The interplay between magnetism and electronic structure in topological materials

Abstract

Over the past 40 years, topological materials have emerged as a fascinating new class of phases of matter, characterized by their robust fundamental properties that remain invariant under smooth changes of material parameters, capturing widespread interest and driving extensive research in the field. The more recent realization of magnetic topological materials has unlocked new research directions, as these materials display a remarkable interplay between magnetic order and topological electronic properties. This connection leads to various exotic phenomena and emergent quantum states, such as the quantum anomalous Hall effect, axion insulators, and magnetic Weyl semimetals. Moreover, these materials provide opportunities to study topological phase transitions with easily tunable magnetic fields, facilitating a deeper understanding of the underlying physics and paving the way for the exploration of novel phenomena rooted in unique topological properties. In the intrinsic antiferromagnetic topological insulator MnBi$_{2}$Te$_{4}$, various topological phases across different dimensions and types of magnetism provide a unique platform for studying the interplay between band topology and magnetic order. The ground state of bulk MnBi$_{2}$Te$_{4}$ is an antiferromagnetic topological insulator protected by the combined half-layer lattice translation and time-reversal symmetry ($S = \tau_{1/2}\mathcal{T}$). In the thin film limit, both quantum anomalous Hall insulator states and axion insulator states have been reported in odd and even septuple layers, respectively. In the bulk field-induced ferromagnetic state, MnBi$_{2}$Te$_{4}$ has been predicted to be an ideal type-II Weyl semimetal with a single pair of Weyl nodes. Moreover, due to the intertwined electronic structures and magnetic orders, it is possible to tune the type-II Weyl semimetal to a type-I Weyl semimetal across a Lifshitz transition by altering the magnetic field angle. Furthermore, the highly tunable properties of MnBi$_{2-x}$Sb$_{x}$Te$_{4}$ make it an adaptable platform for investigating other topological phases through Lifshitz transitions under external fields such as strain and pressure. In this thesis, I investigate the electronic structures and their interplay with magnetism in the magnetic topological material MnBi$_{2-x}$Sb$_{x}$Te$_{4}$, identifying distinct Lifshitz transitions. We first use quantum oscillations as a probe to study the electronic structure of MnBi$_{2-x}$Sb$_{x}$Te$_{4}$ in the field-induced ferromagnetic state, where Sb substitution effectively tunes the chemical potential. We then identify the field-induced ferromagnetic MnBi$_{2-x}$Sb$_{x}$Te$_{4}$ as an ideal type-II Weyl semimetal with a single pair of Weyl nodes near the Fermi energy. By employing a combination of quantum oscillations and high-field Hall measurements, we demonstrate that the evolution of Fermi surfaces can only be explained by the band structure of an ideal type-II Weyl semimetal. Additionally, We observe a strong dependence of the anomalous Hall conductivity on doping near the charge neutrality point, displaying a singular, heartbeat-like behavior as the Fermi level is tuned across the Weyl nodes. This unique behavior is in agreement with the theoretical predictions for a type-II WSM. Furthermore, we utilize the external magnetic field angle as a tuning knob and observe evidence of an in-situ controlled Lifshitz transition from a type-II Weyl semimetal to a type-I Weyl semimetal as the magnetic field angle rotates from the crystal c-axis to the a-b plane. Finally, we investigate the effect of hydrostatic pressure on the electronic structures and magnetic properties of FM-z MnBi$_{2-x}$Sb$_{x}$Te$_{4}$, revealing extreme sensitivity and possible creation of a new pair of Weyl nodes in response to external pressure. Our work deepens the understanding of Weyl semimetals through a comprehensive study of an ideal Weyl semimetal, highlighting MnBi$_{2-x}$Sb$_{x}$Te$_{4}$ as an exceptional platform for further investigations into Weyl physics. Additionally, our findings pave the way for future research on magnetic topological materials and external-field-controlled Lifshitz transitions, foreshadowing exciting developments in the field of topological materials.