ACADEMIC RESEARCH • 學術研究 2023 UMAGAZINE 27 • 澳大新語 65 2D materials have gained widespread attention in both the scientific community and industry. To tap into the potential of these materials, our team at the University of Macau (UM) and the University of Texas at Austin (UT Austin) has proposed a new framework to understand how polarons form in 2D crystals and why they are so different in 2D and 3D structures, seeking to advance novel 2D applications in different fields. Interactions between Electrons and Phonons May Deform Materials This research project is a collaboration between me and Prof Feliciano Giustino in the Department of Physics at UT Austin. The concept of polarons was introduced in the 1930s by the Soviet physicist Lev D. Landau, who won the Nobel Prize in Physics in 1962. In the 1950s, polarons were observed experimentally for the first time. Over the decades, discoveries in this field have significantly contributed to advancements in photocatalysts, light-emitting diodes, solar energy harvesting, and beyond. To comprehend our theoretical framework, it is necessary to understand what a polaron is. Imagine yourself as an electron, attempting to enter a crystal lattice comprising several tens of thousands of atoms. As you move freely around, you quickly realise that the atoms surrounding you are shaking gently, thereby generating some vibrational patterns like ripples, namely phonons. Soon after, you start to interact with these phonons, a phenomenon known as electron-phonon interaction. When these interactions are strong enough, you find yourself becoming much heavier because you are now accompanied by a cloud of phonons that moves together with you. This not only makes you and the phonon cloud look like a massive particle, but also gives you the ability to deform the surrounding parts of the crystal structure and alter its physical properties. The intense interaction between the electron and the vibrations makes the electron behave differently than normal free electrons in a perfect crystal, which is called an electron polaron - a type of polarons. Polarons may be understood as a group of interacting particles that can change the properties of their host materials, rather than being a particular fundamental particle. They function much like when you walk inside a building, your friends surround and walk with you, and then your close interactions provide a collective power able to deform the building’s structure. In some cases, a polaron can trap itself, or become ‘self-trapped’, somewhere within the material’s structure. A trapped polaron can alter material properties, including an ability to modify the conductivities of electricity and heat, renormalise band gaps, and become more profound and stable than band electrons. A New Framework for Studying Polarons Nearly a century since polarons were first studied, it remains challenging to describe and predict the behaviour of polarons, largely because early polaron theories were developed based on relatively simple mathematical models. In fact, studying polarons and the related deformation of materials can involve describing at least ten thousand atoms and electrons within a material, a task that even certain modern supercomputers would find difficult. To fill this theoretical gap, we have developed a general theoretical framework that enables the computation of electronic and structural properties related to electron-phonon interactions in 2D and 3D materials. We have also clarified the analytical form, essentially a mathematical expression, of the interactions between electrons and phonons separated by long distances. Based on this newly developed framework, we have 本圖顯示了坱體（即三維）的白色石墨烯的球桿模型；硼原子和氮化物原子分 別以綠色和藍色標示。 This picture shows a ball-stick model of bulk (3D) white graphene, where boron and nitride atoms are visible in green and blue respectively.
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