Emmy Noether. A not well known female scientist

ORIGINAL: Yonatan Zunger

Portrait of Emmy Noether.  (1910). nhn.ou.edu/

There are some people who are simply insufficiently famous, and Emmy Noether is one of them. Now, mathematicians may claim her as one of their own, merely because she was a professor of mathematics for several decades and made more foundational and revolutionary contributions to the study of groups, rings, and algebras than I could easily list in a post, pioneering numerous basic techniques and having important mathematical structures named after her. But all of this manages to pale next to her contribution to physics; and being an ex-physicist, and thus feeling no reason not to be horribly biased about this, I want to tell you about Noether's Theorem: her 1915 proof that is, perhaps, the single most important result in mathematical physics. And when I say the single most important result, I mean not only that most of modern physics is built on top of it, but working theoretical physicists actually use this theorem several times a day.

Her theorem relates two seemingly unrelated things: symmetries and conserved charges. A physical system has a symmetry if there's some way to transform it which leaves all of its behavior the same. For example, if you took the entire Solar System and moved it three feet to the left, nobody could tell the difference. Similarly, if you rotated a sphere around any of its axes, nothing about them would change. Some symmetries are discrete, which means that they can only take on a fixed set of jumps: for example, you can rotate a square by 0°, 90°, 180°, or 270° and it will look the same, but if you rotate it by 260° it will look different. Other symmetries are continuous, which means that there's a continuous range of transformations you can make: e.g., you can rotate a circle by any angle, rotate a sphere by any angle along three different axes, or translate (shift) a physical system by any distance along any of three axes, or forward and backwards in time. Noether's Theorem actually applies to both kinds of symmetry, but the continuous ones are the most interesting ones.

There's an obvious reason that symmetry is important in physics: it tells you about things you can ignore, and strip out of your calculation, e.g. the overall angle of your experiment. 

Giving graphene the bends makes it transistor-ready

ORIGINAL: New Scientist

 by Douglas Heaven

23 November 2012

Transistor-ready (Image: Alfred Pasieka/Getty)

Sometimes bending something destroys it, but graphene grown on a rippling surface develops the semiconducting properties required for it to act as a transistor. The technique could be what's needed for the wonder material to finally replace silicon as the bedrock of computing.

Graphene is a sheet of carbon just one atom thick, with the atoms arranged in a hexagonal grid, like chicken wire. As well as being thin, super-strong and very flexible, this structure allows electrons to zip through at high speeds. It therefore seems poised to become the basis for ultra-fast computers.

But there's a problem. Materials used to make transistors have to be able to switch current on and off to create logic circuits. This switchability depends on there being a difference, known as a band gap, between the energy possessed by the material's free electrons, and the energy they would need to move around and conduct electricity. Only applying the right amount of external energy allows electrons to jump the band gap to become conducting.

Semiconductors like silicon have band gaps, making for good transistors. But because of its natural conductivity, graphene has a band gap of zero – making it unsuitable for transistors.

Nanoribbon solution

Various solutions have been proposed for turning graphene into a semiconductor, including adding an insulating layer between two layers of graphene to reduce its conductivity, or carving it into very narrow ribbons, which alters its structure, making it easier to turn current off.

However, both of these use conventional etching techniques, placing limits on just how small such graphene transistors could get. For example, creating ribbons any less than 10 nanometres wide has until now left them with edges so ragged that the band gap disappears.

Now Ed Conrad at the Georgia Institute of Technology in Atlanta and colleagues have found a way to create much narrower nanoribbons, without destroying their semiconductor capabilities, in a much simpler way.

The trick was to grow graphene sheets on a rippling surface covered in parallel trenches, each 18 nanometres deep. The team found that where the surface of the sheet dipped into a trench, the graphene's properties became semiconducting, with a band gap of 0.5 electronvolts, rather like the nanoribbons. Crucially, however, these strips of semiconductor were just 1.5 nanometres wide and sleek, not ragged.

Silicon replacement?

"The results are very important, because the existence of a band gap makes it possible to use graphene in nanoelectronics," says Luis Brey at the Materials Science Institute in Madrid, Spain. But the reason the gap exists is not yet clear. "More theoretical work is needed in order to understand how a 0.5 electronvolt gap appears in this structure," he says.

Chris Howard at University College London calls the work a strong development that opens up many potential applications, including high-performance electronics.

Silicon won't be replaced just yet, adds Conrad. "But graphene could push Moore's law to its limits."

Journal reference: Nature Physics, DOI: 10.1038/nphys2487