Recent work on graphene shows that the electron’s spin might arise because space at very small distances is not smooth, but rather segmented like a chessboard.
The standard cartoon of an electron shows a spinning sphere with positive or negative angular momentum, as illustrated in blue or gold above. However, such cartoons are fundamentally misleading: compelling experimental evidence indicates that electrons are ideal point particles, with no finite radius or internal structure that could possibly spin.
A quantum mechanical model of electron transport in graphene, a single layer of graphite (shown as a black honeycomb), presents a possible resolution to this puzzle. An electron in graphene hops from carbon atom to carbon atom as if moving on a chessboard with triangular tiles. At low energies the individual tiles are unresolved, but the electron acquires an “internal” spin quantum number which reflects whether it is on the blue or the gold tiles. Thus the electron’s spin could arise not from rotational motion of its substructure, but rather from the discrete, chessboard-like structure of space.
Credit: Chris Regan/CNSI
Physicists at UCLA set out to design a
better transistor and ended up discovering a new way to think about the
structure of space.
Space is usually considered infinitely
divisible—given any two positions, there is always a position halfway between.
But in a recent study aimed at developing ultra-fast transistors using
graphene, researchers from the UCLA Department of Physics and Astronomy and the
California NanoSystems Institute show that dividing space into discrete
locations, like a chessboard, may explain how point-like electrons, which have
no finite radius, manage to carry their intrinsic angular momentum, or spin.
While studying graphene’s electronic
properties, professor Chris Regan and graduate student Matthew Mecklenburg
found that a particle can acquire spin by living in a space with two types of
positions—dark tiles and light tiles. The particle seems to spin if the tiles
are so close together that their separation cannot be detected.
“An electron’s spin might arise because
space at very small distances is not smooth, but rather segmented, like a
chessboard,” Regan said.
Their findings are published in Physical Review Letters.
In quantum mechanics, spin up and spin down
refer to the two types of states that can be assigned to an electron. That the
electron’s spin can have only two values helps explain the stability of matter,
the nature of the chemical bond, and many other fundamental phenomena.
However, it is not clear how the electron
manages the rotational motion implied by its spin. If the electron had a
radius, the implied surface would have to be moving faster than the speed of light,
violating the theory of relativity. And experiments show that the electron does
not have a radius; it is thought to be a pure point particle with no surface or
substructure that could possibly spin.
In 1928, British physicist Paul Dirac showed
that the spin of the electron is intimately related to the structure of
space-time. His elegant argument combined quantum mechanics with special
relativity, Einstein’s theory of space-time.
Dirac’s equation, far from merely
accommodating spin, actually demands it. But while showing that relativistic
quantum mechanics requires spin, the equation does not give a mechanical
picture explaining how a point particle manages to carry angular momentum, nor
why this spin is two-valued.
Unveiling a concept that is at once novel
and deceptively simple, Regan and Mecklenburg found that electrons’ two-valued
spin can arise from having two types of tiles—light and dark—in a
chessboard-like space. And they developed this quantum mechanical model while
working on the practical problem of how to make better transistors out of a new
material called graphene.
Graphene is an atomically-thin layer of
carbon atoms arranged in a honeycomb structure. First isolated in 2004 by Andre
Geim and Kostya Novoselov, graphene has a wealth of extraordinary electronic
properties, such as high electron mobility and current capacity. In fact, these
properties hold such promise for revolutionary advances that Geim and Novoselov
were awarded the 2010 Nobel Prize a mere six years after their achievement.
Regan and Mecklenburg
are part of a UCLA effort to develop extremely fast transistors using this new
“We wanted to calculate the amplification
of a graphene transistor,” Mecklenburg
said. “Our collaboration was building them and needed to know how well
they were going to work.”
This calculation involved understanding how
light interacts with the electrons in graphene.
The electrons in graphene move by hopping
from carbon atom to carbon atom, as if hopping on a chessboard. The graphene
chessboard tiles are triangular, with the dark tiles pointing “up” and
light ones pointing “down.” When an electron in graphene absorbs a
photon, it hops from light tiles to dark ones. Mecklenburg
and Regan showed that this transition is equivalent to flipping a spin from
“up” to “down.”
In other words, confining the electrons in
graphene to specific, discrete positions in space gives them spin. This spin,
which derives from the special geometry of graphene’s honeycomb lattice, is in
addition to and distinct from the usual spin carried by the electron. In
graphene the additional spin reflects the unresolved chessboard-like structure
to the space that the electron occupies.
“My adviser [Regan] spent his PhD
studying the structure of the electron,” Mecklenburg
said. “So he was very excited to see that spin can emerge from a lattice.
It makes you wonder if the usual electron spin could be generated in the same
“It’s not yet clear if this work will
be more useful in particle or condensed matter physics,” Regan said,
“but it would be odd if graphene’s honeycomb structure was the only
lattice capable of generating spin.”