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What Are Some Topology Applications in Science?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

Topology applications in science

Topology applications in science

What Is Topology?

Topology is a difficult topic to discuss, yet here I am about to embark on a (hopefully) interesting article about it. To over-simplify, topology involves studying how surfaces can change from one to another.

Mathematically, it is complex, but that doesn’t prevent us from tackling this topic in the physics world. Challenges are a good thing to encounter, tackle, and overcome. Now, let’s get to it.

Changing Light Rotations

Scientists have had the ability to alter the polarization of light for years via the magneto-optical effect, which cashes in on the magnetic portion of electromagnetism and applies an external magnetic field to tug on our light selectively. The materials we usually use for this are insulators, but the light undergoes the changes inside the material.

With the arrival of topological insulators (which allow for charge to flow with little to no resistance on their exteriors due to their insulator nature on the interior while being a conductor on the exterior), this change happens on the surface instead, according to work by the Institute of Solid State Physics at TU Wien. The surface’s electric field is the deciding factor, with the light entering and exiting the insulator allowing for two changes to the angle.

On top of that, the changes that occur are quantized, meaning it happens in discrete values and not in a continuous matter. In fact, these steps are manipulated based only on constants from nature. The material of the insulator itself does nothing to alter this, nor does the geometry of the surface (Aigner).

Non-Scattered Light

Light and prisms are a fun pairing, producing lots of physics that we can see and enjoy. We often use them to break down light into its component parts and produce a rainbow. This scattering process results from the different wavelengths of light being bent differently by the material they are entering. What if we could instead just have the light travel around the surface instead?

Researchers from International Center for Materials Nanoarchitechtonics and the National Institute for Materials Science accomplished this with a topological insulator made of a photonic crystal which is either insulator or semiconductor silicon nanorods oriented to create a hexagonal lattice within the material. The surface now has an electrical spin that allows the light to travel unimpeded by the refractive material it enters. By changing the size of this surface by bringing the rods closer, the effect improves (Tanifuji).

Light play.

Light play.

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Topological Layers

In another application of topological insulators, scientists from Princeton University, Rutgers University, and Lawrence Berkley National Laboratory created a layered material with normal insulators (indium with bismuth selenide) alternating with topological ones (just the bismuth selenide). By changing the materials used to develop each insulator type, scientists “can control the hopping of electron-like particles, called Dirac fermions, through the material.”

Adding more of the topological insulator by altering the indium levels reduces current flow but making it thinner allows for the fermions to tunnel to the next layer with relative ease, depending on the orientation of the stacked layers. This creates a 1D quantum lattice that scientists can fine-tune into a topological phase of matter. With this setup, experiments are already being devised to use this as a search for Majorana and Weyl fermion properties (Zandonella).

Topological phases

Topological phases

Topological Phase Changes

Like how our materials go through phase changes, so can topological materials but in a more…unusual way. Take, for example, BACOVO (or BaCo2V2O8), an essentially 1D quantum material that orders itself into a helical structure. Scientists from the University of Geneva, the University Grenoble Alpes, CEA, and CNRS used neutron scattering to delve into the topological excitations BACOVO undergoes.

By using their magnetic moments to disturb BACOVO, scientists gleaned information about the phase transitions it undergoes and found a surprise: two different topological mechanisms were at play at the same time. They compete with each other until only one remains, then the material undergoes its quantum phase change (Giamarchi).

The helical structure of BACOVO.

The helical structure of BACOVO.

Quadruple Topological Insulators

Normally, electronic materials either have a positive or a negative charge, hence a dipole moment. Topological insulators, on the other hand, have quadruple moments, which result in groupings of 4, with subgroupings providing the four charge combinations.

This behavior was studied with an analog accomplished using circuit boards with a tiling property. Each tile had four resonators (which take in EM waves at specific frequencies) and created a crystal-like structure that mimed topological insulators upon putting the boards end-to-end. Each center was like an atom, and the circuit pathways acted like bonds between atoms, with the ends of the circuit acting like conductors to fully extend the comparison. By applying microwaves to this rig, researchers were able to see electron behavior (because photons are the carriers of EM force). By studying the locations with the most absorption, the pattern indicated the four corners as predicted, which would only arise from a quadruple moment as theorized by topological insulators (Yoksoulian).

The circuit tile.

The circuit tile.

Works Cited

  • Aigner, Florian. “Measured for the first time: Direction of light waves changed by quantum effect.” innovations report, 24 May 2017. Web. 22 May 2019.
  • Giamarchi, Thierry. “The apparent inner calm of quantum materials.” innovations report, 08 May 2018. Web. 22 May 2019.
  • Tanifuji, Mikiko. “Discovery of a New Photonic Crystal where Light Propagates through the Surface without being Scattered.” innovations report, 23 Sept. 2015. Web. 21 May 2019.
  • Yoksoulian, Lois. “Researchers demonstrate existence of new form of electronic matter.” innovations report, 15 Mar. 2018. Web. 23 May 2019.
  • Zandonella, Catherine. “Artificial topological matter opens new research directions.” innovations report, 06 Apr. 2017. Web. 22 May 2019.

© 2020 Leonard Kelley

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