S04E14: The Thespian Catalyst

Graphene is so yesterday.   This decade’s material-of-the-century are the tellurides.

At his official 2010 Nobel Prize acceptance lecture in Stockholm, Dr. Novoselov shows graphene, and Sheldon.

In his lecture, Sheldon told  his class (and about 15 million onlookers) about the strange behavior seen recently in certain compounds of bismuth, tellurium and tin. These strange new substances are insulators conductors insulators insulators and conductors simultaneously.  These tellurides and their cousins are part of a new class of recently discovered materials called, as Sheldon said,  topological insulators.

In materials such as typical plastics, electrons are pinned to the underlying structure and don’t move.    Because they can be used to keep conductors from shorting out, they are called insulators.  Relative to the best conductors, the electrical conductivity of the best insulators is 10²⁶ smaller, that’s a factor of 10,000,0000,000,000,000,000,000,000.   Few quantities in physics vary by so much.

On the whiteboards tonight, viewers saw bismuth telluride, cadmium telluride, and mercury telluride  making cameo appearances.    In these materials, the bulk volume is insulating–while the surfaces conduct.  At the same time.  How can that be?

Some clever wag may point out we could do this by just electroplating some plastic.  That was one of Richard Feynman’s first jobs and would be conductive on the outside but insulating in the middle.  But the difference here is that would be two materials.  Physicists never imagined this could be done with a single material at once.

The key difference from normal insulators is the reason they are called “topological”.  The description stems from the branch of mathematics called topology that characterizes the fundamental shapes of objects.   You can stretch a doughnut to form a coffee cup (one hole), but cannot make it into an object with two holes.   In the same way, the underlying structure of electron orbitals in an ordinary insulator can be represented by a simple loop.  A loop topologically distinct from the simplest possible knot:  a trefoil knot.

The structure of electron orbits in topological insulators are akin to the trefoil knot.

It turns out the interactions of the electrons’ spin with their orbital angular momentum creates a mathematical structure described by the trefoil knot.   For reasons beyond the ability of your science consultant to understand, the difference becomes apparent on the surface of the material: becoming metallic and conductive for the topological insulators but remaining non-conductive for normal insulators.  If you have a good explanation, please leave a comment.

Such effects have been seen before, but only with difficult-to-create flat structures.  But now, just like Hollywood, physicists have gone 3D with the advent  bismuth telluride.  Topological insulators can be created with standard semiconductor fabrication technology.  The simultaneous insulating and conducting nature of  the topological insulators is not an effect that can only be produced in expensive labs with high vacuums or extreme cooling.   These materials behave this way even at room temperature on the lab bench, or even held in your hand.

Work has heated up over the last five years and  many other compounds have been found to display not only the dual properties of topological insulators, crystals made of bismuth, selenium and copper have been made superconducting,moving electrons with no dissipation at all.

Topological insulators hold promise for new types of computing and materials whose applications we have not even thought of yet.  Their behavior is interesting in and of itself to physicists.  Sad to say, some popular articles have fallen prey yet again to the monopole falacy. This is the same annoying error that Sheldon complained about to Ira Flatow on NPR’s Science Friday.   Now in this latest article (and others) it says one of the interesting features of topological insulators is to make quasi-particle versions of axions, analogues of what are being sought in elementary particle physics.  However, just as with the magnetic monopole claims, that article misses the point completely:   Particle physicists don’t look for new particles  just to see their mathematical behavior.  We look for them because their existence  means something about the Universe.  In the case of the axion, it would validate certain explanations about why deep symmetries exist in nature. Axions could even be the dark matter in the galaxy.  But an axion-like-thing observed in a condensed matter system is not an axion.  It has none of that meaning.    Materials are topological insulators are still interesting in their own right. Such popular articles mislead readers at a deep level and do a disservice to these new materials by compromising the description of why they actually are interesting.

In fact topological insulators are so promising, we can only hope Sheldon’s boards will some day make a second appearance in Stockholm.  (And if, like Sheldon’s students, you want to tweet how boring this post is…hit the button below.)