What Are Some Topology Applications in Science?

Updated on May 15, 2020
1701TheOriginal profile image

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

Source

Topology is a difficult topic to talk about, yet here I am about to embark on a (hopefully) interesting article about it. To over-simplify, topology involves the study of 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, to tackle, to 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 applying 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. Often, we use them to break down light into its component parts and producing a rainbow. This process of scattering is a result of 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 moment that allows the light to travel unimpeded by the refractive material it enters. By changing the size of this surface by bringing in the rods closer, the effect gets better (Tanifuji).

Light play.
Light play. | Source

Topological Layers

In another application of topological insulators, scientists from Princeton University, the Rutgers University and the 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 ends up essentially creating 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).

Source

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 which 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 that BACOVO undergoes.

By using their magnetic moments to disturb BACOVO, scientists gleamed 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. | Source

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 4 charge combinations.

This behavior was studied with an analogue accomplished using circuit boards with a tiling property. Each tile had four resonators (which take in EM waves at specific frequencies) and upon putting the boards end-to-end created a crystal-like structure that mimed topological insulators. 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, and the pattern indicated the four corners as predicted, which would only arise form a quadruple moment as theorized by topological insulators (Yoksoulian).

The circuit tile.
The circuit tile. | Source

Works Cited

  • Aigner, Florian. “Measured for the first time: Direction of light waves changed by quantum effect.” Innovations-report.com. innovations report, 24 May 2017. Web. 22 May 2019.
  • Giamarchi, Thierry. “The apparent inner calm of quantum materials.” Innovations-report.com. 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.com. innovations report, 23 Sept. 2015. Web. 21 May 2019.
  • Yoksoulian, Lois. “Researchers demonstrate existence of new form of electronic matter.” Innovations-report.com. innovations report, 15 Mar. 2018. Web. 23 May 2019.
  • Zandonella, Catherine. “Artificial topological matter opens new research directions.” Innovations-report.com. innovations report, 06 Apr. 2017. Web. 22 May 2019.

Questions & Answers

    © 2020 Leonard Kelley

    Comments

      0 of 8192 characters used
      Post Comment

      No comments yet.

      working

      This website uses cookies

      As a user in the EEA, your approval is needed on a few things. To provide a better website experience, owlcation.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

      For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://maven.io/company/pages/privacy

      Show Details
      Necessary
      HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
      LoginThis is necessary to sign in to the HubPages Service.
      Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
      AkismetThis is used to detect comment spam. (Privacy Policy)
      HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
      HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
      Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
      CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
      Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
      Features
      Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
      Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
      Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
      Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
      Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
      VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
      PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
      Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
      MavenThis supports the Maven widget and search functionality. (Privacy Policy)
      Marketing
      Google AdSenseThis is an ad network. (Privacy Policy)
      Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
      Index ExchangeThis is an ad network. (Privacy Policy)
      SovrnThis is an ad network. (Privacy Policy)
      Facebook AdsThis is an ad network. (Privacy Policy)
      Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
      AppNexusThis is an ad network. (Privacy Policy)
      OpenxThis is an ad network. (Privacy Policy)
      Rubicon ProjectThis is an ad network. (Privacy Policy)
      TripleLiftThis is an ad network. (Privacy Policy)
      Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
      Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
      Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
      Statistics
      Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
      ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
      Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
      ClickscoThis is a data management platform studying reader behavior (Privacy Policy)