Today, we are going to tackle a topic that every science journalist fears deeply: topological insulators. Fear not dear reader, once your head explodes, you'll feel nothing. Besides, these aren't just any topological insulators, they're topological insulator lasers, which definitely makes the pain worthwhile.

The question that should be foremost in your mind is: why would you combine the least-easily explained concept in physics with something so cool as lasers? And the answer is because it makes for a pretty good laser.

Before we get to how a topological insulator can improve a laser, let's take a look at what makes a laser so difficult.

You make one tiny mistake...

Lasers are delicate beasts. Defects, in the form of dust, the alignment of mirrors, and myriad other details reduce their efficiency and can even cause a laser to destroy itself. Yes, I have painful, personal experience of this.

The problems go further than that though. When you make a laser, what you often want is a specific color of light and a specific intensity profile to the laser beam. Nature, however, just wants to mess with you. At very low power, you will (assuming competence in design and construction) get what you desire.

But as you ramp the input power up, new colors will start to show up: your laser may produce several colors at once. The new colors may even suppress the color you desire. This dance of colors will destabilize the output power. Even the beam profile will start to get messed up as the power increases.

Much time and effort is devoted to engineering away these problems.

OK, sigh, topology it is

This is where the idea of topological states comes in. This is not so complex as it sounds, but to understand it, we are going to abandon lights and lasers for electrons and insulators. And not once mention topology.

Imagine we have a crystalline material. All the atoms are arranged in an ordered array. The electrons should be thought of as waves, sloshing around the nuclei. Waves mix, though, so some mix so that they add up to a stronger wave, and others mix in such a way that they cancel out to become weaker. The result is that the electrons must have certain wavelengths and energies that correspond to waves that don't cancel out.

When you sum all this up, you end up with two bands of energies. In the lower band, the electrons don't have much energy and are confined, staying close to their home nuclei. In the higher-energy band, the electrons are free, like the buffalo, to wander through the vast crystalline prairie. These are conducting electrons.

No electrons have energies that fall in the gap between the two bands, because those are the waves that cancel out. That brings us back to insulators. Insulators are materials for which the gap between the two bands is so large that the top band is basically empty.

This is true everywhere except at the surface. The surface is where the nice, regular array of nuclei stops, and the symmetry that gives us the two bands is broken. So, for some materials, the interior is an insulator, but the surface may allow electrons to occupy states that conduct.

Surfaces are weird

It gets better, though. In some cases, the surface states can take on a very peculiar nature. Electrons moving in one direction along a surface have their spin—spin is the orientation of their intrinsic angular momentum—oriented in one direction. To reverse direction, the spin also has to flip. These states are described by the mathematics of topology, which is where the name and the fear come from.

In any material, collisions that reverse an electron's direction are very common. Every atom that is just slightly out of place, every missing atom in a flat surface, and every atom of the wrong sort is a defect just waiting to whack the electron back in the direction it came from. This sort of collision only requires that the atom recoil slightly and jiggle in place for a bit, and atoms have complete freedom to do that.

What these atoms can't easily do is flip the electron's spin. This is hard because if the electron's spin flips, then a spin elsewhere has to flip. That might be an electron that is still bound to an atom. For that bound electron to flip its spin, it probably has to change its energy significantly. And, if you remember from above, changing an electron's energy in an insulator is really difficult.

What does that all mean? Let's imagine that I apply a voltage across my insulator. In the bulk of the insulator, nothing happens. But, on the surface, electrons start to flow. Normally, these electrons would scatter like crazy off of all the surface defects. But, because doing so requires them to flip spin, that can't happen unless they can also give up some energy. There is no easy way to give up energy, so the electrons flow nicely from one end to the other, as if the defects did not exist.

So, while most of the material is happily resisting the flow of electrons, they're flowing with minimal resistance on the surface.

You promised me lasers

By now, you might sort of see where we are going with this. These surface states contain electrons that are protected from scattering off of defects. If you can construct a laser so that the light is in a protected state, it should be very efficient. Those states should also have a specific energy and momentum. That means that the emission color of the laser should be a well-defined wavelength, and the spatial profile of the emission should remain in just one shape.

On the other hand, the math that is used to understand these protected surface states assumes that you can't amplify the number of electrons, while a laser does exactly that to photons. So, no one was exactly sure if a topological insulator laser could exist.

And now we know that it does.

Swapping electrons for photons

Let's go back to our crystal: an ordered array of atoms that has an empty conduction band. We're going to replace that with rings of optical waveguides that are close enough to each other that light can leak from one waveguide to another (remember this; it's going to be important in a moment). These waveguides are constructed from a material that, when excited appropriately, can emit light. When not excited, it can absorb light. If we do nothing, then the whole 2D crystal is an insulator: no matter where we inject light, it goes nowhere.

Alternatively, we could excite the whole crystal (this is done by shining laser light on the lattice). With the lights on, the crystal will behave like a conductor: if we inject light, it will be amplified and travel around the crystal.

Finally, we can create an edge conductor by only exciting the rings that are on the outside of the crystal. Now, light that is injected into the crystal must travel around the edge—it is absorbed in the interior.

However, this is not a protected state, and defects will still scatter light. The protected state comes about because of the way light leaks from one ring, through the nearest neighbor, and on to the ring beyond that. This is done with intermediary rings that are carefully placed to shift the phase of the light as it jumps from ring to ring.

To summarize: the way the rings are excited ensures that light can only travel around the edges, while the way the rings are interconnected ensures that light can only be scattered out of the ring if it changes color. (To be more precise, light that is not in the protected state is scattered out of the crystal immediately, leaving only light that is in the protected state.) The remaining light is then amplified by the laser gain material, so that it quickly dominates.

This research really demonstrates the importance of modeling. If the researchers had not been able to model the laser accurately, they would never have been able to get the design right. On the experimental side, the fabrication tolerances must have been amazingly tight. We talk about how these topological states are protected from defects, but I'm not sure that applies to the placement of the rings that create the topological state in the first place. I think that had to be very carefully done, otherwise the energy gap between the topologically protected state and unprotected states would have been smeared out, which would have ruined the laser's performance.

Amazingly enough, though, it seems to work. The researchers constructed several crystals that either supported a protected edge state or an unprotected edge state. The comparison between the two shows that the protected state is really protected: you can knock out rings and the laser keeps going nicely. The laser that operates in the protected state is much more efficient. And, as you crank the power to the laser up, new colors do not show up in the topological insulator laser, while they do in the laser with an unprotected edge state.

This is exciting research. These sorts of lasers—those with a very specific color and a sharply defined wavelength—are critical to things like 5G networks and space-based interferometers. For high-end applications, I can imagine these leaving the lab pretty soon.

Science, 2018, DOI: 10.1126/science.aar4005

Science, 2018, DOI: 10.1126/science.aar4003 (About DOIs).