IEEE Spectrum July, 2011 - 56

Topological
insulaTors

going in the same direction-
as part of a current-they collectively function as a magnet.
Continued from page 42
This effect is present in ordinary quantum wells but is
100 to 1000 times as strong in topological insulators.
Researchers have proposed several devices that take
advantage of this strong coupling between current density and
magnetic moment. Imagine putting a magnetic layer, such as
that used to store bits in a hard disk, on top of a topological
insulator. By running a small current in the topological insulator, one could efficiently read bits stored in the magnetic layer;
by running a larger current, the spin density induced in the
topological insulator could flip the state of the magnetic bit,
thereby writing over it.
Second, topological insulators are wonderfully robust
in the face of disorder. They retain their unique insulating/
surface-conducting character even when dosed with impurities and harried by noise. This ability is just another manifestation of a paradox of quantum behavior, which is unpredictable
on a quantum level but highly reliable on a macro level.
Such robustness was apparent in superconductivity, the
first macroscopic quantum behavior discovered, as well as in
its related phenomenon, superfluidity (the ability of supercold
helium to flow without viscosity). Both superfluids and superconductors show their properties in real materials that invariably contain impurities and inhomogeneities.
One source of this robustness is the topological invariance mentioned earlier. Just as the hole in a doughnut remains
a hole even when you wrench the material into the shape of a

coffee cup, 2-D electron gases have robust topological states
that retain their character in the face of disorder. These states
were originally observed in such gases only at very low temperatures and in very high magnetic fields.
u u u

n the summer of 2006, the three research groups mentioned
above predicted the existence of topological insulators by
considering the possibility that topological invariants may
come from spin-orbit coupling. As one of the people involved
in these predictions at the University of California, I can give
some anecdotal insight into how they came to happen.
We were inspired by a key 2005 paper by Charles Kane
and Eugene Mele of the University of
Pennsylvania. It explained a model
co m me nt s?
system in one lower dimension: A 2-D Write to us at
system such as a quantum well can have spectrum.ieee.
one-dimensional quantum wires at its org/insulator0711
edge, generated by spin-orbit coupling.
At that time, physicists had already
found many topological states in 2-D systems, both experimentally and theoretically, but the Kane-Mele proposal was
different in several obvious and not-so-obvious ways. I spent
the spring of 2006 working with Leon Balents of UCSB to
find a different formulation of the work of Kane and Mele that
would let us understand its connection to these older phases.
After a few weeks of intense mathematical fiddling, usually
Whitepaperad_1-4:Layout 1 9/12/08 1:17 PM Page 1
with a World Cup match playing in the background, it became
clear that there could be a 3-D version of their state, which was

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Table of Contents for the Digital Edition of IEEE Spectrum July, 2011