UCLA

Since the theoretical proposals of topological phases of matter and topological phase transitions, the experimental realization of topological materials and associated emerging phenomena had become an essential goal in condensed matter physics. The experimental discoveries of the quantum Hall effect (QHE), the quantum spin Hall effect (QSHE), and three-dimensional (3D) time-reversal symmetry protected topological insulators (TIs) further sparked intensive research effort, leading to a kaleidoscope of topological phases and realizations of diverse topological materials, such as Dirac semimetals, Weyl semimetals, magnetic topological insulators, topological superconductor, etc. A topological phase of matter is distinguished from trivial materials by showing a nonzero topological invariant and topologically protected surface states, which result in exotic phenomena in its transport, thermodynamic, optical and other physical properties. Practically, new topological phases may be realized by combining the topological band structure with other physical aspects. For example, breaking time reversal symmetry in an existing TI by introducing ferromagnetism or net magnetization, a gaped surface state with dissipationless edge conduction may emerge, resulting in the quantum anomalous Hall effect (QAHE) in the absence of external magnetic field.

My thesis focuses on the study of topological materials with two major research themes. One is the synthesis, characterization and tuning of ternary Mn-Bi-Te magnetic topological insulators, including the synthetic exploration of new magnetic topological insulators, with a focus on the investigation of the interplay of magnetism and band topology through doping and external pressure. The other involves investigating proposed topological superconductor candidates through external stimuli, such as uniaxial strain and hydrostatic pressure, to enhance our understanding of superconductivity in such material systems.

QAHE was first realized in magnetically doped TI Cr$_{0.15}$(Bi$_{0.1}$Sb$_{0.9}$)$_{0.85}$Te$_{0.3}$ thin film in 2013. However, doped materials brought inevitable sample inhomogeneity, and thus the phenomenon was only observed at very low temperature, in the range of mK. To overcome this material challenge, it is believed that intrinsic magnetic TIs, i.e., stoichiometric magnetic TIs without doping, will be superior due to their higher magnetic and electronic homogeneity compared to doped materials. The first intrinsic magnetic TI MnBi$_2$Te$_4$ was discovered in 2018. It is an antiferromagnetic (AFM) TI with van der Wall (vdW) coupling that orders below 24 K. Its spins align ferromagnetically (FM) in individual planes but AFM between neighboring layers. Due to its vdW nature, it can be exfoliated and fabricated into odd-layer devices with net magnetization, theoretically proposed as QAH insulators, or into even-layer devices that preserve AFM, proposed as axion insulators. QAH effect was soon observed experimentally at 1.6 K and zero field in a 5-layer device with Hall signal plateau at $0.998h/e^2$ while Layer Hall effect and quantum metric nonlinear Hall effect were observed in 6-layer devices. To better engineer the magnetic properties of this family, growth trails had led to the discovery of new intrinsic magnetic TIs that with alternating [Bi$_{2}$Te$_{3}$] and magnetic [MnBi$_2$Te$_4$] layers, forming the natural heterostructural series of MnBi$_{2n}$Te$_{3n+2}$. In this family of compound, Mn layer is brought apart by adding more layers of Bi$_{2}$Te$_{3}$, causing the phase to eventually evolve from AFM TI in MnBi$_2$Te$_4$ to FM axion insulator in MnBi$_{8}$Te$_{13}$.

Although field-induced quantized Hall conductance has been reported by a few groups in both odd- and even-layer MnBi$_2$Te$_4$ devices, there is only one report showing the observation of zero-field QAHE. Several major reasons why it remains challenging to realize QAH in this system: chemical disorders in the bulk samples; chemical disorders introduced during the device fabrication process; weak net magnetism in odd-layer devices. Synthesis efforts are needed to reduce the chemical disorders, particularly the Mn$_{Bi}$ antisites that are most detrimental to the realization of a universal surface gap and thus QAH, to improve the outcome while the weak net magnetism in devices can be addressed by achieving a ferromagnetic (FM) ground state in bulk sample. Mn(Bi$_{1-x}$Sb$_x$)$_2$Te$_4$ was made with the hope that it might address the problems. The doping indeed induces FM ground state of the Mn sublattice. However, it also significantly increases the Mn$_{Bi}$ antisite concentration from around 2\% to about 16\%, forming a secondary FM Mn sublattice that aligns antiferromagnetically with the dominant Mn sublattice. As a result, the Hall conductance in devices made from Sb-doped samples is far from the quantization value. Therefore, progress in solving this outstanding material challenge remains unsatisfactory. The theme of my thesis work on the Mn-Bi-Te system focuses on addressing these issues by conducting doping trials to suppress Mn$_{Bi}$ antisites (chapter 3), investigating the competition between FM and AFM energy scales in the system (chapter 4), and searching for new magnetic topological insulators (chapter 5).

Chapter 3 reports our study of the effect of Pb substitution of Mn in MnBi$_2$Te$_4$. We grew single crystals of (Mn$_{1-x}$Pb$_x$)Bi$_2$Te$_4$ (0 $\leq x \leq$0.82) and investigated the evolution of crystal structure, magnetic order and band topology upon doping. With increasing $x$, the amount of the Mn$_{Bi}$ antisites is reduced, and the magnetic dilution effect manifested as a decrease of ordering temperature and magnetic interactions is observed. First-principles density functional theory calculations (DFT) reveal potential topological phase transitions in this doping series with two gapless points appear at $x = 0.44$ and $x = 0.66$. Chapter 4 summarizes our study of the effect of hydrostatic pressure on the metamagnetic phase transitions in the Sb doped MnBi$_4$Te$_7$ series. We show that external pressure, which enhances the interlayer hopping without introducing chemical disorders, triggers multiple metamagnetic transitions upon cooling in the topological van der Waals magnets Mn(Bi$_{1–x}$Sb$_x$)$_4$Te$_7$, where the antiferromagnetic interlayer superexchange coupling competes with the ferromagnetic interlayer coupling mediated by the antisite Mn spins. The temperature–pressure phase diagrams reveal that while the ordering temperature from the paramagnetic to ordered states is almost pressure-independent, the metamagnetic transitions show nontrivial pressure and temperature dependence, even re-entrance. For these highly anisotropic magnets, we attribute the former to the ordering temperature being only weakly dependent on the intralayer parameters and the latter to the parametrically different pressure and temperature dependence of the two interlayer couplings. Our independent probing of these disparate magnetic interactions paves an avenue for efficient magnetic manipulations in van der Waals magnets. Chapter 5 reports our synthetic exploration which leads to the discovery of new magnetic topological insulators. By doping Mn into (Ge$_{1-\delta})$$_2$Bi$_2$Te$_5$, we successfully grew (Ge$_{1-\delta-x}$Mn$_x$)$_2$Bi$_2$Te$_5$ ($x\leq 0.47$, $0.11 \leq \delta \leq 0.20$) single crystals. Upon doping up to $x = 0.47$, the lattice parameter $c$ decreases by 0.8\%, while the lattice parameter $a$ remains nearly unchanged. Significant Ge vacancies and Ge/Bi site mixing are revealed via elemental analysis as well as refinements of the neutron and X-ray diffraction data, resulting in holes dominating the charge transport. At $x = 0.47$, below 10.8 K, a bilayer A-type antiferromagnetic ordered state emerges, featuring an ordered moment of 3.0(3) $\mu_{B}$/Mn at 5 K, with the $c$ axis as the easy axis. Magnetization data unveil a much stronger interlayer antiferromagnetic exchange interaction and a much smaller uniaxial anisotropy compared to MnBi$_{2}$Te$_{4}$. We attribute the former to the shorter superexchange path and the latter to the smaller ligand-field splitting in (Ge$_{1-\delta-x}$Mn$_x$)$_2$Bi$_2$Te$_5$. Our study demonstrates that this series of materials holds promise for the investigation of the Layer Hall effect and quantum metric nonlinear Hall effect.

Topological superconductors are proposed to host intriguing phenomena such as Majorana fermions, which form the foundation of topological quantum computing. Chapter 6 of this dissertation summarizes our study of the uniaxial-strain tuning of superconductivity in the Kagome topological superconductor candidate CsV$_3$Sb$_5$. It shows a superconducting temperature $T_c=3.3$ K and a charge-density-wave (CDW) temperature at $T_{\rm{CDW}}=94.5$ K. Upon applying uniaxial strain from -0.90\% to 0.90\%, we found $T_c$ increases while $T_{\rm{CDW}}$ decreases. These opposite response suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the $c$ axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in $T_c$ with decreasing lattice parameter $c$ is caused primarily by the suppression of $T_{\rm{CDW}}$, rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of $T_{\rm{CDW}}$ with respect to the changes in the $c$ axis arises from the impact of the latter on the trilinear coupling between the $M_1^+$ and $L_2^-$ phonon modes associated with the CDW. Overall, our work reveals that the $c$-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is crucial for the phase diagram of CsV$_3$⁢Sb$_5$.

In summary, we have successfully reduced the amount of the Mn$_{Bi}$ antisites by substituting Mn with Pb in MnBi$_2$Te$_4$ and revealed the roles of the interlayer coupling, intralayer coupling and magnetic anisotropy play in tuning the competition between AFM and FM energy scales in Sb doped MnBi$_4$Te$_7$ by applying hydrostatic pressure. Moreover, structure engineering helps us to discover new topological insulating phase (Ge$_{1-\delta-x}$Mn$_x$)$_2$Bi$_2$Te$_5$. Our work on the strain effect in topological superconductor candidate CsV$_3$Sb$_5$ has revealed the competition between CDW and superconductivity and suggested the important role of the trilinear coupling of phonon modes in CDW. Our work advances the understanding of the interplay of magnetism, band topology and superconductivity in magnetic/superconducting topological material systems.