Identification of Topological Phases in three- and two-dimensional ZrTe₅

Topological insulators have been intensively studied over the past decades. Among them, zirconium pentatelluride (ZrTe₅) stands out as one of the most intriguing systems, exhibiting a range of remarkable phenomena such as the nonlinear anomalous Hall effect, three-dimensional (3D) quantum Hall effect (QHE), superconductivity, and topological phase transition tuned by strain. Structurally, ZrTe₅ consists of bonded atomic layers held together by van der Waals forces. Despite extensive studies, identifying a topological phase in 3D bulk ZrTe₅ has proven challenging, and the minimum number of layers required to sustain its exotic quantum responses, such as QHE, is still unclear.



In this work, we employ density functional theory (DFT) to study the electronic structure and quantum oscillations exhibited by various topological phases of 3D bulk ZrTe₅. By analysing patterns in band structures, Fermi surfaces, and Shubnikov-de Haas (SdH) oscillations, we demonstrate that distinct topological phases can be identified without performing conventional calculations of topological invariants or boundary state contributions.



Extending the research to two-dimensional systems, we investigate the bilayer configuration of ZrTe₅. The latter is widely regarded as the 2D limit where bulk-like quantum phenomena emerge owing to its structural similarity to the 3D crystal. Using DFT combined with symmetry analysis, we study signatures of possible 2D topological phases and explore the emergence of a 2D spin QHE.