Seeking topological phase transition applying pressure to Ag3AuSe2 and Ag3Te2Au

Abstract

[EN] For many years the Solid State Physics has contributed significantly to the modern society, giving a profound understanding of how semiconductors behave, which led to a revolution with the improvement of transistors. Furthermore, the striking advances in computation have assisted to solve numerically heavy calculus, such as the ones arisen from Quantum Theory, which includes calculations regarding crystals. Recently, a whole new field of Solid State Physics has arisen, the Topological Materials, but we will focus on the Topological Insulators (TI). A topological insulator is a material with non-trivial symmetry-protected topological order that behaves as an insulator in its interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material. However, having a conducting surface is not unique to topological insulators, since ordinary band insulators can also support conductive surface states. What makes TI special is that their surface states are symmetry-protected by particle number conservation and time-reversal symmetry. Topological insulators are characterized by an index (known as Z2 topological invariants) similar to the genus1 in topology. As long as time-reversal symmetry is preserved, in other words, as long as there is no magnetism, the Z2 index cannot change by small perturbations and the conducting states at the surface are symmetry-protected. A brand new way to study TI is presented in the literature [1], where they use Group Theory in order to determine the topology of crystals. One important property of these topological invariants is that they are robust against perturbations. In a few years, different phases displaying topological properties have been found: topological insulators, Weyl semimetals and non symmorphic materials whose electric properties are protected by time reversal symmetry or some crystalline symmetry. A Weyl node is basically a band crossing close to the Fermi level, where the dispersion is linear and is protected by time reversal or inversion symmetry. Consequently, the charge carriers, responsible for electrical conduction, can be considered as massless fermions, supported theoretically by the Dirac equation. The main objective of this project is to seek topological materials, for this purpose we will study two crystals, Ag3AuSe2 and Ag3Te2Au. These materials are trivial insulators under zero pressure, therefore, we will apply pressure to each material and calculate their band structure, with the information obtained from those calculations we will be able to determine if the material is topological or not, as we will explain in section B. In this dossier we will start introducing topological matter, then we will explain some basics about the Density Functional Theory (DFT), and we will define some important concepts about topology, which are related with the topic of this project, such as representations and irreducible representations. Next we will expose some general properties of the materials we are studying (symmetry group, lattice parameters, band structure...). After that we will apply pressure to the materials and observe how the band structure changes, yielding to new topological properties. Finally, we will present some conclusions about the results we obtain.