A team of scientists from Princeton University has measured the energies of electrons in a new class of quantum materials and has found them to follow a fractal pattern. Fractals are self-repeating patterns that occur on different length scales and can be seen in nature in a variety of settings, including snowflakes, ferns, and coastlines. The image shows a quantum version of a fractal pattern, known as “Hofstadter’s butterfly,” which has long been predicted, but the new study marks the first time it has been directly observed experimentally in a real material. Credit: Yazdani group

Researchers Captured Elusive Quantum Hofstadter’s Butterfly Pattern

Princeton physicists accidentally discovered and directly visualized Hofstadter’s butterfly—a theoretical fractal pattern of electron energy levels predicted in 1976—using scanning tunneling microscopy on twisted bilayer graphene, revealing not only the long-sought fractal energy spectrum but also new quantum phenomena driven by electron interactions beyond Hofstadter’s original calculations.

About this cookie policy

This Cookie Policy explains what cookies are and how we use them, the types of cookies we use i.e, the information we collect using cookies and how that information is used, and how to control the cookie preferences. For further information on how we use, store, and keep your personal data secure, see our Privacy Policy.You can at any time change or withdraw your consent from the Cookie Declaration on our website
Learn more about who we are, how you can contact us, and how we process personal data in our Privacy Policy.
Your consent applies to the following domains: thequantumfacts.com
[user_consent_state]

What are cookies ?

Cookies are small text files that are used to store small pieces of information. They are stored on your device when the website is loaded on your browser. These cookies help us make the website function properly, make it more secure, provide better user experience, and understand how the website performs and to analyze what works and where it needs improvement.

How do we use cookies ?

As most of the online services, our website uses first-party and third-party cookies for several purposes. First-party cookies are mostly necessary for the website to function the right way, and they do not collect any of your personally identifiable data.The third-party cookies used on our website are mainly for understanding how the website performs, how you interact with our website, keeping our services secure, providing advertisements that are relevant to you, and all in all providing you with a better and improved user experience and help speed up your future interactions with our website.

What types of cookies do we use ?

Essential: Some cookies are essential for you to be able to experience the full functionality of our site. They allow us to maintain user sessions and prevent any security threats. They do not collect or store any personal information. For example, these cookies allow you to log-in to your account and add products to your basket, and checkout securely.Statistics: These cookies store information like the number of visitors to the website, the number of unique visitors, which pages of the website have been visited, the source of the visit, etc. These data help us understand and analyze how well the website performs and where it needs improvement.

Marketing: Our website displays advertisements. These cookies are used to personalize the advertisements that we show to you so that they are meaningful to you. These cookies also help us keep track of the efficiency of these ad campaigns.
The information stored in these cookies may also be used by the third-party ad providers to show you ads on other websites on the browser as well.

Functional: These are the cookies that help certain non-essential functionalities on our website. These functionalities include embedding content like videos or sharing content of the website on social media platforms.

Preferences: These cookies help us store your settings and browsing preferences like language preferences so that you have a better and efficient experience on future visits to the website.
[cookie_audit columns=”cookie,description” heading=”The below list details the cookies used in our website.”]

How can I control the cookie preferences ?

Should you decide to change your preferences later through your browsing session, you can click on the “Manage consent” tab on your screen. This will display the consent notice again enabling you to change your preferences or withdraw your consent entirely.In addition to this, different browsers provide different methods to block and delete cookies used by websites. You can change the settings of your browser to block/delete the cookies. To find out more about how to manage and delete cookies, visit wikipedia.org, www.allaboutcookies.org.