertaining and has some deep, beautiful animations that describe bits of string theory and (a real highlight) energy fluctuations in a vacuum.

As for me, I just submitted a paper to a journal called Applied Physics Letters entitled “Strong nonlinear optical response of graphene in the terahertz regime”.

With the development of things like Lasers, we’ve been able to make really strong, intense light sources. Most of physics has been formulated in the linear regime, because in general things change slowly. When you think about a circle, if you zoom into a small arc on the circle, and then zoom in some more, and just keep going, eventually the arc will just look like a straight line. If you have a ball rolling along the arc whose size is really really small compared to the arc, then you might as well do your physics along a straight plane, because that’s much simpler.

Even though the red ball is rolling inside a sphere, its motion can be approximated (in the short term) by motion along a plane

Well most of physics gets away with this sort of approximation. In particular, Ohm’s (so-called) law which is the well known V = IR has an equivalent field equation J = σE, which is that the current J is proportional to the field E by some factor σ. (σ is the conductivity tensor). The details don’t matter too much, except to note that it’s completely wrong. I have no idea what the actual relationship between J and E is, all I know is that all relationships (within reason) can be approximated by a polynomial, and the first significant term in a polynomial is the linear term. And so

J = σ₁E + σ₂E² + σ₃E³ + … ≈ σ₁E

So long as E is really small, this works just fine. But if E is big (like with a laser) you have to consider the next terms. We calculated

J ≈ σ₁E + σ₂E² + σ₃E³

and found that the second term is zero. So there’s just the first order term, and the third order term. The first order term is simple: light hits graphene, and graphene absorbs it. The third order term is still pretty simple, there are two parts to it:

1. Two photons hit graphene, one of them is absorbed, the other re-emitted.
2. Three photons hit graphene and they’re all absorbed.
   

   Three conductivity terms. The inside right one is the regular 'linear' conductivity. The other right hand side one is the frequency tripler. The one on the left is a correction to the linear term at strong fields, low temperatures, and low frequencies.

   The first one will alter graphene’s famous “universal conductivity” if the field is strong enough. The second is a frequency tripling term. This means that you hit graphene with some frequency, and the output is that frequency tripled. This is potentially a useful effect.

   Well, that’s our most recent result. It’s under review by APL right now… Should be good!