topological insulator

Researchers at the SLAC laboratory have shown theoretically that the surface states of topological insulators generate more intense harmonics when subject to circularly-polarized light. [Image: Greg Stewart, SLAC National Accelerator Laboratory]

Physicists are keen to find out more about the unusual properties of “topological insulators,” materials that conduct electricity on their surface even though they are bulk insulators—and which could have applications in quantum information processing.

Now, researchers in the U.S. have found that a new optical technique should be able to probe even the most fleeting effects within a three-dimensional topological insulator. They have shown theoretically that when exposed to polarized light from an intense laser source, the bulk and surface states of such a material should generate very distinct signatures (Phys. Rev. A, doi: 10.1103/PhysRevA.103.023101).

Probing electron behavior

The electrons inside topological insulators have wavefunctions that evolve in such a way that they cannot be smoothly changed to match those of ordinary insulators or a vacuum—just as it isn’t possible to smoothly change a sphere so that it becomes a doughnut. Instead, the electronic wavefunctions’ topology shifts abruptly at the material’s boundary, resulting in a topologically-protected conducting surface.

This effect relies on two quantum-mechanical ingredients. One is spin-orbit coupling, the interaction between an electron’s intrinsic angular momentum and the momentum due to its orbital motion. This allows the valence and conduction bands to have their shapes inverted and even intersect one another.

The other element is time-reversal symmetry protection, which means that spin-up electrons propagate in one direction while spin-down electrons travel in the opposite direction—without affecting one another. “In a sense, the surface states act like divided highways, which clearly separates traffic into two directions,” says Shambhu Ghimire of the SLAC National Accelerator Laboratory in Menlo Park, CA, USA.

3D topological insulators

The topological insulator studied in the latest work by Ghimire and colleagues at SLAC and Stanford University, USA, is made from the semiconductor bismuth selenide. The heavy bismuth atoms provide a strong spin-orbital force, while time-reversal symmetry is protected by what Ghimire describes as the material’s nondegenerate surface bands. With the electrons’ spin and momentum locked to one another, reversing the particles’ direction would mean flipping their spin—which isn’t possible.

Such 3D topological insulators were discovered experimentally a little over a decade ago and have since been the object of intense study by research groups around the world. Among their possible applications are transistors that generate no heat when they operate and spin-based electronics. The all-optical method exploited in the latest research adds to the suite of spectroscopic techniques used to probe these materials, with the advantage, says Ghimire, that the sample does not need to be in a special condition such as being placed inside a vacuum chamber.

Ghimire and co-workers embarked on experimental studies of topological insulators by investigating under what conditions the materials would generate higher harmonics of incoming laser light. This comes after having carried out such experiments on conventional insulators and semiconductors for about a decade.

Switching to theory

Unfortunately, the researchers had to put their new work on hold when the COVID-19 pandemic led SLAC to halt all but the most essential experiments at the lab. So, they switched instead to theory, elaborating a computer model that could reproduce the experiments they were planning to carry out. Those calculations have now turned up an unexpected difference in the response of the material’s bulk and surface states to certain polarizations of the light.

The researchers found that the intensities of all harmonics generated in the bulk should drop to zero as the light’s polarization becomes more elliptic—in other words, as it is varied from purely linear to circular. That behavior, they point out, is in line with the generation of harmonics inside gases.

But they found quite a different response in the case of the material’s surface states. They calculated that the harmonics’ intensity actually increases as the laser light becomes more elliptical, and it reaches a maximum when the light is fully circularly-polarized.

The researchers say that while they did the calculations specifically for bismuth selenide, their results should apply to all 3D topological insulators. They acknowledge that their model has its limitations, including the fact that it cannot account for electronic transitions between the surface and bulk states induced by the laser pulses. Nevertheless, they hope that their study will “spark interest in the materials-science community.”